hexapod locomotion: a nonlinear dynamical systems...

Ricardo Daniel Costa Campos

Hexapod Locomotion:a Nonlinear Dynamical Systems Approach

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Universidade do MinhoEscola de Engenharia

Setembro de 2010

Tese de MestradoCiclo de Estudos Integrados Conducentes aoGrau de Mestre em Engenharia Electrónica Industrial e Computadores

Trabalho efectuado sob a orientação daProfessora Doutora Cristina Santos

Ricardo Daniel Costa Campos

Hexapod Locomotion:a Nonlinear Dynamical Systems Approach

Universidade do MinhoEscola de Engenharia

Abstract

Over recent years the technological progress has been growing interest in the study of

legged robots, taking a leading role in the development and improvement of these type of

machines. Walking machines have distinct advantages over wheeled robots, mainly, uneven

terrains navigation, capacity to overcome obstacles as well as better balance and stability

on unstructured or inclined terrains. However, the generation of robust locomotion on these

articulated robots, is still a difficult problem to solve, inparticular due to high number of

degrees of freedom that compose a legged robot and have to be controlled.

In this work we focus our research on hexapod machines using their inherent capacity of

walking in a wide variety of terrains which is one of their most important features. The aims

of this work are design and implement a bio-inspired controller architecture able to generate

a stable and robust locomotion in hexapod robots functionally divided in three layers.

The proposed architecture is able to generate different hexapodal gaits, switch between

the most common gaits and correct the posture of the robot in several different situations

where the robot balance is affected. Motor patterns are generated by coupled Central Pattern

Generators (CPGs), formulated as nonlinear oscillators. We proposed a CPG network that

enables the stable locomotion of the robot and switching between their different gaits. These

patterns are modulated by a drive signal, changing the oscillators frequency, amplitude and

the coupling parameters among the oscillators, proportionally to the drive signal strength.

Locomotion initiation, stopping and smooth gait switchingare achieved by changing the

drive signal. The velocity is changed accordingly and a natural hexapod locomotion is gen-

erated. In this contribution was also developed a posture controller for hexapod robots using

the dynamical systems approach.

Results were performed in simulation and a simulation modelof the Chiara hexapod

robot was developed. Results demonstrate the capability ofthe controller both to locomotion

generation and smooth gait transition. The postural controller is also tested in different

situations in which the hexapod robot is expected to maintain balance. The presented results

prove its reliability and robustness.

Keywords:Walking robot; locomotion; central pattern generator; dynamical systems; bio

control; mobile robots; nonlinear control systems; robot dynamics; robot programming.

i

Resumo

Nos ultimos anos o progresso tecnologico tem feito crescer o interesse no estudo de

robos com pernas, tendo um papel importante no desenvolvimento e na melhoria deste tipo

de maquinas. Maquinas com pernas tem vantagens distintas sobre os robos de rodas, prin-

cipalmente, navegacao em terrenos irregulares, capacidade de atravessar obstaculos, bem

como melhor equilıbrio e estabilidade em terrenos inclinados ou nao-estruturados. No en-

tanto, a geracao de locomocao robusta nestes robos articulados, e ainda um problema difıcil

de resolver, em particular devido ao elevado numero de graus de liberdade que compoem um

robo com pernas e que tem de ser controlados.

Neste trabalho focamos a nossa investigacao em maquinashexapodes usando a sua iner-

ente capacidade de andar numa ampla variedade de terrenos, aqual e uma das suas mais

importantes caracterısticas. Os objectivos deste trabalho sao projectar e implementar a ar-

quitectura para um controlador bio-inspirado capaz de gerar uma locomocao robusta e estavel

em robos hexapodes, funcionalmente dividida em tres camadas. A arquitectura proposta e

capaz de gerar diferentes tipos de movimentos dos hexapodes, transitar entre os seus tipos de

movimentos mais comuns e corrigir a postura do robo em varias situacoes diferentes onde

o equilıbrio do robo e afectado. Os padroes motores saogerados por Geradores de Padrao

Central (CPGs), formulados como osciladores nao-lineares. Propusemos uma rede CPG que

permite a locomocao estavel do robo e a transicao entre os seus diferentes movimentos. Estes

padroes sao modulados por um sinal modulatorio, alterando a frequencia, amplitude dos os-

ciladores e os parametros de acoplamento entre os osciladores, proporcionalmente ao valor

do sinal modulatorio. O iniciar, parar da locomocao e a transicao suave de movimento sao

alcancados mudando o sinal modulatorio. A velocidade e alterada em conformidade, e uma

locomocao natural do hexapode e gerada. Nesta contribuicao foi tambem desenvolvido um

controlador de postura para robos hexapodes usando uma abordagem de sistemas dinamicos.

Os resultados sao realizados em simulacao e foi desenvolvido um modelo de simulacao

do robo hexapode Chiara. Os resultados demonstram a capacidade do controlador tanto para

geracao de locomocao como para transicao suave de movimento. O controlador postural e

tambem testado em diferentes situacoes nas quais se espera que o robo hexapode mantenha

o equilıbrio. Os resultados apresentados provam a sua fiabilidade e robustez.

ii

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Biological Hexapod Locomotion 6

2.1 Invertebrate Nervous Systems . . . . . . . . . . . . . . . . . . . . . .. . 7

2.1.1 The Central Nervous System . . . . . . . . . . . . . . . . . . . . . 9

2.2 Central Pattern Generators . . . . . . . . . . . . . . . . . . . . . . . .. . 13

2.2.1 Central Pattern Generators in Invertebrate Systems .. . . . . . . . 14

2.3 Proposed Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

2.3.1 Controller Requirements . . . . . . . . . . . . . . . . . . . . . . . 17

3 State of the Art 20

3.1 Legged Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Hexapod Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Control Models of Hexapod Locomotion . . . . . . . . . . . . . . . .. . . 40

3.3.1 Central Pattern Generation Approaches . . . . . . . . . . . .. . . 40

3.3.2 Finite State based Approaches . . . . . . . . . . . . . . . . . . . .43

3.3.3 Coordination based Approaches . . . . . . . . . . . . . . . . . . .43

3.4 Gait Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.5 Posture Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4 Development of Chiara Robot using Webots Simulator 49

4.1 Chiara Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

iii

iv CONTENTS

4.1.1 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.1.2 Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.1.3 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2 Shape Simplification using Solidworks . . . . . . . . . . . . . . .. . . . . 54

4.3 Webots Model of the Hexapod Robot . . . . . . . . . . . . . . . . . . . .. 55

4.3.1 Servo Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.3.2 Physics Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3.3 TouchSensor Node . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5 Hexapod Locomotion Generation 63

5.1 Gait Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2 Locomotor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.3 CPGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.4 Interlimb coordination . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75

5.5 Gait Generation Experiments . . . . . . . . . . . . . . . . . . . . . . .. . 76

5.5.1 Metachronal Gait . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.5.2 Ripple Gait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.5.3 Tripod Gait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6 Gait Transition 84

6.1 Gait Transition Mechanism . . . . . . . . . . . . . . . . . . . . . . . . .. 84

6.2 Initiating/stopping locomotion . . . . . . . . . . . . . . . . . . .. . . . . 84

6.3 Duty factor modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .85

6.4 Gait phases modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .85

6.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7 Posture Control 94

7.1 Lateral Posture Control . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94

7.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

8 Conclusions 107

8.1 Results Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

List of Figures

2.1 Brain (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Ventral Nerve Cord (from [1]). . . . . . . . . . . . . . . . . . . . . . .. . 9

2.3 Commissure (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

2.4 Intersegmental Connectives (from [1]). . . . . . . . . . . . . .. . . . . . . 10

2.5 Protocerebrum (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . .. 10

2.6 Deutocerebrum (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . .. 11

2.7 Tritocerebrum (from [1]). . . . . . . . . . . . . . . . . . . . . . . . . .. . 11

2.8 Subesophageal Ganglion (from [1]). . . . . . . . . . . . . . . . . .. . . . 12

2.9 Circumesophageal Connectives (from [1]). . . . . . . . . . . .. . . . . . . 12

2.10 Thoracic Ganglia (from [1]). . . . . . . . . . . . . . . . . . . . . . .. . . 12

2.11 Abdominal Ganglia (from [1]). . . . . . . . . . . . . . . . . . . . . .. . . 13

2.12 Left: Functional division of the motor controller structures in the nervous

system of invertebrate. Right: Proposed locomotor controller architecture. . 16

3.1 Robot I (from [2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Robot II (from [2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Biobot (from [3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Tarry I and Tarry II (from [4]). . . . . . . . . . . . . . . . . . . . . . .. . 24

3.5 Hamlet (from [5]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.6 RHex (from [6]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.7 Robot III (from [2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.8 Lauron III (from [7]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.9 Genghis II (from [8]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.10 TUM Walking Machine (from [4]). . . . . . . . . . . . . . . . . . . . .. . 26

3.11 Gregor I (from [9]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

v

vi LIST OF FIGURES

3.12 Chiara (from [10]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

3.13 Lynxmotion (from [11]). . . . . . . . . . . . . . . . . . . . . . . . . . .. 28

3.14 Arthron (from [12]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28

3.15 HexCrawler (from [13]). . . . . . . . . . . . . . . . . . . . . . . . . . .. 28

3.16 a) BILL-Ant-p robot (from [14]). b) Acromyrmex versicolor (from [14]). . 29

3.17 a) Periplaneta americana (from [15]). b) Sprawlita (from [15]). . . . . . . . 30

3.18 Whegs. a) Whegs I (from [16]). b) Whegs II (from [16]). . .. . . . . . . . 30

3.19 LEMUR. a) LEMUR I (from [17]). b) LEMUR II (from [18]). . .. . . . . 31

3.20 ATHLETE ( 3.20(a) from [19], 3.20(b) from [20], 3.20(c)from [21]). . . . 31

3.21 AQUA Legged Underwater robot.a) AQUA with flexible fins underwater (from [22]).

b) AQUA with amphibious legs exiting the water (from [22]). .. . . . . . . 32

3.22 iRobots Ariel (from [22]). . . . . . . . . . . . . . . . . . . . . . . . .. . . 32

3.23 RiSE (from [23]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.24 COMET-IV (from [24]). . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.25 Walking Harvester (from [25]). . . . . . . . . . . . . . . . . . . . .. . . . 34

4.1 First Chiara prototype, built July 2008 (from [10]). . . .. . . . . . . . . . 50

4.2 Production Chiara Version (from [26]). . . . . . . . . . . . . . .. . . . . . 50

4.3 Chiara Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51

4.4 Dynamixel AX-12 Servo ( 4.4(b) from [27]). . . . . . . . . . . . .. . . . 52

4.5 The two frames provided with Dynamixel AX-12 Servo. a) OF-12SH (from [27]).

b) OF-12S (from [27]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.6 Dynamixel AX-S1 Infrared Rangefinder ( 4.6(b) from [28]). . . . . . . . . 53

4.7 Chiara Solidworks Model. . . . . . . . . . . . . . . . . . . . . . . . . . .54

4.8 a) OF-12SH shape before simplification. b) OF-12SH shapeafter simplifi-

cation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.9 Webots diagram. a) Scene Tree. b) Webots operation. . . . .. . . . . . . . 56

4.10 Chiara Developed Model. a) Model of the Chiara robot rendered in Webots

platform. b) Chiara model rendered in Webots with his bounding objects

highlighted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.11 Developed model of the Chiara robot. a) Directions of rotation of each joint.

b) Chiara joints description. . . . . . . . . . . . . . . . . . . . . . . . . .. 58

4.12 Specification of the Servo node in Webots. . . . . . . . . . . . .. . . . . . 59

LIST OF FIGURES vii

4.13 Specification of the Physics node in Webots. . . . . . . . . . .. . . . . . . 61

4.14 Specification of the TouchSensor node in Webots. . . . . . .. . . . . . . . 62

5.1 Legs Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.2 Gait diagram depicting event sequences for three different hexapodal gaits.

White color indicates that the foot is in ground contact. a) Metachronal (low

- speed) Gait. b) Ripple (medium - speed) Gait. c) Tripod (fast - speed) Gait. 65

5.3 Relative phases for the most common hexapodal gaits. a) Metachronal gait.

b) Ripple gait. c) Tripod gait. . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.4 System’s overall architecture. The network of CPGs generate the motions of

locomotion for the coxa joints. The posture control mechanism generates the

necessary discrete movements on the femur and tibia, to correct the robot’s

body orientation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.5 a) Fixed point at (0, 0) withµ = −1, yi = 0, α = 0.5 andω = π . b) Oscil-

latory harmonic solution. The initial condition (xo,yo) = (0,−0.5), xi (solid

blue line) andzi (solid red line).The oscillator relaxes toxi = 0 andzi = 0. . 68

5.6 Solutions of the oscillator (4.2, 4.3). a) Limit-cycle with amplitude of 1,

µ = 1, yi = 0. The initial condition (xo,yo) = (0,−0.5), α = 0.5 andω = π .

b) Harmonic solution where thex variable is the solid blue line andz is the

solid red line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.7 Oscillatory solution with an amplitude of 2. . . . . . . . . . .. . . . . . . 70

5.8 Trajectory modulation through changes in theyi values (offset) when rhyth-

mic motion is turned off (µ < 0). The solid blue line is thexi solution and

the dashed red line isyi where the resultingxi trajectory converges asymp-

totically to the current value ofyi . . . . . . . . . . . . . . . . . . . . . . . 70

5.9 Trajectory modulation through changes in theyi values (offset) when rhyth-

mic motion is turned on (µ > 0). The solid blue line is thexi solution and

the dashed red line isyi where the resulting harmonicxi trajectory oscillates

around the offset (yi value). . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.10 Amplitude modulation of the generated trajectoriesxi andzi (top) by modi-

fying theµ parameter (bottom). Thexi variable is the solid blue line and the

zi is the solid red line (top figure). . . . . . . . . . . . . . . . . . . . . . . 71

viii LIST OF FIGURES

5.11 Frequency modulation of the generated trajectoriesxi andzi (top) by modi-

fying theω parameter (bottom). Thexi variable is the solid blue line andzi

is the solid red line (top figure). . . . . . . . . . . . . . . . . . . . . . . .. 72

5.12 Limit-cycle directions and resulting trajectories for ω > 0. a) Limit-cycle

with amplitude of 1 withω = 10. b) Generated trajectoriesxi andzi . Thexi

variable is the solid blue line and thezi is the solid red line. . . . . . . . . . 72

5.13 Limit-cycle directions and resulting trajectories for ω < 0. a) Limit-cycle

with amplitude of 1 withω = −10. b) Generated trajectoriesxi andzi . The

xi variable is the solid blue line and thezi is the solid red line. . . . . . . . . 73

5.14 Generated trajectoriesxi (solid blue line) andzi (solid red line). ForTsw= 0.3

and initialβ = 0.5, att = 4 s theβ value is changed to 0.9. . . . . . . . . . 74

5.15 Generated trajectoriesxi (solid blue line) andzi (solid red line) for different

signs ofω andβ = 0.8. a)xi andzi solutions forω < 0. b)xi andzi solutions

for ω > 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.16 Coupling Network to achieve interlimb coordination. .. . . . . . . . . . . 75

5.17 Top: Generated coxa jointsxi trajectories. Bottom: Recordedxi trajectories

from the servos. Solid blue line represents L1 trajectory, solid dark green is

R1 trajectory, solid red line is L2 trajectory, light blue represents R2 trajec-

tory, dashed purple is L3 trajectory and dashed light green is R3 trajectory.

The recordedxi trajectories are very closely to the generated onesxi . . . . . 77

5.18 Recordedxi trajectories from the servos (dashed line) and generated coxa

jointsxi trajectories (solid line) for metachronal gait. . . . . . . . . .. . . 78

5.19 Achieved footfall sequence for Metachronal gait. Below each feet sequence

are depicted the corresponding recordedxi trajectories from the coxa servos. 78







jointsxi trajectories (solid line) for ripple gait. . . . . . . . . . . . . . .. 80

LIST OF FIGURES ix

5.22 Achieved footfall sequence for Ripple gait. Below eachfeet sequence are

depicted the corresponding recordedxi trajectories from the coxa servos. . . 80







jointsxi trajectories (solid line) for tripod gait. . . . . . . . . . . . . . .. 82

5.25 Achieved footfall sequence for Tripod gait. Below eachfeet sequence are

depicted the corresponding recordedxi trajectories from the coxa servos. . . 83

6.1 Abrupt Transition. a) Top: Modulatory drive,m, is abruptly changed be-

tween the gaits transition. a) Bottom: Duty factor modulation. b) Recorded

xi trajectories from the servos betweent = 15sandt = 20swhere the robot

performs the metachronal gait. c) Recordedxi trajectories from the servos

betweent = 35 s andt = 40 s when the robot finishes the transition to rip-

ple gait. d) Recordedxi trajectories from the servos betweent = 55 s and

t = 60s when the robot finishes the transition to tripod gait. . . . . . .. . . 87

6.2 Gradual Transition. a) Top: Modulatory drive,m, is gradually changed be-

tween the gaits transition. a) Bottom: Duty factor modulation. b) Recorded

xi trajectories from the servos betweent = 15sandt = 20swhere the robot

performs the metachronal gait. c) Recordedxi trajectories from the servos

betweent = 40 s andt = 45 s when the robot finishes the transition to rip-

ple gait. d) Recordedxi trajectories from the servos betweent = 85 s and

t = 90swhen the robot finishes the transition to tripod gait. In thissituation

the robot takes more time to achieve the desired behaviors. .. . . . . . . . 88

x LIST OF FIGURES

6.3 a) Top: Modulatory drive,m, is abruptly changed to 2 att = 10 s when the

robot is performing the transition between tripod gait and ripple gait. From

t =30s, m, is gradually decreased in order to achieve the metachronalgait. a)

Bottom: Duty factor modulation. b) Recordedxi trajectories from the servos

betweent = 0 s andt = 5 s when the robot is in tripod gait. c) Recordedxi

trajectories from the servos betweent = 10 s andt = 15 s where the robot

is starting the transition to ripple gait. d) Recordedxi trajectories from the

servos betweent = 25 s andt = 30 s when the robot is in full ripple gait.

e) Recordedxi trajectories from the servos between 55s and 60s when the

robot is already performing the metachronal gait. . . . . . . . .. . . . . . 90

6.4 Feet Sequence betweent = 0 s and t = 5 s. L1, L2, L3, R1, R2 andR3

demonstrate the readings from the touch sensors from these legs. x1, x2,

x3, x4, x5 and x6 present the recorded trajectories from coxa servos for the

respective legs(L1,L2,L3,R1,R2 and R3). . . . . . . . . . . . . . . . . . 91

6.5 Feet Sequence betweent = 10 s andt = 15 s. L1, L2, L3, R1, R2 andR3












7.1 Lateral posture control. Process of stretch and fold thelegs. a) Robot stretch-

ing the right legs and folding the left legs. b) Normal position of the robot.

c) Robot stretching the left legs and folding the right legs.. . . . . . . . . 95

7.2 Functionf (φ). When−0.2 < φ > 0.2, f (φ) has the value zero and else-

where f (φ) has the value 0.8φ . . . . . . . . . . . . . . . . . . . . . . . . . 96

LIST OF FIGURES xi

7.3 Posture control scheme where only the used structure to one leg of the hexa-

pod is demonstrated since the procedure for the other legs isthe same. . . . 96

7.4 Posture control experiments: a) Lateral tiltφ of the robot (solid blue line) and

platform inclination (dashed red line). b)yFemur trajectories for the left front

leg (solid blue line) and right front leg (dashed red line). c) yTibia trajectories

for the left front leg (solid blue line) and right front leg (dashed red line). d)

yFemur trajectories for the left front leg (solid blue line) and right front leg

(dashed red line). e) ˙yTibia trajectories for the left front leg (solid blue line)

and right front leg (dashed red line). . . . . . . . . . . . . . . . . . . .. . 98

7.5 Robot behavior during the posture control in first experiment. a)t = 2 s.

b) t = 10 s. c)t = 12 s. d)t = 16 s. e)t = 20 s. f) t = 26 s. g)t = 28 s.

h) t = 30 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.6 Posture control experiments: Top figure: Lateral tiltφ of the robot (solid

blue line) and platform inclination (dashed red line); Middle figure: yFemur

trajectories for the left front leg (solid blue line) and right front leg (dashed

red line); Bottom figure: ˙yTibia trajectories for the left front leg (solid blue

line) and right front leg (dashed red line). . . . . . . . . . . . . . .. . . . 100








7.8 Robot behavior during the posture control in second experiment. a)t = 10 s.

b) t = 15 s. c)t = 20 s. d)t = 21 s. e)t = 21.5 s. f) t = 22 s. g)t = 24 s.

h) t = 27 s. i)t = 30 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

xii LIST OF FIGURES








7.10 Robot behavior during the posture control in third experiment. a)t = 10 s.

b) t = 15 s. c)t = 19 s. d)t = 20 s. e)t = 23 s. f) t = 26 s. g)t = 28 s.

h) t = 30 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.11 Posture control experiments: Top figure: Lateral tiltφ of the robot (solid

blue line) and platform inclination (dashed red line); Middle figure: yFemur

trajectories for the left front leg (solid blue line) and right front leg (dashed

red line); Bottom figure: ˙yTibia trajectories for the left front leg (solid blue

line) and right front leg (dashed red line). . . . . . . . . . . . . . .. . . . 106

List of Tables

3.1 Robots Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34

3.2 Robots Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35

4.1 Specification of Servos nodes parameters for Chiara simulation model. . . . 58

4.2 Specification of Servos nodes parameters for Chiara simulation model (Con-

tinuation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.3 Specification of Physics nodes parameters for Chiara simulation model. . . 61

4.4 Specification of Physics nodes parameters for Chiara simulation model (Con-

tinuation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1 Relative Phases between oscillators. . . . . . . . . . . . . . . .. . . . . . 75

5.2 Parameter values used in the gait generation experiments. . . . . . . . . . . 76

5.3 Parameter values used in metachronal gait generation experiments. . . . . . 76

5.4 Parameter values used in ripple gait generation experiments. . . . . . . . . 79

5.5 Parameter values used in tripod gait generation experiments. . . . . . . . . 81

7.1 Parameter values used in the posture control experiments. . . . . . . . . . . 97

xiii

Chapter 1

Introduction

This report presents and describes in detail all the realized work in the study of hexapod

locomotion during about an year in the Adaptive System Behaviour Group of Industrial

Electronics Department at University of Minho in Portugal.The main goal of this work is

the development of a robust controller to the hexapod robot in order to reproduce the most

common hexapodal gaits based on biologically inspired robotic locomotion and dynamical

systems as a tool. In this work we propose a bio-inspired controller architecture to the hexa-

pod locomotion based on the concept of Central Pattern Generators that are rhythmogenic

regions located in the spinal cord of animals and on the functional architecture of the animal

motor control system. With this work is demonstrated that using the biological concepts and

the dynamical systems it is possible to implement the behaviors of the animals into robots.

1.1 Motivation

Many research groups have been studying approaches for the control of locomotion in hexapo-

dal walking robots. The motivation of this interest by the hexapodal platform is mainly due

to its physical nature extremely stable and also because thecapacity of walking in rough

terrains that is one of the most important features of hexapod insects. Additionally, since the

hexapod has redundant legs compared to other legged robots,it is possible for this sort of

walking machine to be able to continue operation in the eventof disabled limbs.

On uneven and rough terrains the walking robots have clear advantages over conventional

robots, using wheels or tracks, because these kinds of surfaces may be comprised by several

kinds of obstacles, holes, steps and ditches.

By the fact of the legged robots can select the points of the ground they tread, becomes

easier with this type of machine to avoid obstacles, holes and remains with a stable locomo-

1

2 CHAPTER 1. INTRODUCTION

tion on different kinds of surfaces. The articulation of their limbs also provides to the legged

robots a stable and smoother locomotion in uneven terrains as well as a faster adaptation to

irregularities.

However, the control of a walking machine locomotion is a difficult and complex task

mainly due to the high number of degrees of freedom (DOFs) that composes the robot. More-

over the controller of a legged robot must have the capacity to deal with constant changes

on body dynamics by lifting and placing the feet, and unpredictable dynamics during the

contact of a foot with the ground. This controller also must have the ability of adapt the leg

movements in order to support the robot body and not letting the robot fall.

1.2 Objectives

This work is a combination of different important concepts.The purpose of this work re-

quires an high use of dynamical systems theory, bio-inspired controllers and robotics. The

main goal of this work is, in a first step, start a detailed study of the type of existing hexapod

robots and the several models of bio-inspired controllers to reproduce their locomotion.

On this work we want to generate the most common hexapodal gaits and also smoothly

switch among these according to changes in the walking velocity to achieve stable locomo-

tion. The generated gaits are metachronal gait (”wave gait”) that specifies slow walking,

ripple gait corresponding to a medium speed gait and the fastspeed tripod gait.

In order to achieve smooth walking from low speed to high speed, robotic gait switching,

similarly to their biological counterparts [29], should take place continuously with both the

duty factor and the interlimb phase relationships properlyadjusted.

In this work we propose a bio-inspired closed-loop controller architecture, based on bi-

ological principles of the animals, with a particular focuson reproduce a stable locomotion,

that allow a gait changing through the control of a small set of parameters and allow a correct

posture control of the robot in several different situations as inclined surfaces in which the

hexapod robot is expected to maintain balance.

In this work we make use of the dynamical systems framework topropose a two-layer

architecture based in the invertebrate biological motor systems [29, 30].

The lower level generates movement patterns using networksof Central Pattern Genera-

tors (CPGs) modelled by nonlinear oscillators.

Interlimb coordination is achieved by coupling six CPGs in anetwork. This network

1.2. OBJECTIVES 3

must produce coordinated rhythms of motor activity, i.e. the correct pattern for locomotion.

These systems are solved using numerical integration and sent to the lower level PIDs of the

joints.

The second layer should model very basically the brainstem command centers for ini-

tiating, regulating and stopping CPGs activity and therefore initiate a walking gait, switch

among gaits and stop the locomotion. This layer should receive a modulatory signal that

regulates the CPGs activity. This signal strength is mappedonto different sets of the CPG

parameters, and hence result in the different motor behaviours.

A unique signal should be able to achieve interlimb coordination and control both the

velocity and the gait transition.

Furthermore, we also should include sensory feedback to correct the robot body orienta-

tion with respect to lateral inclination. The goal is to propose a lateral posture mechanism in

which the measured roll corrects the robot posture and adapts the generated locomotion on

inclined terrains by generating discrete trajectories forthe femur and tibia.

In order to fulfill the objectives mentioned above we need a robot. After making a com-

plete state of the art of the existing hexapod robots we should choose one of them and de-

velop a simulation prototype on Webots robotics platform. In this work all tests should be

performed in simulation environment using this robotics simulator.

So, to accomplish the purposes of this thesis the following main objectives should be

achieved:

• Prepare a proper state of the art of existing hexapod robots.

Choose a real robot to develop its prototype in the Webots simulator using the VRML

language.

• Design a six coupled CPGs network, formulated as nonlinear oscillators as a modular

generator for discrete and rhythmic primitives, that when superimposed result in complex

movements. These nonlinear oscillators generate smooth trajectories modulated by simple

parameters change. This CPG network should also coordinateall the movements of the joints

in a limb in order to generate the required limb movements. The use of the nonlinear oscilla-

tors allows a proper coordination between all members of therobot to reproduce the desired

patterns of movement.

4 CHAPTER 1. INTRODUCTION

•Develop a mechanism in order to achieve a smooth gait transition through a simple drive

signal. Locomotion initiation, stopping and smooth gait switching is achieved by changing

the drive signal. The velocity is changed accordingly and a natural hexapod locomotion is

generated.

• Propose a lateral posture mechanism in which the measured roll corrects the robot

posture and adapts the generated locomotion on inclined surfaces by generating discrete tra-

jectories for the femur and tibia. This method should include sensory feedback to correct the

robot body orientation with respect to lateral inclination.

1.3 Structure of the Thesis

This thesis is organized as follows:

In chapter 2 is presented a study of biologically inspired robots based mainly in the

nervous systems of invertebrate animals.

Chapter 3 provides a state of the art of existing hexapod robots describing their main

features and the different hexapod control models approaches.

The development of chosen hexapod robot using Webots Simulator is described in chap-

ter 4.

In chapter 5 is introduced the locomotion of the robot, describing the CPG coupling

network, CPG design and hexapodal gaits generation.

Chapter 6 explains the implemented mechanism of switch between the most common

hexapodal gaits using a simple modulatory drive to regulatethe activity of the CPGs signal.

In chapter 7 is demonstrated the lateral posture mechanism to compensate the robot lat-

eral tilt using a dynamical systems approach.

Finally, in chapter 8 are presented the most important conclusions, discussing the ob-

tained results and are suggested proposals for future work.

1.4. PUBLICATIONS 5

1.4 Publications

During the last year of work in CAR-ASBG group, was possible to publish two articles in

national and international conferences:

• ”Hexapod Locomotion: a Nonlinear Dynamical Systems Approach” , Ricardo Cam-

pos, Vitor Matos and Cristina Santos. Accepted in 36th Annual Conference of the IEEE

Industrial Electronics Society (IECON2010), Phoenix, USA.

• ”Gait Generation For a Simulated Hexapod Robot: a NonlinearDynamical Systems

Approach” , Ricardo Campos, Vitor Matos, Miguel Oliveira and Cristina Santos. Accepted

in 9th Portuguese Conference On Automatic Control (Controlo 2010), Coimbra, Portugal.

Chapter 2

Biological Hexapod Locomotion

Since few years, great interest has been directed to the study of biologically inspired robots [31].

This kind of robots include different degrees of biologicalinspiration and involves theories

like robotics, neuroscience or biology. Talk about biologically inspired robots, normally

refers to robotic animal models that are useful to a better exploration of biological behav-

iors [32].

Biologically inspired robots can be defined as the intersection of biology and robotics.

If we understand how a biological system works we may be able to develop something that

works the same way. Due the advances in neurobiology and technology has been a large

growth in the interest on the possibility of developing robots with the capabilities of ani-

mals [33].

The most common knowledge is that robots and animals are bothmoving, behaving

systems and both incorporate sensors, actuators as well as require an autonomous control

system that provides them the capacity of successfully carry out various tasks in a dynamic

world [34].

The intensive researches in ’biorobotics’ indicate that the study of autonomous robots

is analogous to the study of animal behavior and robots couldbe used as models of ani-

mals [35].

It is easy to verify that animals have the capacity of locomoting in several different kinds

of terrain and navigating in complex environments where thecurrent robots have many dif-

ficulties. Also, they have the ability of adapt the walking performance to environment con-

ditions, adjust the performed movements and correct the balance of their body.

The locomotor circuits in the nervous system of animals havebeen intensively studied in

order to verify their functional organization and crucial features.

6

2.1. INVERTEBRATE NERVOUS SYSTEMS 7

Abilities as stepping and adapting the movements of animalsmake the locomotor circuits

in the nervous system a fundamental subject of study of researchers on the field of legged

robotics.

For the aim of this work we take inspiration from nervous systems of animals hoping that

their motor control capacities improve the development of our controller. We do not want to

model the nervous systems of animals but understand how the nervous system works when

generating the locomotor movements, while interacting with sensory information.

Invertebrate neuroscience, in particular, is providing many neural ’circuit diagrams’ that

can be applied as sensorimotor controllers for robotics.

The main goal is to design a hexapod controller able to generate the locomotor move-

ments, integrating concepts of the structure organizationof invertebrate nervous system and

functions in order to increase flexibility, adaptability and performance of the walking robot.

Hexapod robot is one of the most typical robots, that is seen like a walking robot that

imitates limb structure and motion control of insects or arthropod animals and can walk in

unstructured terrain with a high probability of success [36].

Due to the existing redundant limb, hexapod robot could continue its movement even if

limb is lost.

These important advantages and others that will be evidenced in this work, make it reli-

able for some autonomous and high-reliability works, like field scouting, underwater search-

ing, space exploring, disaster areas, rigs, excavations, and much others important applica-

tions [37].

2.1 Invertebrate Nervous Systems

All animals without a backbone (spinal column) are considered invertebrates such as insects,

worms, jellyfish, spiders. Invertebrates are useful animals to several researches because their

nervous system has a similar operation process as that of vertebrates [38].

The nervous system is a network of specialized cells that control all body functions,

controlling all the organs and muscles, sending, receivingand processing nerve impulses

throughout the body.

An invertebrate nervous system is a network of cells, calledneurons, that function as an

”information highway” inside the body.

The nervous system has two main functions which are indispensable to maintain the life

8 CHAPTER 2. BIOLOGICAL HEXAPOD LOCOMOTION

of the organism. First, sensory receptors allow the organism to control its external environ-

ment and detect possible changes as an increase in temperature.

Then, the nervous system activates structures such as muscles and glands, allowing the

organism to respond properly to the environmental changes.Second, the nervous system

also provides the capacity to control the organism’s internal environment, monitoring heart

rate so that enough blood is delivered to organs, or measuring nutrient levels to alert if an

organism needs food.

All nervous systems have these basic abilities but their structure and complexity varies

greatly depending on the types of organisms.

In vertebrate systems, it is divided into the central nervous system (CNS), that is com-

posed by the brain and spinal cord, and the peripheral nervous system (PNS), which have the

nerves responsible for transporting information to and from the CNS.

On the other hand, invertebrate nervous systems may or may not have distinct periph-

eral and central regions. However, communication with and response to the environment

still occurs [39]. Usually invertebrate systems are much less complex than vertebrate ner-

vous systems which may contain a trillion neurons, that are primary cells types found in the

nervous system, and an invertebrate may have as few as 305 [39].

Overall, invertebrate nervous systems are less complex than the nervous systems found in

vertebrates, but there is still a certain complexity depending on the type of invertebrate. There

is a particular separation of peripheral and central nervous systems in invertebrate animals

such as insects and mollusks, like the squid. Usually, in theanimal’s midline there are neuron

cell bodies grouped into clusters called ganglia. A ganglion is a group of interconnected

neurons with the function of process sensory information orcontrol motor outputs.

The peripheral part of the nervous system is composed by the extensions of the cells

in these ganglia where some have function of transporting sensory information from the

environment to the ganglia, and others transport signals from the ganglia to obtain a response

such as movement.

This type of functional organization allows a segmentation, where each ganglion has the

capacity to respond to and control an individual segment of the body. In order to coordinate

the segments, these ganglia are linked to each other in a chainlike fashion by a nerve cord,

that is a bundle of neurons that runs the length of the animal [39]. Next is detailed explained

the Central Nervous System (CNS) of an invertebrate.


2.1.1 The Central Nervous System

Invertebrate animals, specifically the insects which are addressed during this work, have a

relatively simple central nervous system consisting in a dorsal brain (Fig. 2.1) linked to a

ventral nerve cord (Fig. 2.2) that can be defined as paired segmental ganglia running along

the ventral midline of the thorax and abdomen [1].

Figure 2.1: Brain (from [1]).

Figure 2.2: Ventral Nerve Cord (from [1]).

Ganglia of each segment are connected to one another by a short medial nerve called

commissure (Fig. 2.3) and also linked by intersegmental connectives (Fig. 2.4) to ganglia in

adjacent body segments [1].

Normally, the central nervous system is rather ladder-likein appearance, where a ladder

is a vertical or inclined set of rungs or steps. In central nervous system the commissures can

be considered the rungs of the ladder and intersegmental connectives are the rails.

An invertebrate brain is a complex of six fused ganglia (three pairs) placed dorsally in-

side the head capsule. The invertebrate brain is divided into different parts (Protocerebrum,

Deutocerebrum and Tritocerebrum) where each controls a limited set of activities in the in-


Figure 2.3: Commissure (from [1]).

Figure 2.4: Intersegmental Connectives (from [1]).

vertebrate body [1].

In Protocerebrum (Fig. 2.5), the first pair of ganglia are largely related with vision, inner-

vating the compound eyes and ocelli.

Figure 2.5: Protocerebrum (from [1]).

The second pair of ganglia, Deutocerebrum (Fig. 2.6), are responsible for the monitor-

ing of sensory information collected by the antennae. The third pair of ganglia, Tritocere-

brum (Fig. 2.7), innervates the labrum (the labrum is a smallsclerite, that is a hardened

body part, articulated the lower margin of the insect’s ”face” , concealing some or most of

the mandibles) and integrate sensory information acquiredfrom proto- and deutocerebrums.


They also connect the brain with the rest of the ventral nervecord and the stomodaeal ner-

vous system which has the function of control the internal organs. The commissure for the

Tritocerebrum is around the digestive system, allowing us to understand that these ganglia

were initially placed behind the mouth and migrated forward(around the esophagus) during

evolution [1].

Figure 2.6: Deutocerebrum (from [1]).

Figure 2.7: Tritocerebrum (from [1]).

Below the brain and esophagus is ventrally placed (in the head capsule) another set of

fused ganglia, jointly called the subesophageal ganglion (Fig. 2.8). This structure is com-

posed by neural elements from the three primitive body segments which merged with the

head to form mouthparts. In the most recent insects, the subesophageal ganglion has the

function of innervate not only mandibles, maxillae, and labium, but also the hypopharynx,

salivary glands, and neck muscles.

A pair of circumesophageal connectives (Fig. 2.9) is aroundthe the digestive system in

order to connect the brain and subesophageal complex together.

Three pairs of thoracic ganglia (Fig. 2.10), sometimes fused, are located in the thorax to

control locomotion by innervating the legs and wings, and associated with these ganglia are


Figure 2.8: Subesophageal Ganglion (from [1]).

Figure 2.9: Circumesophageal Connectives (from [1]).

also the thoracic muscles and sensory receptors.

Figure 2.10: Thoracic Ganglia (from [1]).

Similarly, abdominal ganglia (Fig. 2.11) has the function of control the movements of

abdominal muscles. In thorax and abdomen the spiracles are examined by a pair of lateral

nerves that arise from each segmental ganglion. A pair of terminal abdominal ganglia, nor-

mally fused in order to form an extensive caudal ganglion, innervates the anus, internal and

external genitalia as well as sensory receptors placed on the insect’s back end [1].

2.2. CENTRAL PATTERN GENERATORS 13

Figure 2.11: Abdominal Ganglia (from [1]).

2.2 Central Pattern Generators

The subject of controlling locomotion in robots has been largely studied where neuroscience

and robotics can successfully interact. The interaction between biology and robotics is very

important.

Central pattern generators (CPGs) are considered neural circuits able to produce coordi-

nated patterns of rhythmic output signals while receiving only simple input signals. Usually,

CPG models can be implemented using the paradigm of neural networks or systems of cou-

pled oscillators. In robotics, CPG models can be applied forcontrolling the locomotion of

articulated robots [40].

Robots are effective platforms that can be used as scientifictools to have a better under-

standing of the functioning of biological CPGs. There are several methods for designing and

developing CPGs able to control distinct modes of locomotion. The capacity to successfully

move in complex environments as irregular terrain is a distinct property of animals. It is a

crucial factor to their survival, i.e. to avoid predators, to found food, and to find mates for

reproduction.

This singular property of animals means that several aspects of animals morphologies

and central nervous systems have been defined by certain constraints related to locomotor

skills.

In the same way, providing adequate locomotor skills to robots have a lot of importance

in order to design and develop robots that can have the capacity to perform diverse tasks in

different types of environments.

This set of facts for biology and robotics has led to multipleinteresting interactions


between the two fields in one main goal, with robotics taking inspiration from biology in

morphology, modes of locomotion, and control mechanisms. Several robots functional or-

ganizations are widely inspired by animal morphologies andbehaviors, from snake robots,

quadruped robots, hexapod robots to humanoid robots.

Central pattern generators (CPGs) can be found in both invertebrate and vertebrate an-

imals. In the development of locomotor neural circuits found both in invertebrate and ver-

tebrate animals, CPGs are also fundamental building blocksdue their different important

properties such as distributed control, capacity to deal with redundancies, fast control loops,

and enabling modulation of locomotion using simple controlsignals. These distinct abilities,

when defined as mathematical models, make CPGs interesting building blocks for locomo-

tion controllers in robots. CPGs define many rhythmic behaviors both in invertebrate and

vertebrate animals [40].

CPGs can generate complex locomotor behaviors but also switch between very different

gaits while receiving only simple input signals [41].

Therefore, from a control point of view, CPGs have the capacity to implement some

type of internal models who have the knowledge of which command signals need to be

rhythmically produced to have a desired speed of locomotion.

In the different types of CPG models implemented in roboticsit is normally cited the

connectionist models ( [42]; [43]), vector maps ( [44]), andsystems of coupled oscillators

( [45]; [46]; [47]; [48]). Only, in exceptional circumstances spiking neural network models

have been applied ( [49]).

Concluding, CPG models have been used to control the locomotion of robots and are

increasingly applied in the robotics community. This issuewill be addressed in more detail

more later in this thesis.

2.2.1 Central Pattern Generators in Invertebrate Systems

As previously reviewed, Central Pattern Generators (CPGs)are neural circuits able to gener-

ate organized and repetitive motor patterns, such as feeding, locomotion and respiration.

Recent work on invertebrate CPGs ( [50]) has provided relevant data about how rhythmic

motor patterns are produced as well as the mechanism that is used to be controlled by higher-

order command and modulatory interneurons.

There has been a larger interest in CPGs, due the fact that outputs of these circuits are

2.2. CENTRAL PATTERN GENERATORS 15

easy to measure, and their functional structure important to animal functional organization

both in vertebrates and in invertebrates [51], [52].

Research on invertebrate CPGs with small numbers of easily identified neurons has used

several principles with relevant importance to the organization of CPGs and other circuits in

the brain.

Important rhythmic movements such as breathing, walking, swimming and feeding are

produced by CPGs. The most simple demonstration that motor patterns can be centrally

generated, using CPGs, without sensory input is the result of a great number of preparations

that generate fictive motor patterns when are extracted fromthe animal and studied invitro.

Fictive motor patterns are defined as the signals recorded from the ventral nerve cord during

certain preparations, which do not result in locomotor movements.

In the case of several invertebrate preparations, the relationship among these fictive motor

patterns and those generated by the animal’s behavior, leading to evidence that solutions

investigated invitro have a lot of relevance to the generation of behavior.

In the last years have seen an enormous set of new research on the development of CPGs

in vertebrates [53], [54] such as molecular methods, genetic manipulations, and the develop-

ment of more new invitro preparations leading researchers to conclude that identification of

CPG neurons in the vertebrate spinal cord and brainstem willbe a possible situation.

At the same time, has been a slow evolution on the developmentof CPGs in inverte-

brates and there is still relatively little knowledge aboutthe adult CPGs of the invertebrate

preparations.

It has been proposed that the CPG for each limb is composed by neural circuits, the

unit-CPG, where each unit controls one joint in a limb [55].

The organization and structure of the CPG is very important considering the required

flexibility when generating the different types of limb movements during locomotion. This

interlimb coordination of the generated motor patterns depends of the limb movements to

perform, because when walking forward the unit-CPGs can be coordinated in a way and for

walking backwards it may required different coordination in order to generate a different

activation pattern.

It is believed that the network of CPGs in invertebrate systems is along the ventral nerve

cord.


2.3 Proposed Architecture

The main aim of this project is develop a bio-inspired controller architecture for the au-

tonomous generation, modulation and planning of robust andcomplex motor behaviors for

legged robots in specific for hexapods. We explore an approach that uses dynamical systems

to implement the locomotor controller. Due to their intrinsic stability property, the dynami-

cal systems have often proven to ensure a robust control of the movements in time-varying

environments.

The architecture for this locomotor controller (fig. 2.12) is divided in three layers, func-

tionally similar to the motor control systems involved in goal-directed locomotion in inver-

tebrates.

Figure 2.12: Left: Functional division of the motor controller structures in the nervous system ofinvertebrate. Right: Proposed locomotor controller architecture.

In layer one of proposed architecture are generated the motor patterns of limbs by a

CPG network of six coupled nonlinear oscillators. It is demonstrated the role of ventral

nerve cord where are located the segmental ganglia (thoracic ganglia and abdominal ganglia)

responsible of limb movements. This layer provides the capacity of generate and coordinate

2.3. PROPOSED ARCHITECTURE 17

the movements on the limbs in order to achieve the locomotor movements, as well generating

movements for performing other tasks.

Assuming that any movement can be decomposed in simple discrete, goal-directed tra-

jectories, and rhythmic motor primitives, as oscillatory trajectories based on amplitude and

frequency, the movements can be generated in a modular fashion.

These assumptions allow us simplify the complexity associated to the design of dynam-

ical systems, respond quickly to stimuli, and an easy switching between behaviors, because

it turns a high dimensional trajectory generation problem into a simple selection between

pre-defined behaviors.

The second layer has as abilities mimics the functionalities of segmental ganglia (thoracic

ganglia and abdominal ganglia) in invertebrates and it is responsible for selecting a motor

program as well as sending the commands to the CPG network at the right time in order

to reproduce the limb movements. A set of parameters composea motor program and are

needed by the network to generate the trajectories in order to complete a task.

The third layer is responsible for planning normally by the specification and selection

between independent voluntary movements and behaviours. This layer addresses higher

regions of dorsal brain generating the needed commands for tasks such as locomotion initi-

ation, gait switch, speed change, steering and obstacle avoidance, reaching and environment

exploration.

The proposed CPG generates on-line trajectories in a modular way, coordinating all the

joints in a limb, allowing stepping in any direction.

A CPG network was designed in order to control the limbs of a legged robot, in our case

an hexapod, with the aim of achieve locomotion. The second layer has also a role of control

the CPG network for the motor programs of locomotion initiation and gait switching.

2.3.1 Controller Requirements

The design and development of locomotor controller should take into account certain re-

quirements in order to control a robotic platform. The controller should generate smooth

trajectories, in order to result in smooth movements. The controller also should be stable and

reliable to small perturbations, integrating the possibility of deal with deviations in results

and enabling feedback integration, making the locomotion more robust.

The aim is to develop a locomotor controller for an hexapod robot, inspired in the neural


systems of invertebrate animals, applying concepts of their functional organization. From an

extensive research in the understanding locomotor systemsof animals, we are prepared to

define several required features that must be included in thelocomotor controller in order to

achieve locomotion and obtain flexibility and adaptabilitywhich are intrinsic characteristics

of animals.

Summarizing, the desired locomotor controller should contain the following require-

ments:

• Hierarchically organization of neural circuits, one unit-CPG per joint;

• Self-contained rhythmic generation for each limb, the CPG;

• Independent control of swing and stance phase durations in order to achieve different

velocities;

• Coordination between the different joints of a limb in orderto correctly generate the

locomotor movements;

• Coordination between the limbs in order to achieve the desired hexapodal gaits;

• Motor patterns generated by CPGs should be modulated by a drive signal, changing the

oscillators frequency, amplitude and the coupling parameters among the oscillators, propor-

tionally to the drive signal strength;

• Locomotion initiation, stopping and smooth gait switchingshould be achieved by

changing the drive signal;

• Include a lateral posture mechanism in which the measured roll corrects the robot pos-

ture adapting the generated locomotion on inclined surfaces by generating discrete trajec-

tories for the femur and tibia. This method should include sensory feedback to correct the

robot body orientation to keep its balance in disturbance situations.

In the next chapter will be presented a complete state of the art about legged robots,

2.3. PROPOSED ARCHITECTURE 19

especially hexapod robots and their different control models. Also will be described some

important research in hexapodal gait transitions and hexapod posture controllers that are

themes with very importance in this work.

Chapter 3

State of the Art

In this chapter will be described de main features of legged robots enunciating the most

important advantages and disadvantages of this type of machines. Also, will be provided

a state of the art of existing hexapod robots describing their main characteristics and the

different hexapod control models approaches. In this part of the thesis will be also addressed

a state of the art of subjects as hexapodal gait transitions and hexapod posture controllers

that were used in this work.

3.1 Legged Robots

In this section will be presented and described the diversity of legged robots. In this per-

spective are enhanced the main features of locomotion systems for legged robots namely the

advantages and disadvantages.

Advantages of legged robots

As advantage the legged robots have greater mobility in natural surroundings, because these

vehicles can use insulated support for each foot, unlike traditional machines with wheels,

that need a continuous support surface. These vehicles havea distinct capacity to walk on

uneven terrain, using a mechanism of change the configuration of the legs in order to adapt

to surface irregularities, and therefore are inherently suited to locomotion on this kind of

terrain. The use of multiple DOFs in the joints of the legs provides machines with legs the

capacity of change their direction of motion without slipping. There is still the possibility of

vary the height to the ground by introducing a damping effectand decoupling between the

irregularities of the terrain and the body of the walking machine. These machines can move

”embraced” to the land that travel in situations of movement, for example, on the outside

20

3.1. LEGGED ROBOTS 21

of tubes, to increase their ability to balance ( [56]). Another recent important advantage is

the fault tolerance during locomotion where a failure in oneof the wheels, that compose

these type of machines, results in great loss of mobility, due the fact that all the wheels

should always be in contact with the ground during locomotion. However, walking ma-

chines can maintain the stability and keeping the movement with one or more legs damaged

( [57]; [58]; [59]; [60]; [61]; [62]).

It is important to note that the legs can be used not only for locomotion, but also with

the vehicle stationary, where the upper body can work while feet are fixed to the ground,

acting as a support base to help the movement of a manipulator( [63]; [64]) or a tool ( [65])

mounted on the body.

Alternatively, the legged robots, rather than having a handle on your body can use one or

more of their legs to manipulate objects such as various animals use them for tasks such as

hold, manipulate and transport objects.

Limitations of legged robots

Despite the above referenced aspects suggest that legged locomotion is advantageous com-

pared to wheeled vehicles it is important to note that these vehicles still suffer from severe

limitations such as: require a large number of actuators to move the legs with multiple DOFs,

low speeds, are difficult to build, require complex control algorithms, and have a high energy

consumption.

Application fields

Mobile robots are vehicles that can replace humans in order to avoid endangering the life of

any hazardous task or in areas in which humans can not easily access.

The legged robots can be used in exploration of remote locations and hostile environ-

ments such as volcanoes ( [66]), seabed ( [67]; [68]), in space or on planets ( [69]; [70];

[71]; [72]; [73]), in nuclear power stations or locations with high levels of radiation, in min-

eral exploration, in disaster areas, in search and rescue operations, in military operations.

Beyond this type of applications the vehicles with legs can also be used in a wide variety

of tasks such as: cutting and transporting trees in forests,in aid to humans in the transport of

cargo ( [74]; [75]), excavation and construction ( [76]), medical applications ( [77]) and as

an alternative to wheelchairs ( [78]; [79]), in services, especially in applications to support

22 CHAPTER 3. STATE OF THE ART

people in buildings ( [80]; [81]).

Today, such robots can be placed in homes to be used in severalsituations as service

robots ( [82]), entertainment ( [83]; [84]), accompanying,educational ( [85]) and other im-

portant tasks.

However it is not yet possible to say with certainty that these robots are an effective

alternative for locomotion to vehicles with wheels or caterpillar because of the many working

situations that must be solved.

3.2 Hexapod Robots

There are several kinds of hexapod robots with different number of degrees of freedom, joints

and articulations. The main aim and advantage of these machines has been locomotion over

rough, irregular terrain.

The hexapods have complex dynamic approaches due to their high number of legs and

articulations and due to the difficulty to coordinate the several degrees of freedom of the

robot.

Walking machines, especially hexapods, are a sort of robotswhich their motion can be

similar to insect movements. These robots successfully walk in unstructured terrain and may

serve as vehicles of scientific study to postulate or test hypotheses about animal locomo-

tion [86].

Several research groups have developed studies for the control of locomotion in hexapo-

dal walking robots. The main motivation to their interest isthat the hexapodal machine

has a physical nature extremely stable. Since the hexapod has redundant legs compared to

quadruped robots, it is theoretically possible to be able tocontinue operation in the event of

disabled limbs [35].

In natural terrains, legs performance is often superior to wheels mainly because they

avoid undesirable footholds and make discrete contacts where wheels must propel with con-

tinuous rolling contact [87].

The development of six-legged robots enables the generation of static stable gaits and

these kind of machines have the capacity to walk even if one ortwo limbs are lost. More-

over, hexapod legs are usually developed with 3 DOFs which allow them Omni-directional

walking [12].

An important feature of these robots is their capacity to perform tasks that could endanger

3.2. HEXAPOD ROBOTS 23

the life of a human. Actually most of them are only prototypes, but in the future these

machines will be used to explore a space, geological and archeological places on the earth,

or to help people in rescue actions [36].

Their application include distinct areas as mining, exploration, military, rescue, industrial

environments and recreation [5].

On one hand, legged robots, mainly hexapods, possess clear advantages over wheeled

robots like obstacle climbing capability and mechanical graceful degradation. Hexapod

robots are widely used in abrupt outdoor areas (forests, volcanoes, mountains, etc.) that are

the kind of environments where legged robots result advantageous with respect to wheeled

ones [8].

Summarizing, the biggest advantage of hexapod robots is their capacity of walking over

rough terrain where the wheeled locomotion is very complicated. Their main disadvantage

is the difficult control due the multiple DOFs.

Then are presented some models of hexapod robots and will be described their most

important features. Also will be described their mechanical characteristics and the research

groups that have used them. In order to facilitate understanding the description of each robot,

there are tables (Tables 3.1, 3.2 ,3.3 , 3.4 and 3.5) with the submission of its most important

features.

Figure 3.1 presents Robot I. This hexapod robot is used on thework of K.S.Espenschied

in [88] and was developed in Case Western Reserve Universityas Robot II and Robot III.

Figure 3.1: Robot I (from [2]).

Robot II (Fig. 3.2) is used by K.S.Espenschied et al. in [89],where they study the diffi-

culty of legged robots to walk on rough terrain.


Figure 3.2: Robot II (from [2]).

Biobot (Fig. 3.3) is an hexapod robot based on the features ofan agile insect, used in [3].

This hexapod has a great speed and agility. Each leg of the robot has three segments, corre-

sponding to the three main segments of insect legs: coxa, femur, and tibia.

Figure 3.3: Biobot (from [3]).

Figure 3.4 presents Tarry I and Tarry II built by the Department of Engineering Mechanics

at the University of Duisberg [90]. Tarry II is similar to Tarry I, but more loosely based on

the stick insect.

Figure 3.4: Tarry I and Tarry II (from [4]).

Hamlet (Fig. 3.5) is an hexapod walker used by M.Fielding et al. in [5] and was con-

structed at the University of Canterbury, New Zealand. Its legs are all identical and each

have three revolute joints.

U.Saranli et al. use the RHex (Fig. 3.6) in [6]. RHex design consists of a rigid body


with six compliant legs, each one with a only degree of freedom. Thus, RHex has only six

actuators which each hip has one motor gives a mechanical simplicity to achieve reliable and

robust operation in real tasks.

Figure 3.5: Hamlet (from [5]).

Figure 3.6: RHex (from [6]).

In figure 3.7 we have the Robot III used in [91]. This robot has atotal of 24 degrees of

freedom, where each rear leg has three DOF, each middle leg four DOF and each front leg

five DOF. Its functional organization is based on the structure of cockroach and try to imitate

their behavior.

Figure 3.7: Robot III (from [2]).

Figure 3.8 shows the Lauron III hexapod robot. This robot is used in [7]. Lauron III is the


result of about ten years of progressive improvement on the previous configurations, Lauron

I and II. Each leg of this hexapod model has three degrees of freedom where each foot has

three-axis force sensor, and each motor has a current sensorthat detect forces opposing to its

movement.

J.M.Porta and E.Celaya use the Genghis II (Fig. 3.9) hexapodrobot in [8]. The aim of

this project is possible without a map of the terrain and the controller can be used by robots

with low computational and sensing requirements. Genghis II has force sensors at each joint.

Figure 3.8: Lauron III (from [7]).

Figure 3.9: Genghis II (from [8]).

TUM Walking Machine (Fig. 3.10) began created by Dr. Friedrich Pfeiffer in 1991 [92].

This robot, like the others listed above, is based on the stick insect.

Figure 3.10: TUM Walking Machine (from [4]).


Gregor I (Fig. 3.11) is an hexapod robot used on the work of P.Arena and his group [9].

The main goal of this work is reproduce the cockroach’s extraordinary agility where the

locomotion control is based on the theory of the Central Pattern Generator.

Figure 3.11: Gregor I (from [9]).

Gregor I has a biological inspiration where each leg pair hasa unique design. Front

legs are used to provide enough flexibility to allow efficientobstacle approach and effective

postural control. Middle leg design is like front leg designand have to provide part of the

forward thrust. Rear legs are divided into two segments and the most important function of

rear legs is powerful thrust. The front leg pair and the middle leg pair have three Degrees of

Freedom (DOF) on each leg, and the rear leg pair has two Degrees of Freedom.

Chiara (Fig. 3.12) is one of the most recent hexapod robots. The first prototype was

developed at Carnegie Mellon University’s Tekkotsu lab in 2008 [93]. This robot has 3

DOFs in each leg except in the right front leg that is a specialleg and has 4 DOFs. Each leg

is about 30 cm long and the arm is about 35 cm long.

Figure 3.12: Chiara (from [10]).

Figure 3.13 presents Lynxmotion Hexapod Robot BH3-R that isan hexapod robot used

by J.Currie and his team in [11]. Their work describe the process to evolve an hexapod robot

walking gait within a simulated software environment. Eachof the six legs of Lynxmotion

has three Degrees of Freedom (DOF), represented as a pelvic joint, a hip joint, and a knee


joint. This robot has a round body symmetry.

Figure 3.13: Lynxmotion (from [11]).

Figure 3.14 shows ARTHRON. This is an hexapod robot used in [12].

Figure 3.14: Arthron (from [12]).

In [13] they use an hexapod robot called HexCrawler (Fig. 3.15).

Figure 3.15: HexCrawler (from [13]).

Lewinger and his group [14] propose the new robot BILL-Ant-p(Fig. 3.16) that is power


and control autonomous, capable of navigating uneven terrain, manipulating objects within

the environment, very strong for its size and relatively inexpensive compared to other similar

robots. This robot is based on insects behavior and is composed by 3 DOFs on each leg with

six force-sensing feet, a 3-DOF neck and head, and actuated mandibles with force-sensing

pincers for a total of 28 degrees of freedom.

(a) (b)

Figure 3.16: a) BILL-Ant-p robot (from [14]). b) Acromyrmexversicolor (from [14]).

Based on the principles of animal locomotion Cham et al. [94]developed an hexapod

robot called Sprawlita (Fig. 3.17) following the basic principles of locomotion of cock-

roaches: self-stabilizing posture, different functions for the legs, passive visco-elastic struc-

ture, control by advance open-loop and integrated construction. This walking machine is

considered a biomimetic robot because is based on the biologically-inspired robotics princi-

ples.

The robot has six rotational liabilities DOFs corresponding to the link compliant hip of

the leg with the body of the robot. Moreover, each leg has another DOF, prismatic, driven by

a pneumatic cylinder.

Each of these legs can be rotated using a servomotor, which allows you to change your

direction and take actions such as braking and accelerating. Due to the use of these principles

in its construction, the robot has a strength unusual for robots of this size and are capable of

traveling on land regularly with a speed of six body lengths per second.


(a) (b)

Figure 3.17: a) Periplaneta americana (from [15]). b) Sprawlita (from [15]).

A slightly different approach of the existing robots consists on the use of the concept

designed by ”Wheel−With−Legs”. Normally these robots have only an independent ro-

tational DOF and use principles of locomotion similar to thehexapod robot called RHex.

Despite their simplicity, these robots can walk, run, bend and so dynamically stable. One of

these kind of robots, called Whegs I (Fig. 3.18(a)) was presented by Quinn et al. in [95]. Its

six appendices, designed by Whegs, consist of three equallyspaced rays. The mechanisms

that make this robot allows you to move on different terrain types in a similar way to cock-

roach and according to the authors is faster than any other robot with legs of similar size and

can climb over larger obstacles.

In [16], is presented a posterior version of this robot, called Whegs II (Fig. 3.18(b)).

(a) (b)

Figure 3.18: Whegs. a) Whegs I (from [16]). b) Whegs II (from [16]).

Another important kind of hexapod robots are the machines used in spacial missions

because the assembly, inspection, and maintenance requirements of permanent installations

in space require robotic platforms that provide a high levelof operational flexibility relative

to the mass and volume of the robotic system. In figure 3.19 we have the two versions of the

LEMUR robot.

In [96] they use the LEMUR II robot.


(a) (b)

Figure 3.19: LEMUR. a) LEMUR I (from [17]). b) LEMUR II (from [18]).

In [20] the group study the motion of a large and highly mobilesix-legged lunar robot

called ATHLETE (Fig. 3.20), developed by the Jet PropulsionLaboratory. This robot has

the ability to roll rapidly on rotating wheels over flat smooth terrain and walk carefully on

fixed wheels over irregular and steep terrain.

This vehicle rolls on wheels in the majority of the situations, but can use the wheels as

feet to walk when necessary like in rough terrain.

Each ATHLETE has a payload capacity of 450 kilograms , with the capability of docking

multiple ATHLETE vehicles together to support larger loads.

ATHLETE is much larger than the most common robotic systems previously used and

has a diameter of around 4 m and a reach of around 6 m.

(a) (b) (c)

Figure 3.20: ATHLETE ( 3.20(a) from [19], 3.20(b) from [20],3.20(c) from [21]).

An interesting feature of the legged robots is the fact that they can move in several dis-

tinct kinds of terrains but already exist legged robots thatmove underwater that resemble

lobsters or crabs. Figure 3.21 presents AQUA that is one of the most famous legged under-

water vehicles. This robot was developed in [97] with funding from the Canadian Institute

for Robotics and Intelligent Systems (IRIS). AQUA is an amphibious hexapod robot with

six independently-controlled leg actuators and was specifically designed for amphibious lo-


comotion.

(a) (b)

Figure 3.21: AQUA Legged Underwater robot.a) AQUA with flexible fins underwater (from [22]). b)AQUA with amphibious legs exiting the water (from [22]).

One of the most important features of this robot is the ability to switch from walking

to swimming gaits as it moves from a sand beach or surf-zone todeep water. The physical

structure of this hexapod is based on the popular hexapod robot called RHex.

The robot has the capacity of walk in rugged terrains, and with the use of amphibious

legs, it can also swim in water. In order to obtain these desired behaviors, several legs

have been designed for the appropriate terrain: semi-circle compliant legs for rugged terrain,

amphibious straight legs for beach and water, flippers for underwater swimming.

In figure 3.22 we have another hexapod underwater robot called iRobots Ariel.

Figure 3.22: iRobots Ariel (from [22]).

In figure 3.23 is presented a new concept of hexapod robot. This is an hexapod robot

called RiSE used in [23] that is able to climb on a variety of vertical surfaces as well as

demonstrates horizontal mobility.


Figure 3.23: RiSE (from [23]).

A new mechanism is applied in RiSE that uses compliant microspines on its feet to reli-

able attach to textured vertical surfaces, such as stucco, in order to carry the load of the robot

while it climbs.

In [24] the research group designed the COMET-IV robot (Fig.3.24). To realize a syn-

chronous control between virtual 3D animation and COMET-IVphysical on the real environ-

ment they propose the online 3D virtual reality technique. This research group has developed

a series of mine detection and clearance robots, like COMET-I, COMET-II, COMET-III [98].

In figure 3.25 is demonstrated the Walking Harvester hexapodrobot that has been devel-

oped by Plustech Oy Ltd. This vehicle has 3 DOFs on each leg with hydraulic drive, using

a diesel engine to power, and can reach a maximum speed of 1ms−1. This robot requires an

human operator to control the machine via a joystick and due to its enormous applicability

this robot has been honored with several awards.

Figure 3.24: COMET-IV (from [24]).


(a)

Figure 3.25: Walking Harvester (from [25]).

Robot Name Physical StructureWeight (Kg) Length (cm) Width (cm) Height (cm) Number of Legs

Robot I 1 50 30 − 6Robot II 1 50 25 50 6Biobot 11 58 14 23 6Tarry I 2.2 40 15 30 6Tarry II 2.9 50 20 40 6Hamlet 13 − − 40 6RHex 7 53 20 15 6

Robot III 13.61 76.2 − − 6Lauron I 12 80 30 70 6Lauron II 16 70 30 70 6Lauron III 18 50 30 80 6Genghis II 1 40 15 − 6

TUM 23 80 40 100 6Gregor I 1.2 30 9 4 6Chiara − 30 10 40 6

Lynxmotion BH3-R 4.6 − − − 6Arthron 2.3 − 54.8 9.8 6

HexCrawler 1.8 50.8 40.64 12.45 6BILL-Ant-p 2.85 47 33 16 6Sprawlita − 16 − − 6Whegs I − − − − 6Whegs II − − − − 6LEMUR I − − − − 6LEMUR II 9 − − − 6ATHLETE − − − − 6

AQUA 18 66 21 13 6iRobots Ariel − − − − 6

RiSE 2.8 41 − − 6COMET-IV 2000 250 330 280 6

Walking Harvester − − − − 6

Table 3.1: Robots Description.


Robot Name Mechanical Features (DOFs)Total Per Leg Achieved Velocity (m/s)

Robot I 12 2 0.14Robot II 18 3 0.14Biobot 18 3 −Tarry I 18 3 0.15Tarry II 18 3 0.20Hamlet 18 3 0.1RHex 6 1 0.55

Robot III 24 − −Lauron I 18 3 1.0Lauron II 18 3 0.5Lauron III 18 3 0.4Genghis II 6 2 −

TUM 18 3 0.3Gregor I 16 − −Chiara 22 − −

Lynxmotion BH3-R 18 3 −Arthron 18 3 −

HexCrawler 12 2 −BILL-Ant-p 18 3 0.004Sprawlita 12 2 0.55Whegs I 6 1 1.527Whegs II 6 1 −LEMUR I − − −LEMUR II 24 4 −ATHLETE 36 6 −

AQUA − − −iRobots Ariel − − −

RiSE 12 2 −COMET-IV 24 4 −

Walking Harvester 18 3 1



Robot Name Purposes-Project Aims

Robot I Test the control of locomotion in the hexapod

robot using three mechanisms believed to be

responsible for leg coordination in the stick insect.

continued on the next page


Table 3.3: Robots Description.(continued)


Robot II Propose a strategy to more stable rough terrain

locomotion in the hexapod robot using biologically

based distributed control and local reflexes.

Biobot Prove how sensory feedback can serve as the basis

of the control system for the robot to achieve the necessary

adaptability of locomotion over rough terrain exhibited byinsects.

Tarry I Develop an autonomous hexapod vehicle to successfully

navigate on uneven terrains while under operator control,

to autonomously explore and define what path to take when

moving to a pre-defined goal.

Tarry II Develop an autonomous hexapod vehicle to successfully

navigate on uneven terrains while under operator control,

to autonomously explore and define what path to take when

moving to a pre-defined goal.

Hamlet Verify the effectiveness of combined force and position

control to keep robust walking on unknown environments.

RHex Describe the design an control of this hexapod robot

and compare with others legged robots.

Robot III Try to get the biologically inspired legged

robot to walk.

Lauron I −Lauron II −Lauron III Propose a control structure for the walking

robot and prove their hierarchical walk controller.

Genghis II Develop of a reactive controller that allow

the movement of a legged robot during an arbitrary

trajectory with a high accuracy and performance.

TUM Introduce a model of hexapod walking machine

following biological principles.

Gregor I Implementation both structure and locomotion

control of the robot inspired in biological

observations in cockroaches.

Chiara Open source educational robot.

Lynxmotion BH3-R Use a Genetic Algorithm (GA) to evolve

walking gaits for the robot.

Arthron Describe its mechanical construction demonstrating





the Kinematic calculation and a control system.

HexCrawler Propose a study of the use of the Soar cognitive

architecture in order to control gait selection

of the six-legged robot.

BILL-Ant-p Development of a new biologically inspired

legged robot.

Sprawlita Development of an hexapod robot following the

basic principles of locomotion of cockroaches.

Whegs I Use a concept of movement based on the behavior

of cockroaches.

Whegs II Use a concept of movement based on the behavior

of cockroaches.

LEMUR I Design an Hexapod robot for assembly, inspection,

and maintenance tasks at space installations.

LEMUR II Design an Hexapod robot for assembly, inspection,

and maintenance tasks at space installations.

ATHLETE Designed to scramble across terrain so rough and

such terrain is abundant on the Moon, most of

which is rough, mountainous, and heavily cratered.

AQUA Develop a platform able to walking on land, crawling

at the bottom of the sea, swimming on the surface

and underwater, and diving to a depth of 10 m.

iRobots Ariel Development of an hexapod robot able to walk

either on land or underwater in the turbulent surf zone.

RiSE Propose a revolutionary method of applying feedback

control for legged robots, by directly modifying

parameters of a robots gait pattern.

COMET-IV Design of an hydraulically actuated hexapod robot for

multitasks on outdoor situations with the unknown environment

applying a teleoperation-based system in order to deal with

extreme environment.

Walking Harvester Development of an hexapod robot to work in forests.



Robot Name Bio Inspired Research Group

Robot I Yes Case Western Reserve University Biorobotics Lab

Robot II Yes Case Western Reserve University Biorobotics Lab

Biobot Yes Department of Entomology, University of Illinois

Tarry I Yes Department of Engineering Mechanics at the

University of Duisberg

Tarry II Yes Department of Engineering Mechanics at the

University of Duisberg

Hamlet Yes University of Canterbury, New Zealand

RHex Yes University of Michigan

Robot III Yes Case Western Reserve University

Lauron I − −Lauron II − −Lauron III − Institut de Robotica i Informatica Industrial

Barcelona, Spain

Genghis II Yes Institut de Robotica i Informatica Industrial

Barcelona, Spain

TUM Yes Technische Universitt Mnchen

Gregor I Yes Dipartimento di Ingegneria Elettrica Elettronica

e dei Sistemi Universita degli Studi di Catania,Italy

Chiara No Carnegie Mellon University’s Tekkotsu lab

Lynxmotion BH3-R − Engineering Research Institute, AUT

University

Arthron − P. Graca, Student Member, IEEE, J. Zimon, IEEE

Member

HexCrawler − Department of Aerospace Engineering, The

Pennsylvania State University

BILL-Ant-p Yes Department of Electrical Engineering and

Computer Science, Case Western Reserve

University, Cleveland

Sprawlita Yes Cham, Jorge G.; Bailey, Sean A.; Clark,

Jonathan E.; Full, Robert J.; CutKosky Mark R.

Whegs I Yes Case Western Reserve University, Cleveland,

Ohio, U.S.A

Whegs II Yes Case Western Reserve University, Cleveland,

Ohio, U.S.A

LEMUR I Yes −continued on the next page



Robot Name Bio Inspired Research Group

LEMUR II Yes Jet Propulsion Laboratory, California

Institute of Technology

ATHLETE − Kris Hauser, Timothy Bretl, Jean-Claude

Latombe, and Brian Wilcox

AQUA − C. Georgiadis et al.

iRobots Ariel − −RiSE Yes The Robotics Institute, Carnegie Mellon

University

COMET-IV − Graduate School of Science and Technology

, Chiba University, Japan

Walking Harvester − Plustech Oy Ltd


Robot Name Cost (dolares) Year

Robot I − 1993

Robot II − 1996

Biobot − 2000

Tarry I − 1992

Tarry II − 1998

Hamlet − 2001

RHex − 2001

Robot III − 2002

Lauron I − −Lauron II − −Lauron III − 2003

Genghis II − 2004

TUM − 1991

Gregor I − 2006

Chiara 3000 2008

Lynxmotion BH3-R 712.47 2008

Arthron − 2009

HexCrawler 549.95 2008

BILL-Ant-p − 2005

Sprawlita − 2002




Robot Name Cost (dolares) Year

Whegs I − 2003

Whegs II − 2003

LEMUR I − −LEMUR II − 2002

ATHLETE − 2006

AQUA − 2004

iRobots Ariel − −RiSE − 2006

COMET-IV − 2009

Walking Harvester − −

3.3 Control Models of Hexapod Locomotion

Several research groups have suggested different approaches for control and generation of

locomotion in hexapod robots. Their physical nature extremely stable and the capacity to

walk on rough terrain are the most important motivations to continue the study of this kind

of locomotion.

The several approaches for the control of locomotion in hexapods can be divided into

three main categories, central pattern generation approaches, finite state approaches and co-

ordination based approaches [99].

3.3.1 Central Pattern Generation Approaches

Central Pattern Generators (CPGs) are defined as spine-neural networks able to autonomously

produce coordinated rhythmic output signals in vertebrateanimals [100]. They are able to

generate these complex patterns without sensory feedback and without any rhythmic inputs,

when activated by simple commands that encode their rhythmic activation, frequency and

amplitude.

In robotics, the most common way to design CPGs is using artificial neural networks or

systems of coupled oscillators with sensory feedback [101].

After the revive of interest for artificial Neural Networks,a lot of different implemen-

tations for this concept have been studied and developed. The main disadvantage of the

3.3. CONTROL MODELS OF HEXAPOD LOCOMOTION 41

majority of neural network implementations is the number ofinterconnections between neu-

rons [102]. So, to reduce the number of interconnections buthold the advantages of parallel

processing, in 1988 [103], Chua and Yang proposed the Cellular Neural Networks (CNN’s)

where neurons were only connected to other neurons inside a certain neighborhood.

CNNs are a new class of information-processing systems. They are compared with neural

networks because they are a large-scale nonlinear analog circuits able to process signals in

real time. They have some of the main features of neural networks and have important

applications as image processing and pattern recognition.The basic unit of CNNs is called a

cell [103]. CNNs can be used to modulate CPGs. Normally, CPGs are designed as networks

of nonlinear oscillators coupled together and CNN paradigmprovides a framework for the

implementation of these nonlinear oscillators where each oscillator is defined as a cell of a

CNN [9].

CPGs are often modeled and built by means of coupled nonlinear oscillators [104]. Sev-

eral works on hexapod robots have used coupled oscillators like Hopf, Van der Pol [105],

Rayleigh [106], Matsuoka [107], [108], or Fitzhugh-Nagumo.

In [109], J. J. Collins and Ian Stewart realize a mathematical study of Hopf oscillator

to investigate the modeling of Central Pattern Generators (CPGs) in hexapods by different

networks of six coupled nonlinear oscillators. Hopf is a nonlinear dynamical oscillator that

presents an Hopf bifurcation wherex andz are the state variables that present oscillatory

harmonic solutions or a stable fixed point.

They concluded that some generic patterns of motion in several networks of six coupled

nonlinear oscillators correspond to the common walking gaits adopted by hexapods.

In [32], the control of biologically inspired robot is realized using an analog distributed

system working as Central Pattern Generator that performs the locomotion control and the

leg controller is constitute by CNNs. The main aim of this work was to investigate the best

way to include in the biologically inspired CPG an attitude control.

The WalkNet structure proposed by Cruse [35] is based on the neural control structure of

the insect Carausius morosus. It is a system of interconnected neural networks that emulates

the circuitry that coordinates locomotion in the insect.

L.Fortuna and his group, in [110], use Cellular Neural Networks (CNNs) to provide a de-

centralized locomotion control of an hexapod robot using anapproach based on locomotion

control in the stick insect. They apply the Walknet model to implement the decentralized


locomotion control. In this work they investigate the structure of a network of coupled

nonlinear dynamical systems that provides the same complexbehavior of the stick insect

locomotion generator.

This group concluded that using CNNs to realize the leg controllers on the Walknet model

of decentralized locomotion, the local influences can be a suitable way to model the stick

insect gait even when exists a change in the dynamics of each cell.

In [111] they propose a CPG implemented through CNNs for an hexapod in order to

control the direction of the robot and also include feedbackfrom sensors.

In [112] it is proposed a new design of a CNN to control hexapodrobot movement. They

propose new state equations that reduce the number of CNN pattern generation cells from

12 to 6, which reduce the system architecture. With only 6 cells they obtain the same results

like when use 12 cells. This fact can reduce the complexity ofCNN circuit.

In [15] it is used a coupled nonlinear oscillator to control the locomotion of an hexapod

robot. The nonlinear oscillator is a two neuron Matsuoka oscillator with mutual inhibition.

In this work it is possible conclude that beyond being an adaptive controller, the coupled

nonlinear oscillator is also robust to sensor failure.

In the Matsuoka oscillator model, the two first order differential equations demonstrate

the behavior of each neuron, where the input variables definethe firing rate and fatigue of

each neuron, respectively. The output of each neuron represents the positive part of the firing

rate. The network output is represented by the difference between these referenced outputs.

There are two parameters that define the first order time constants for the firing rate and the

fatigue.

In [9], Cellular Nonlinear Networks play the role of an artificial CPG to the locomotion

control. The structure of the adopted CPG is based on nonlinear oscillators coupled together

forming a network that generates a pattern of synchronization to control robot actuators.

This work have a good results where the adopted structure is suitable for the locomotion

control of the legged robot with complex design legs. Also, the hexapod walks at the travel

speed of 0.1 body length per second and has the capacity to negotiate obstacles with success,

more than 170% of the height of its mass center.

In our approach we apply coupled CPGs, formulated as Hopf nonlinear oscillators in

order to generate motor patterns. The required motions of the limbs for locomotion are

produced using a network of CPGs, on-line generating coordinated trajectories for the coxa

3.3. CONTROL MODELS OF HEXAPOD LOCOMOTION 43

joints, which we can modulate through simple and predictable parameter changes.

3.3.2 Finite State based Approaches

In the CPG approaches, a gait is pre-selected and a CPG provides each leg with a trajectory

signal.

Unlike the CPG approaches, the finite state approaches incorporate a set of conditions

that place the robot into one of several states, previously determined by a set of rules for

several types of environmental interactions (i.e., walking over flat terrain). This method

basically uses finite state machines to control hexapod locomotion.

The point of view behind this approach considers the locomotion as a sequence of events,

rather than a continuous dynamical process. The advantage of this method is that it makes

possible the constitution of any gait pattern as a sequence of states, and the control of the

gait then requires only a finite algorithm for description.

In [113], Y.Tanaka and Y.Matoba develop an hexapod walking robot to be used in the

houses and work shops where there are several obstacles and stairs to overcome. The hexa-

pod used in this work has eight CPUs for controlling the movement of twenty driving motors

and to detect the environments around it. They use the finite state based approaches to con-

trol the robot. The software that controls each CPU has a set of functions like check the state

of emergency-stop key and necessary treatment, driving motors and reading the states of mo-

tors, calculating the pulse numbers and speed for elevatingand lowering the legs, detecting

the distance to the wall and obstacle.

Basically they follow a set of conditions that place the robot into a determined state.

In [114], they also make use of finite state approaches to control the hexapod robot RHex.

In this work they present the design, modeling and control ofRHex. With a set of simulations

and experiments they prove that, by using finite state approaches, the Rhex can achieve

dynamically stable walking, running and turning.

These above works use finite state approaches to control the hexapod robot and there are

other groups working in the same method.

3.3.3 Coordination based Approaches

In the coordination based approaches the gait is not statically defined and the behavior result

from some sort of coordination system. This kind of system normally is able to more easily


traverse hostile terrain. Some groups have used this approach to control hexapod robots.

In [115] it is developed a biologically inspired distributed neural-network controller to

control an hexapod robot. In this work they conclude and clarify that the biologically inspired

controller for hexapod locomotion is quite robust.

The WalkNet structure is another important approach for thecontrol of locomotion in

hexapodal walking robots. This approach, as previously referred, was proposed by Cruse et

al. [35] and basically consists on a system of interconnected neural networks. Cruse’s neural

network consists of three main subsystems, designed of swing net (that generates a leg’s

trajectory during swing phase), stance net (that does the same for the stance phase), and the

selector net (that decides the trajectories to use for each leg).

A. Calvitti and R. D. Beer make use of this approach in [116]. In this work they clarify

the role of individual coordination mechanisms using a system of two coupled oscillators on

the leg. They focus their work on the Cruse [35] model where the position at which a leg

switches state depends of the state of adjacent legs using a specific network of coordination

mechanisms.

In [117], the researchers study the emergence of stable gaits in robots locomotion using

the coordination based approach.

In [118], Eric klavins et al. use this approach on their work.They employ this method to

generate locomotion on an hexapod robot.

It is possible conclude that several groups have used the coordination based approaches

to generate the hexapod locomotion.

3.4 Gait Transition

In this work the generated gaits are metachronal gait (”wavegait”) that specifies slow walk-

ing, ripple gait corresponding to a medium speed gait and thefast speed tripod gait. One of

the aims is also propose a mechanism in order to switch between these different gaits of an

hexapod robot.


similarly to their biological counterparts [29], should take place continuously with both the

duty factor and the interlimb phase relationships properlyadjusted.

This gait switching issue in hexapod robots has already beenaddressed.

[62] proposes a new gait rule named ”adaptive wave gait”. It is combined the adap-

3.4. GAIT TRANSITION 45

tive wave gait and a synchronized motion control, to reproduce the gait generation and gait

transition in a smooth way. Our work is based on this approachmainly because of its sim-

plicity and with the proposed method it is possible to realize a smooth and effective transition

between the desired gaits.

Another contribution to this issue is proposed in [119]. Three insect inspired controllers

implemented on an autonomous hexapod robot are compared to verify the locomotion per-

formance and the efficiency on gait transitions. In order to develop the controllers they used

reflex-based mechanisms and pattern-based mechanisms (CPGs). The reflexive controllers

exploit sensory stimulus and response reactions to reproduce the hexapod locomotion and

gait transition but unlike these, pattern-based controllers depend more upon pre-programmed

patterns of behavior that can be influenced by external events.

They concluded that the controller based on Central PatternGenerators (CPGs) per-

formed the best of the three controllers. The robot performed smoothly transition between

its three gaits (”wave gait”, ripple gait and tripod gait).

In [87] they propose an architecture that allows safe and efficient walking in rough terrain.

They add planning that allows the hexapod to anticipate changes in its gait. They develop

a behavior-based controller that allows change arbitrarily among gaits and keep the stability

in rough terrains. Two robot behaviors called ’contact foot’ and ’free foot’ are studied. The

’contact foot’ behavior causes the foot to achieve and maintain contact with the ground while

the ’free foot’ causes the foot to stay free, out-of-contactwith the terrain. They conclude that

the coordination of these two robot behaviors enables transitions between fixed gaits.

In [23] they present methods to correctly transition between different gaits. The processes

of gait transition are applied to smoothly switch from a tripod walking gait to a metachronal

wave gait used to climb stairs. In the proposed mechanisms they define transitions as a series

of phase offset modifications where each changes the parameters of a gait slightly, until

achieving the desired gait. This method results in midway configurations for which some

legs are playing one gait, and the rest the other because legsswitch, one by one, from one

gait to another.

Around the same time, Nishii [120], proposes a method to estimate the cost of transport

for legged locomotion where the resultant locomotor pattern, which makes the appropriate

cost, presenting several features of the pattern observed in legged animals. So, they estimate

the cost for force generation using a simple equation and consider the essential property of


energy cost to trigger a gait transition and the other features of legged locomotion. Their

results indicate that the gait transition occurs when a larger number of stance legs suppress

the total cost to support the body or in other words that gait transition occurs due to the

change in the balance of costs for swinging the leg and supporting the body.

A more recent approach [121] of this problem introduces a newformalism for coordina-

tion of periodic tasks which can be applied on gait transitions for legged robots. They use

’Young Tableaux’ to decompose the space of all periodic legged gaits into a cellular complex

indexed. They find the task of transit between the gaits whilelocomoting over level ground.

With this aim they define a set of dynamical reference generators over the ’Gait Complex’

and develop automated coordination controllers to force the legged system to converge to a

specified cell’s gait. During this process the relative static stability of gaits is verified ap-

proximating their stability margin via transit through a ’Stance Complex’. Integrating these

two mechanisms, ’Gait Complex’ and ’Stance Complex’ they achieved the desired gait tran-

sitions.

3.5 Posture Control

Postural control has been intensively investigated in hexapod robots.

In [89], to improve rough terrain locomotion in a hexapod robot they propose the incor-

poration of biologically based control. Their method consist on use distributed control and

local leg reflexes that enable insects deal with irregular terrain. The application of ’elevator

reflex’ and ’searching reflex’ mechanisms allows the robot toovercome any obstacle that

appear on the terrain and keep the balance.

Wettergreen et al. [87] propose an architecture based on control walking behaviors of the

robot in order to reproduce a correct locomotion in rough terrain. The developed controller

allows transit between the different gaits and maintain balance as well as stability in rough

terrains following the rules based on two robot behaviors called ’contact foot’and ’free foot’.

In [122], they propose and demonstrate a computationally simple algorithm for control-

ling the posture of a complex hexapod robot with several DOFs. In order to keep static

posture and generate body motion the proposed algorithm avoids inverse kinematics by is-

suing feedforward force commands.

[123] proposes a sensorial feedback based control system tohexapod locomotion in

rough terrain. In order to deal with terrain irregularitiesthey use local behaviors such as col-

3.5. POSTURE CONTROL 47

lision reaction and searching for ground only adapting the leg trajectories thus maintaining

the robot balance.

Paolo Arena et al. [32] presented a biologically inspired solution to control an hexapod

locomotion using an analog distributed system that makes the role of a CPG for the loco-

motion control. The attitude control is realized by integrating in the CPG a proportional

integrative controller for each leg.

In [124] they propose two new controllers, one for climbing constant slope inclinations

where the posture control is a very important factor and one for achieving higher speeds using

a gait that incorporates a substantial aerial phase. In order to develop these two controllers

they make use of an underlying open-loop control strategy inparallel with low bandwidth

feedback to modulate its parameters.

The inclination behavior is based in adjusting the angle offsets of individual leg motion

profiles based on inertial sensing of the average surface slope.

Moore et al. [125], propose an open loop controller that allows the RHex robot to reli-

ably climb a wide range of regular, full-size stairs withoutoperator intervention during stair

climbing. The success of any stair climbing algorithm is that the robot must be ’in phase’

with the stairs and this algorithm is defined on finding open loop leg motions, based on linear

trajectory segments connecting angle set points, that maintaining a low pitch, a high constant

body velocity, and a moderate ground clearance.

In [86], they proposed an interesting work that incorporates the concept of postural con-

trol. They propose a control system that provides to the hexapod robot the capacity of walk-

ing with only its two hind legs (bipedal running).

The controller has an hierarchical structure composed by three levels of PD controls for

speed control, inverted pendulum balance control and leg trajectory tracking that enables the

robot walks with only two legs as well as still maintain the balance.

In a more recent approach [126], they propose a control system based on the principles

used by cockroaches to climb obstacles and apply this methodin a bio-inspired hexapod

robot. The proposed control system is composed by two functional parts that work in parallel.

They make use of a Cellular Neural Network for control locomotion and designed an attitude

control system that is based on a Motor Map in order to regulate the posture of the robot to

allow it to overcome obstacles.

Our posture control is based on dynamical systems approach.We compensate lateral


displacement of the body by increasing or decreasing leg height on both sides, performed

by generating discrete trajectories for the femur and tibiajoints correcting the posture and

adapting the locomotion on inclined terrains.

In the next chapter will be detailed described the chosen hexapod robot and its develop-

ment in Webots simulator.

Chapter 4

Development of Chiara Robot usingWebots Simulator

After the realization of an exhaustive state of the art of existing hexapod robots, one of the

most recent hexapod robots caught our attention due their excellent features, which we think

is the best option in order to achieve all the objectives proposed for this work and for future

aims. We have chosen the Chiara robot as the working robot andin this chapter it is described

in detail.

4.1 Chiara Robot

Chiara robot is one of the most recent hexapod platforms provided for several applications.

It is an open source educational robot, developed by the Tekkotsu lab, a research group at

Carnegie Mellon University’s, and is manufactured and soldby RoPro Design, Inc.

It is developed by David S. Touretzky (principal investigator), Gaku Sato (body design),

Ethan Tira-Thompson (software), and David Rice (gripper design).

It is a technological platform that can be used by professorsfor teaching students themes

and subjects of robotics like computer vision, inverse kinematics, map building, navigation,

manipulation, path planning and human-robot interaction.

Chiara is programmed in C++ using the Tekkotsu open source software framework de-

veloped at Carnegie Mellon and available free at www.tekkotsu.org.

The Development of Chiara was funded in part by National Science Foundation award

DUE-0717705.

In figure 4.1 is presented the first Chiara prototype, built July 2008.

49

50 CHAPTER 4. DEVELOPMENT OF CHIARA ROBOT USING WEBOTS SIMULATOR

(a) (b) (c)

(d) (e) (f)

Figure 4.1: First Chiara prototype, built July 2008 (from [10]).

The production version looks somewhat different from the initial prototype (Fig. 4.2) and

under this project, was developed on Webots simulator [127], a simulated Chiara robot based

on this production version.

(a) (b)

(c)

Figure 4.2: Production Chiara Version (from [26]).

4.1.1 Features

In figure 4.3 is provided a complete description of the main Chiara features.

4.1. CHIARA ROBOT 51

Special Leg

Arm with gripper

Dynamixel AX-12 Servo

Logitech webcam

Dynamixel AX-S1 Sensor

OF-12S

OF-12SH

Figure 4.3: Chiara Description.

Chiara is composed by six legs and has a total of 27 DOFs distributed through its body

that is laser-cut acrylic. Each leg has 3 DOFs except the right front leg that has 4 DOFs and

can be considered a special leg, with the ability to manipulate objects. This hexapod has

a 6 DOF arm with gripper that enables grasp and manipulation of several objects. It has a

Logitech webcam and a IR rangefinder for sensor fusion on pan/tilt mount.

A Pico-ITX (x86) computer on board with 1 GHz processor, 1 GB RAM and 80 GB hard

drive is provided with the robot and an Ethernet plus 802.11(b/g) WiFi allows the robot to

communicate with the environment that surrounds.

The robot runs Ubuntu Linux OS and Tekkotsu application development framework using

C++. The Ubuntu Linux OS is free as well as open source and Tekkotsu framework provides

integrated vision/kinematics, teleoperation, and monitoring.

The robot includes audio and LED outputs for human-robot interaction, USB bus allows

extend the robot by adding USB-compatible devices. It has anopen source body design that

lets customize the Chiara by changing component shapes, adding sensors, etc.


The robot comes fully assembled and consists of a set of different parts as motors and

sensors.

4.1.2 Motors

The robot has 24 dynamixel AX-12 servos (Fig. 4.4) with position and force feedback as

well as plus 3 analog microservos in the gripper [10].

(a) (b)

Figure 4.4: Dynamixel AX-12 Servo ( 4.4(b) from [27])..

The Dynamixel AX-12 servo is a small actuator that incorporates a gear reducer, a pre-

cision DC motor and a control circuitry. It produces an high torque, although its small size,

and has the capacity to detect and act upon internal conditions such as changes in internal

temperature or supply voltage.

The Dynamixel AX-12 servo has many advantages as position and speed can be con-

trolled with a resolution of 1024 steps, it is provided with feedback for angular position,

angular velocity, and load torque. This servo is composed byan alarm system that alerts the

user when parameters deviate from user defined ranges (e.g. internal temperature, torque,

voltage, etc) and can also handle the problem automatically(e.g. torque off). The main body

of this unit is constructed with high quality engineering plastic which enables it to handle

high torque loads. In order to avoid no efficiency degradation when subjected to high exter-

nal loads a bearing is included at the final axis. This servo has a status LED that indicates

the error status to the user.

In the mechanical assembly of the Dynamixel AX-12 servo two frames are provided

(Fig. 4.5).

4.1. CHIARA ROBOT 53

(a) (b)

Figure 4.5: The two frames provided with Dynamixel AX-12 Servo. a) OF-12SH (from [27]). b)OF-12S (from [27]).

4.1.3 Sensors

The robot is composed by a Dynamixel AX-S1 infrared rangefinder sensor (Fig. 4.6) that is

mounted directly below the camera and is used for multimodalsensing.

(a) (b)

Figure 4.6: Dynamixel AX-S1 Infrared Rangefinder ( 4.6(b) from [28]).

The Dynamixel Sensor Module AX-S1 is a Smart Sensor Module that integrates impor-

tant features. It makes the task of sound sensor, infrared remote control receiver, infrared

distance sensor, light sensor, buzzer, control unit and network. Although its small size, AX-

S1 is composed by special materials that can withstand even the extreme external force. It

has the capacity of detect subtle changes (alarm system) such as internal temperature, service

voltage and other internal conditions and is able to solve the situations.

This sensor comes with other important features such as three directions infrared sensors

that allow to detect left/center/right distance angle as well as the light and allows to transmit

and receive infrared data between sensor modules due the built-in remote control sensor in

center. Moreover allows to detect current sound level and maximum loudness as well as it

has an ability to count the number of sounds due the built-in micro internal microphone.

In the mechanical assembly of the Dynamixel AX-S1 sensor twoframes are also provided


and are the same used in Dynamixel AX-12 Servo (Fig. 4.5).

For this work was modeled the real Chiara robot for the Webotssimulator. The developers

available the Chiara Solidworks model (Fig. 4.7) to the student community. This model was

used to the development of the robot in the Webots simulator.The aim is that almost all

features of the simulation model are as close as possible to the real model.

Figure 4.7: Chiara Solidworks Model.

4.2 Shape Simplification using Solidworks

The Solidworks platform is a three dimensional mechanical software where is possible to

design a lot of products and things like cars, robots and is employed in several applica-

tions [128]. With this tool was possible model the body partsof the robot and export it to

VRML (Virtual Reality Modeling Language) file format. In Webots it is possible import the

model of the robot in VRML format and use it for the desired simulations.

The ”body parts” of the Chiara Solidworks model are too complex, mainly the legs, they

have a lot of details. With these details, the model of the robot becomes very heavy to render

and simulate on the Webots which could make the simulation very slow taking too long time

to repeat each simulation. For the aim of this work is not necessary this level details.

So, the body parts of the model were simplified on Solidworks platform [128] by re-

moving the minor details, as holes and rough surfaces that only occupy space and are not

fundamental for the simulation environment. The figure 4.8(a) shows the ”OF-12SH” shape

of the robot before simplification where we can verify its certain complexity and figure 4.8(b)

demonstrates the body frame of the robot after the simplification.

4.3. WEBOTS MODEL OF THE HEXAPOD ROBOT 55

(a) (b)

Figure 4.8: a) OF-12SH shape before simplification. b) OF-12SH shape after simplification.

4.3 Webots Model of the Hexapod Robot

The Webots platform was developed by Cyberbotics Ltd and it is a robotics simulation soft-

ware for modeling, programming and simulating different kinds of robots (wheeled robots,

legged robots or flying robots). This simulator provides several properties very important for

modeling such as shape, color, mass, friction, density. It is also possible to add many kinds of

sensors and actuator devices such as distance sensors, motor wheels, cameras, servos, touch

sensors, grippers, emitters, receivers, etc.. Further, itis possible to transfer the developed

code to the real robot.

Webots simulator is based on the Open Dynamics Engine (ODE),an excellent and pow-

erful open source physics engine that works as a library to provide more realistic simulations

and improve the results [127].

A Webots project is composed by a world file that is a 3D virtualenvironment in which

we can create objects and robots to the simulation, and a controller that makes possible

control the robot movement and act on all its servos and sensors. In Webots, a world can

include one or more robots and their environment.

A Scene Tree (Fig. 4.9(a)) is composed by all necessary information to define the graphic

representation and simulation of the 3D world.

The Scene Tree of Webots is structured as a VRML file and contains a list of nodes, each

containing fields. Each field can contain values (text string, numerical values) or nodes.

The Webots simulator supports an important number of VRML nodes such as Back-

ground, PointLight, Viewpoint, WorldInfo, CustomRobot, Shape, Sphere, Transform....etc

In figure 4.9(b) is demonstrated the hierarchy of operation in the Webots environment

containing the different nodes and the controller of the robot.


(a)

Webots

ODE Engine

WorldInfo (…)

Viewpoint (…)

Background (…)

PointLight (…)

CustomRobot

(…)

controller…....

Scene Tree

(b)

Figure 4.9: Webots diagram. a) Scene Tree. b) Webots operation.


The Webots simulator follows the VRML language and the Chiara model simplified in

Solidworks can be easily imported without losing the most important features.

Several modifications were done to simplify the Chiara model, by removing the 6 DOF

arm with gripper and its camera that is used for robot vision programming in order to simplify

the model and the simulation environment.

In Figure 4.10(a) and 4.10(b) is possible to visualize the complete and final hexapod

robot model rendered in Webots.

(a)

(b)

Figure 4.10: Chiara Developed Model. a) Model of the Chiara robot rendered in Webots platform. b)Chiara model rendered in Webots with his bounding objects highlighted.

4.3.1 Servo Node

A Servo node is one of the several existing nodes that is supported by Webots and is used to

add one (active or passive) degree of freedom (DOF) in a mechanical simulation.


There are two types of servos: rotational or linear. A rotational servo is applied to sim-

ulate a rotating motion as the most electric motors, hinges,and other. On the other hand

a linear servo is applied to simulate a sliding motion such aslinear motors, pistons, hy-

draulic/pneumatic cylinders, springs, dampers, etc..

Through these servos we can manipulate all joints of the model and change their position

every moment making the robot move how we wish but according to the servo specifications.

The simulation model of Chiara is developed with only three rotational servos on each

leg except on right front leg that is composed by four rotational servos.

In figure 4.11(a) are demonstrated the directions of rotation of each joint that compose

the hexapod model where the orange lines represent the rotation axes for each joint. The

three rotational joints of each leg are called coxa, femur and tibia following the biological

systems. The right front leg has an additional joint called trochanter (Fig. 4.11(b)).

(a) (b)

Figure 4.11: Developed model of the Chiara robot. a) Directions of rotation of each joint. b) Chiarajoints description.

In Tables 4.1 and 4.2 are presented the chosen values for eachenumerated parameter of

Servos nodes.

Leg maxVelocity (rad/s) maxForce (N*m) MinPosition (rad)

Coxa Femur Tibia

L1 4 1.15 −0.92 −1.74 −1.05L2 4 1.15 −0.92 −1.74 −1.05L3 4 1.15 −1.27 −1.74 −1.05R1 4 1.15 −1.78 −1.74 −1.05R2 4 1.15 −0.92 −1.74 −1.05R3 4 1.15 −0.92 −1.74 −1.05

Table 4.1: Specification of Servos nodes parameters for Chiara simulation model.


Leg maxVelocity (rad/s) maxForce (N*m) MaxPosition (rad)

Coxa Femur Tibia

L1 4 1.15 1 1.74 2.79L2 4 1.15 0.92 1.74 2.79L3 4 1.15 0.92 1.74 2.79R1 4 1.15 1.17 1.74 2.79R2 4 1.15 0.92 1.74 2.79R3 4 1.15 0.92 1.74 2.79

Table 4.2: Specification of Servos nodes parameters for Chiara simulation model (Continuation).

The Figure 4.12 demonstrates the construction of one Servo node (for left front leg coxa

joint) of the developed model in Webots simulator where eachparameter is chosen following

the Dynamixel AX-12 servo specifications.

The effectiveness of the simulation can be best achieved setting the adequate parameters

to the servo nodes.

Figure 4.12: Specification of the Servo node in Webots.


4.3.2 Physics Node

The body of the robot model must comply the physics and features of the real robot. With

the Physics node we can define a number of physics parameters of the robot to be used by

the physics simulation engine.

In simulation of legged robots this node is very important todefine mass repartition and

friction parameters, thus allowing the physics engine to simulate a legged robot accurately.

In this node we choose each value for the different parameters following the features of

the real robot Chiara.

The Physics node is composed by a set of important parameterssuch as mass, density,

bounce, bounceVelocity, coulombFriction, centerOfMass that specify the physical character-

istics of robot model.

The density and mass parameters are used to specify the totalmass of the solid that can

be not only the total robot but also their several parts such as the legs. The body of the robot

weights about 2.280 Kg.

The ”bounce” parameter specifies the bounciness of a solid and it is a value ranging from

0 to 1 where 0 means that the surfaces are not bouncy at all and 1is maximum bounciness.

We set this parameter with value 0.5 for each leg of the robot and its body.

The ”bounceVelocity” parameter specifies the minimum speedof entry indispensable for

bounce and we choose the value 0.01 m/s for all legs of robot and its body considering it to

be an appropriate value.

The ”coulombFriction” parameter defines the friction parameter applied to the solid rang-

ing from 0 to infinity and all of these fields of robot model has the value 0.99.

The ”centerOfMass” parameter defines the position of the center of mass (in meters) of

each solid of the robot and we try follow the specifications ofthe real robot.

In Tables 4.3 and 4.4 are presented the physics parameters ofthe model.

Figure 4.13 demonstrates the construction of a Physics nodeof the developed model in

Webots simulator where each parameter is chosen following the specifications of the real

robot.


Leg Mass (Kg) bounce bounceVelocity (m/s)

Trochanter Coxa Femur Tibia 0.5 0.01

L1 − 0.020 0.150 0.055 0.5 0.01L2 − 0.020 0.150 0.055 0.5 0.01L3 − 0.020 0.150 0.055 0.5 0.01R1 0.0775 0.020 0.150 0.055 0.5 0.01R2 − 0.020 0.150 0.055 0.5 0.01R3 − 0.020 0.150 0.055 0.5 0.01

Table 4.3: Specification of Physics nodes parameters for Chiara simulation model.

Leg coulombFriction centerOfMass

Trochanter Coxa Femur Tibia

X Y Z X Y Z X Y Z X Y Z

L1 0.99 − − − 26 0 0 41.5 0 0 50 12 0L2 0.99 − − − 26 0 0 41.5 0 0 50 12 0L3 0.99 − − − 26 0 0 41.5 0 0 50 12 0R1 0.99 5 0 26.5 26 0 0 41.5 0 0 50 12 0R2 0.99 − − − 26 0 0 41.5 0 0 50 12 0R3 0.99 − − − 26 0 0 41.5 0 0 50 12 0

Table 4.4: Specification of Physics nodes parameters for Chiara simulation model (Continuation).

Figure 4.13: Specification of the Physics node in Webots.

In order to detect collisions were defined ”bounding objects” in the robot model. As the

Chiara model has complex shapes were only used boxes and cylinders as bounding shapes.

The bounding objects are used by the collision detection engine and the figure 4.10(b)

presents the Chiara model in Webots with its bounding shapeshighlighted.

4.3.3 TouchSensor Node

The developed hexapod model has a set of touch sensors, one per leg positioned in the feet.


A TouchSensor node is used to develop two types of touch sensors : ”bumper” and

”force” (pressure) sensors. The bumper sensors simply detect collisions with objects and

return a boolean status while force sensors return the magnitude of the force exerted on their

body by external objects.

In this work were only used ”bumper” sensors in the feet allowing to know if the robot is

really in contact with the world. It returns 1 when a collision occurs and 0 otherwise.

It is important refer that collisions between a TouchSensorand other parts of the same

robot are not considered.

In Figure 4.14 it is possible to visualize the touch sensor node that was used for each leg

of the robot (in this case we can see the TouchSensor node of the left front leg).

Figure 4.14: Specification of the TouchSensor node in Webots.

In this chapter all steps related to the development of Chiara model in Webots were

detail presented. In next chapter a bio-inspired controller able to generate locomotion in the

hexapod robot will be proposed and described.

Chapter 5

Hexapod Locomotion Generation

In this chapter we start the locomotion of the hexapod robot.The most important actions of

animal locomotion as gaits will be described.

We propose a bio-inspired controller able to generate locomotion and reproduce the dif-

ferent type of gaits. Motor patterns are generated by coupled Central Pattern Generators,

formulated as nonlinear oscillators. The results are performed in simulation and described in

detail.

5.1 Gait Description

During animal locomotion one of the most important actions is the coordinated cyclic man-

ner of lifting and placing the legs on the ground. This action, called a gait, is a periodic

relationship among the movement of all limbs during locomotion.

A gait can be characterized [129] by the concepts of cycle time (T), duty factor (β ) and

relative phase (θ ij ).

A gait is defined by the sequence that the legs are lifted and placed, named events of

the gait. The sequence in which the legs are lifted and placedis called a gait event se-

quence [130]. A gait is normally cyclic because the same sequence of lifting and placing

the legs is repeated. The complete cycle of limb movements inwhich all legs have been

lifted and placed exactly once, is a step cycle or also named stride and the necessary time to

complete a step cycle is the cycle time(T).

A stride can be divided into two phases, the stance phase (also called support phase)

and the swing phase (also called transfer phase) where they have independent durations and

their sum gives the cycle time,T. Basically, the stance phase corresponds to the time inter-

val in which the limb is in ground contact and the body is propelled. The duration of the

63

64 CHAPTER 5. HEXAPOD LOCOMOTION GENERATION

stance phase determines the overall period of the step cycleand is defined by the following

expression,

Tst = (β )T (5.1)

In swing phase the leg is swung up and moved to the starting point of the next standing

phase. The next equation presents the expression of the duration of the swing phase,

Tsw= (1−β )T (5.2)

The relationship between the stance phase duration (Tst) and the cycle time (T=Tst + Tsw)

is the duty factorβ ∈ [0,1],

β =Tst

Tst+Tsw(5.3)

The duty factorβ is defined as the fraction of the duration of the step cycle forwhich a

foot is on the ground.

In general, animals increase their locomotion velocity by decreasing the step cycle dura-

tion, increasing the number of steps per second [29]. Observations of animal locomotion led

to the conclusion that this decrease of the cycle time is mainly due to a decrease in the stance

phase duration,Tst. While the stance phase duration is decreased, the swing phase duration,

Tsw, remains practically constant throughout all velocities of locomotion.

We focus our work in the most common hexapodal gaits, used forstraightforward walk-

ing [131]. We follow usual limb conventions [109], the limbsof the left (L) and right (R)

sides of the insect are numbered from front to back. The subindexs stand for the limb num-

ber: 1 is the front leg, 2 is the middle leg and 3 is the rear leg (Fig. 5.1).

R3

L2

L3

L1

R2

R1

Contralateral Limbs

Adjacent Limbs

Figure 5.1: Legs Description.

5.1. GAIT DESCRIPTION 65

It is considered that the first event, and the start of the stride, is chosen as the reference

event when an arbitrary chosen reference limb is set down. The convention used here is that

the reference limb is the right rear leg(R3).

The relative phase of legi is defined as the time elapsed from the setting down of a chosen

reference foot until the foot of legi is set down, given as the fraction of the cycle time. Thus,

consider as reference the right rear limb(R3), the relative phase for all the limbs is given by

θi =∆tiT, (5.4)

whereθi ∈ [0,1], because∆ti ≤ T is the time delay between the placing events of the right

rear leg limb and limbi.

Many of the usual hexapod gaits possess a degree of symmetry,which can in general be

described according to the two following assumptions [132]: 1) no leg moves forward until

the one behind is placed in a supporting position; and 2) legsof the same girdle are always in

strict alternation, performing the step cycle out of phase from each other (0.5 out of phase).

Figures 5.2 and 5.3 depict the gait diagrams and the relativephases for the most common

hexapodal gaits [109]. In Figure 5.2 the white color indicates that the foot is in ground

contact and the black color otherwise.

(a)

(b)

(c)

Figure 5.2: Gait diagram depicting event sequences for three different hexapodal gaits. White colorindicates that the foot is in ground contact. a) Metachronal(low - speed) Gait. b) Ripple (medium -speed) Gait. c) Tripod (fast - speed) Gait.


The Metachronal gait, illustrated in Fig. 5.2(a), is adopted by the hexapod when it moves

slowly, usually with a duty factor ofβ = 34 meaning that during this fraction of the dura-

tion of the step cycle each foot is on the ground. This gait canbe described as a back to

front propagating ”wave”, first moving the limbs on the rightside (with black color in the

figure 5.2(a)) and then the limbs on the left side (with black color in the figure 5.2(a)).

The adjacent limbs of each half of the hexapod body (R3 and R2,R2 and R1) are 600 out

of phase and contralateral limbs (e.g. R3 and L3) are half a period (or 1800) out of phase

(Fig. 5.3(a)). In this gait each leg is lifted of the ground after 16 of the cycle time the reference

leg (R3) be placed in the ground as demonstrated in figure 5.3(a) .

The Ripple Gait (Fig. 5.2(b)) is used by the hexapod to move with a medium speed and

duty factorβ = 58 where each foot is on the ground during this fraction of the cycle time.

The contralateral anterior and posterior legs,i.e. L1 and R3, L3 and R1 move together in

phase (as we can verify in figure 5.2(b) with black color).

Contralateral legs in each segment are half a period (1800) out of phase and the consec-

utive movements of the limbs are one quarter of a period (900) out of phase (Fig. 5.3(b)).

During this gait L1 and R3 start together the movement, then after one quarter of a period

moves R2, more a quarter of a cycle begin their movement R1 andL3 and finally after more

one quarter of a period moves L2 as possible to verify in figure5.3(b).

When an hexapod moves rapidly, it normally uses the tripod gait (Fig. 5.2(c)), with a duty

factor ofβ = 12 meaning that each foot is on the ground during this fraction of the duration

of the step cycle and if the value ofβ is less than12 the hexapod robot is running. At each

move, ipsilateral anterior and posterior legs, and the contralateral middle leg move together

in phase.

At each time, three legs (L1, L3, R2 and R1, R3, L2) move together in phase as demon-

strated with black color in figure 5.2(c). On each segment, contralateral limbs are half a

period (1800) out of phase. The adjacent limbs on the right and left sides are also half a

period (1800) out of phase (Fig. 5.3(c)).

5.2 Locomotor Model

Each leg of the hexapod robot has 3 DOFs, one per joint, exceptthe right front leg that has

4 DOFs. The names of the joints of the hexapod model are definedas coxa, femur and tibia

following the biological inspiration but as the right frontleg is a special leg has more one

5.2. LOCOMOTOR MODEL 67

5/6

4/6

3/6

2/6

1/6

0

(a)

0

3/4

1/2

1/2

1/4

0

(b)

1/2

0

1/2

0

1/2

0

(c)

Figure 5.3: Relative phases for the most common hexapodal gaits. a) Metachronal gait. b) Ripplegait. c) Tripod gait.

joint called trochanter (see Fig. 4.11).

We present a two-layer architecture able to generate the motions of hexapodal locomotion

and able of changing the walking velocity through continuous gait change (fig. 5.4).

Coxa

Femur

Tibia

Robot

En

vir

on

me

ntCentral Pattern

Generators

Lateral posture

control

Lower

layer

Upper

layer

m

¯

¹xi

yF,i

yT,i

Pa

ram

ete

r

mo

du

lati

on

Figure 5.4: System’s overall architecture. The network of CPGs generate the motions of locomotionfor the coxa joints. The posture control mechanism generates the necessary discrete movements onthe femur and tibia, to correct the robot’s body orientation.

We also include a lateral posture mechanism that automatically corrects the body orien-

tation of the robot in respect to lateral inclination.

The lower layer generates the required motions of the limbs for locomotion, using a

network of CPGs, on-line generating coordinated trajectories for the coxa joints, which we

can modulate through simple and predictable parameter changes. These trajectories encode

the values of the joint’s angles and are sent online for the lower level PID controllers of each

coxa joint (fig. 5.4).

The parametersβ andµ are determined by the upper layer, specified through the value of

a single descending command. We are able to change between three basic hexapodal gaits,

controlling the velocity and behaviour of the robot, as locomotion initiation, gait switching

and stopping.


Next will be described the network of CPGs used in the lower layer and the lateral posture

control mechanism will be discussed later in this report.

5.3 CPGs

Movements for all coxa joints are generated by a single nonlinear Hopf oscillator, as follows

xi = α(µ − r2i )(xi −yi)−ωzi (5.5)

zi = α(µ − r2i )zi +ω(xi −yi) (5.6)

wherexi andzi are the state variables,r i =√

(x2i +z2

i ), amplitude of the oscillations is given

by A=√µ , ω specifies the oscillations frequency and relaxation to the limit cycle is given

by 12α µ .

This oscillator generates harmonic solutions for the statevariablesxi andzi where the

variableyi controls the offset for the solution in thexi state variable.

Herein, we consider that the descending phase of thexi trajectory, in which the coxa joint

value is decreasing, corresponds to the stance step phase inwhich the limb moves backwards,

thus propelling the robot forward. The ascending phase is the movement that places the foot

in a more advanced position, ready for the next step, and corresponds to the swing step phase.

This oscillator contains an Hopf bifurcation from a fixed point at xi = yi (whenµ < 0

(Fig. 5.5)) to a structurally stable, harmonic limit cycle,for µ > 0 (Fig. 5.6).

−0.2 −0.1 0 0.1 0.2 0.3 0.4

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

x

z

i

i

(a)

0 1 2 3 4 5 6 7 8

−0.4

−0.2

0

0.2

T ime ( s )

x ,

z

ii

(b)

Figure 5.5: a) Fixed point at (0, 0) withµ =−1, yi = 0, α = 0.5 andω = π. b) Oscillatory harmonicsolution. The initial condition (xo,yo) = (0,−0.5), xi (solid blue line) andzi (solid red line).Theoscillator relaxes toxi = 0 andzi = 0.

5.3. CPGS 69

−1 −0.5 0 0.5 1

−1

−0.5

0

0.5

1z

xi

i

(a)

0 1 2 3 4 5 6 7 8−1

−0.5

0

0.5

1

T ime (s)

x ,

z ii

(b)

Figure 5.6: Solutions of the oscillator (4.2, 4.3). a) Limit-cycle with amplitude of 1,µ = 1, yi = 0.The initial condition (xo,yo) = (0,−0.5), α = 0.5 andω = π. b) Harmonic solution where thexvariable is the solid blue line andz is the solid red line.

The generated trajectory results in a superposition of two types of movements, rhythmic

and discrete, where the rhythmic motion can be switched on oroff by simply settingµ to

positive or negative values, respectively. When the rhythmic motion is switched off by setting

µ to a negative value, the attractor of the Hopf oscillator is no longer a limit cycle but a fixed

point specified by the offset, i.e. byyi variable.

The generated trajectories using the Hopf oscillator can besummarized as

[xi (t)zi (t)

]=

[yi0

],µ < 0

[yi +

√µ cos(ωt)√µ sin(ωt)

],µ > 0

(5.7)

This oscillator generates smooth trajectories due to stable solutions, despite small changes

in the parameters. We motivate the choice of this Hopf oscillator because it can be com-

pletely analytically solved, which facilitates the smoothmodulation of the generated trajec-

tories with respect to their amplitude and frequency (for speed change) according to small

parameter changes, while keeping the general features of the original movements.

With this oscillator we can only turn on its oscillatory activity (Fig. 5.7), stop the oscilla-

tor and generate a discrete movement (Fig. 5.8) by continuously changing the offsetyi where

the resultingxi trajectory follow this change and combining both (Fig. 5.9)by turn on the

oscillator and change the offset where the resulting harmonic xi trajectory oscillates around

the offset (yi) value.

By modifying the offset values (yi variable), we can easily modulate the generated trajec-


tories. Whatever the change is, the system converges almostimmediately to the new solution

of the system where it is easily possible verify the smoothness of the trajectory when the

parameters are changed.

0 2 4 6 8 10 12−2

−1

0

1

2

T ime(s)

xi

Figure 5.7: Oscillatory solution with an amplitude of 2.

0 2 4 6 8 10 12−4

−2

0

2

4

y

0 2 4 6 8 10 12−4

−2

0

2

4

T ime (s)

i x

,y

ii

Figure 5.8: Trajectory modulation through changes in theyi values (offset) when rhythmic motionis turned off (µ < 0). The solid blue line is thexi solution and the dashed red line isyi where theresultingxi trajectory converges asymptotically to the current value of yi .

The amplitude of oscillations, is defined by the value of√µ whenµ > 0 and it is possible

to modulate it by changing the√µ value (Fig. 5.10). Att = 3 swe set the

√µ value to 4 and

the generated trajectoriesxi andzi follow this change oscillating with the same amplitude.

At t = 6 s√µ returns to its initial value (2) and the amplitude of the generated trajectories

are also modulated to their initial state (2). Finally, att = 8 sas√µ is again changed to 4,xi

andzi are also again modulated following the√µ value.

5.3. CPGS 71

0 1 2 3 4 5 6 7 8 9 10−4

−2

0

2

4y

0 2 4 6 8 10 12

−5

0

5

T ime ( s)

i x

,y

ii

Figure 5.9: Trajectory modulation through changes in theyi values (offset) when rhythmic motionis turned on (µ > 0). The solid blue line is thexi solution and the dashed red line isyi where theresulting harmonicxi trajectory oscillates around the offset (yi value).

0 2 4 6 8 10 12−4

−2

0

2

4

0 2 4 6 8 10 12

2

3

4

T ime(s)

√µ

6

6

me

8

8

x ,

z ii

Figure 5.10: Amplitude modulation of the generated trajectoriesxi andzi (top) by modifying theµparameter (bottom). Thexi variable is the solid blue line and thezi is the solid red line (top figure).

Theω parameter defines the frequency of oscillations and varyingits value we can modu-

late the frequency of the generated trajectories (Fig. 5.11). Beginning with a frequency value

of 5 rad s−1, at t = 3 s its value is changed to 2rad s−1 and the oscillator promptly changes

the frequency of the generated trajectories, resulting in asmooth and responsive trajectories.

The same situations occur att = 6 s andt = 8 s where the oscillator adequately responds to


changes in frequency values.

0 2 4 6 8 10 12

−1

0

1

0 2 4 6 8 10 12

2

5

10

15

T ime (s)

ω

6

me

8

x ,

z ii

Figure 5.11: Frequency modulation of the generated trajectoriesxi andzi (top) by modifying theωparameter (bottom). Thexi variable is the solid blue line andzi is the solid red line (top figure).

The direction of the limit-cycle is controlled by the signalof parameterω. Whenω > 0

the limit-cycle rotates counter-clockwise (Fig. 5.12(a))and if ω < 0 it rotates clockwise

(Fig. 5.13(a)). This change in the limit-cycles direction results in the inversion of the gener-

ated trajectories in time.

In figure 5.12 the trajectoryxi is generated beforezi and in figure 5.13 the opposite hap-

pens.

−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

1.5

x

z

i

i

(a)

0 1 2 3 4 5 6 7−1

0

1

T ime(s)

x ,

zi

i

(b)

Figure 5.12: Limit-cycle directions and resulting trajectories forω > 0. a) Limit-cycle with amplitudeof 1 with ω = 10. b) Generated trajectoriesxi andzi . Thexi variable is the solid blue line and thezi

is the solid red line.

5.3. CPGS 73

−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

1.5

zi

xi

(a)

0 1 2 3 4 5 6 7−1

0

1

T ime(s)

x ,

z ii

(b)

Figure 5.13: Limit-cycle directions and resulting trajectories forω < 0. a) Limit-cycle with amplitudeof 1 with ω =−10. b) Generated trajectoriesxi andzi . Thexi variable is the solid blue line and thezi

is the solid red line.

The generatedxi andzi trajectories are inverted in time because the limit-cycle direction.

This oscillator generates anxi oscillatory trajectory in which the ascending and descend-

ing parts have equal durations. In order to achieve an independent control of the duration of

these parts, we employ the following equation proposed by [101],

ω =ωst

e−azi +1+

ωsw

eazi +1, (5.8)

whereω alternates between two different values,ωsw andωst, depending on the step phase

identified by the value of thezi variable. The alternation speed between these two values is

controlled bya.

By controlling the durations of the ascending and descending phase of thexi trajectory,

we are controlling the durations of the swing (Tsw) and stance (Tst) step phases, respectively.

This is achieved by settingωsw = πTsw

(swing frequency) andωst =πTst

(stance frequency).

It is thus possible to generate gaits with a desired duty factor, β , by keeping the swing

frequency constant and specifying the stance frequency according to the duty factor value as

follows,

ωst =1−β

βωsw. (5.9)

In the next figure (5.14) are demonstrated the generated trajectoriesxi and zi for two

different values ofβ . At the beginning is used aβ = 0.5 but att = 4 s this value is changed

to 0.9 and we can verify that the duration of the ascending phase (swing) inxi trajectory is

kept constant, only the duration of the descending phase (stance) changes.


0 1 2 3 4 5 6 7 8−1

−0.5

0

0.5

1

T ime (s)

Swing Stance

4

me

β = 0.5 β = 0.9

x ,

z ii

Figure 5.14: Generated trajectoriesxi (solid blue line) andzi (solid red line). ForTsw= 0.3 and initialβ = 0.5, att = 4 s theβ value is changed to 0.9.

Duringzi < 0, for ω > 0, was defined that the generatedxi trajectory describes the swing

movement of the robot and duringzi > 0 is performed the stance movement. In this situation

the stance phase is the descending trajectory making the robot walk forward.

If ω < 0, the direction of the limit cycle is inverted thus the generatedxi andzi trajectories

are also inverted. In this case the opposite happens where the stance phase is the ascending

trajectory and the robot walks backwards. These differences are better described and demon-

strated in figure 5.15 where it’s possible analyze the changes inxi andzi trajectories whenω

has positive or negative sign.

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

−1

−0.5

0

0.5

1

T ime(s)

x ,

z ii

(a)

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

−1

−0.5

0

0.5

1

x ,

z ii

T ime(s)

(b)

Figure 5.15: Generated trajectoriesxi (solid blue line) andzi (solid red line) for different signs ofωandβ = 0.8. a)xi andzi solutions forω < 0. b)xi andzi solutions forω > 0.

5.4. INTERLIMB COORDINATION 75

The femur joints are controlled as simple as possible: by flexing the femur to a fixed

angle during swing phase, and extending to a fixed angle during the stance phase.

5.4 Interlimb coordination

Interlimb coordination is achieved by coupling, in a given manner, the dynamics of the six

CPGs, each controlling a coxa joint. These couplings ensurethat the limbs stay synchro-

nized, and are given by:[xizi

]=

[α(µ − r2

i

)−ω

ω α(µ − r2

i

)][

xizi

]+∑

j 6=i

R(θ ij)

[0

x j+zjr j

]

wherei, j ∈ {L1,L2,L3,R1,R2,R3}. The linear terms are rotated onto each other by the

rotation matrixR(θ ij), whereθ i

j is the required relative phase between thei and j coxa

oscillators to perform the gait (we exploit the fact thatR(θ) = R−1(−θ)).

Figure 5.16 shows the resulting network of six coxa coupled Hopf oscillators, that allows

interlimb coordination for each gait of the hexapod locomotion.

Le� Front Leg Right Front Leg

Right Middle Leg Le� Middle Leg

Right Rear Leg Le� Rear Leg

θ1

2

θ2

1

θ1

3 θ2

4

θ4

6

θ3

4

1 2

3 4

5 6

θ4

2 θ3

1

θ4

3

θ5

3 θ3

5 θ6

4

θ6

5

θ5

6

Figure 5.16: Coupling Network to achieve interlimb coordination.

Table 5.1 lists the relative phases(θ ij) between the oscillators of the coupling network for

metachronal, ripple and tripod gaits [109].

Gait θ12 θ1

3 θ24 θ3

4 θ35 θ4

6 θ56

Metachronal π π3

π3 π π

3π3 π

Ripple −π −3π2

π2 π π

2π2 π

Tripod π π −π −π −π π π

Table 5.1: Relative Phases between oscillators.


In order to obtain the desired gaits we modulate a set of parameters presented in Table 5.2.

These parameters areβ , µ andωsw previously mentioned.

β µ ωsw (rad s−1)

Table 5.2: Parameter values used in the gait generation experiments.

Using this approach to interlimb coordination we obtain a network of oscillators with

controlled phase relationships, able to generate any type of behavior such as locomotion

with stable and smooth trajectories.

5.5 Gait Generation Experiments

In this work we want to generate the metachronal, ripple and the tripod hexapodal gaits,

according to the CPG-based locomotor generator. All experiments presented in this work

were done in simulation using the Webots simulator.

Parameters for experiments were chosen in regard to stability during the integration pro-

cess and to feasibility of the desired trajectories. The choice toβ , µ andωsw values followed

the Dynamixel AX-12 Servos specifications and also therefore the definitions of the Servo

Nodes for the developed model. Varying theµ andωsw values we can change the velocity of

the hexapod robot.

In these experiments, the robot walks over a plain surface and aTsw= 0.3 s is set for the

three generated gaits. The used cycle time in these experiments was 8 ms and in the three

generated gaits were used same values toβ andµ of the coxa joints.

5.5.1 Metachronal Gait

In this experiment, we setβ = 56, and the relative phases are set according to first row of

Table 5.1. The chosen parameters values in this experiment are demonstrated in Table 5.3.

β µ ωsw (rad s−1)56 100 10.47

Table 5.3: Parameter values used in metachronal gait generation experiments.

The robot moves with a velocity of≈ 0.058 m/s. It is important to refer that we calculate

the velocity of the robot in the three generated gaits using the same way to calculate the

average speed:Vm =distance(m)

time(s) .

5.5. GAIT GENERATION EXPERIMENTS 77

The planned generated coxa jointsxi trajectories are depicted in figure 5.17 as well as

the recordedxi trajectories from the servos wherei ∈ {1,2,3,4,5,6}. We can verify that the

generated trajectories are coordinated as desired.

Note that the six oscillators have a lag of a sixth of one period (60o) as expected. The

solid blue line represents L1 trajectory, solid dark green is R2 trajectory, solid red line is L2

trajectory, light blue represents R2 trajectory, dashed purple is L3 trajectory and the dashed

light green is R3 trajectory (the same nomenclature is used in the other experiments).

−10

−5

0

5

10

xi (

o)

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10

−5

0

5

10

Time (s)

x~i (

o)

Figure 5.17: Top: Generated coxa jointsxi trajectories. Bottom: Recordedxi trajectories from theservos. Solid blue line represents L1 trajectory, solid dark green is R1 trajectory, solid red line is L2trajectory, light blue represents R2 trajectory, dashed purple is L3 trajectory and dashed light green isR3 trajectory. The recordedxi trajectories are very closely to the generated onesxi .

For this gait the adjacent limbs of each half of the hexapod body (R3 and R2, R2 and R1)

are 600 out of phase and contralateral limbs (e.g. R3 and L3) are halfa period (or 1800) out

of phase.

In figure 5.18 we can verify that each recordedxi trajectory (dashed line) from de servos

is very closely to the generated onesxi (solid line) with a slight delay between them.

Readings from the touch sensors in the robot feet are presented in figure 5.19 where

SW indicates swing phase andST indicates the stance phase. This figure also presents the

recordedxi trajectories from the coxa servos for each corresponding leg.

The diagram shows that the sequence of the footfall is correct where the limbs of the

robot move like a ”wave”, one at a time with R3 striking the ground first, then R2, followed

by R1, then L3,followed by L2 and finally L1. However, L2 and R2touch the ground and


−5

0

5

10

L1

−5

0

5

10

R1

−5

0

5

10

L2

−5

0

5

10

R2

−5

0

5

10

L3

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20

−5

0

5

10

Time (s)

R3

Figure 5.18: Recordedxi trajectories from the servos (dashed line) and generated coxa jointsxi tra-jectories (solid line) for metachronal gait.

come to lift during the stance phase (see L2 and R2 panels) resulting in a different duty factor

compared with the real value. The glitches that occur are ’ignored’ in order to calculate the

actual duty factor. As our controller network is working open-loop this problem can mean

that we need to close the loop.

L1

L2

L3

R1

R2

R3

−50510

x~1 (o)

−50510

x~3 (o)

−50510

x~5 (o)

−50510

x~2 (o)

−50510

x~4 (o)

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20

−50510

x~6 (o)

Time (s)

SWST

ST

ST

ST

ST

ST

SW

SW

SW

SW

SW

Figure 5.19: Achieved footfall sequence for Metachronal gait. Below each feet sequence are depictedthe corresponding recordedxi trajectories from the coxa servos.


5.5.2 Ripple Gait

In this experiment, we setβ = 34 and the relative phases are set according to second row

of Table 5.1. The robot moves with a velocity of≈ 0.09 m/s, slightly faster than in the

metachronal gait. For this experiment the chosen parameters values are presented in Ta-

ble 5.4.

β µ ωsw (rad s−1)34 100 10.47

Table 5.4: Parameter values used in ripple gait generation experiments.

Figure 5.20 depicts planned generated coxa jointsxi trajectories as well as the recorded

xi trajectories from the servos.

−10

−5

0

5

10

xi(o)

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10

−5

0

5

10

Time (s)

x~i (

o)


In this gait, trajectories for L1 (solid blue line) and R3 (dashed light green line ) are in-

phase, as well as R1 (solid dark green line) and L3 (dashed purple line) trajectories. The

adjacent legs are a quarter of a period(90o) lagged.

Figure 5.21 shows each recordedxi trajectory from de coxa servos (dashed line) and we

can verify that is very closely to the generated onesxi (solid line). Among them there is a

slight delay that not affect the generation of the gait.

The diagram of the footfall (Fig. 5.22) shows that the sequence of the footfall is correct


−5

0

5

10

L1

−10

0

10

R1

−5

0

5

10

L2

−5

0

5

10

R2

−10

0

10

L3

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20

−505

10

Time (s)

R3

Figure 5.21: Recordedxi trajectories from the servos (dashed line) and generated coxa jointsxi tra-jectories (solid line) for ripple gait.

with each leg striking the ground at the desired time. In thisfigure are also demonstrated the

recordedxi trajectories from the coxa servos for each corresponding leg in order to analyze

the behavior in the swing and stance phases.

L1

L2

L3

R1

R2

R3

−50510

x~1 (o)

−50510

x~3 (o)

−10

0

10

x~5 (o)

−10

0

10

x~2 (o)

−50510

x~4 (o)

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 200

−50510

Time (s)

x~6 (o)

o

16 16.5

SWST

SW

SW

SW

SW

SW

ST

ST

ST

ST

ST

Figure 5.22: Achieved footfall sequence for Ripple gait. Below each feet sequence are depicted thecorresponding recordedxi trajectories from the coxa servos.

But, as occur in metachronal gait generation, L2 and mainly R2 touch and come to lift


several times during the stance phase (see L2 and R2 panels) causing a change in the actual

duty factor. The glitches that occur are also ’ignored’ in order to calculate the actual duty

factor and this situation means that there is a need to close the loop of our controller network.

5.5.3 Tripod Gait

In the tripod gait we have set aβ = 12 and the relative phases are set according to third row

of Table 5.1. A final faster velocity of≈ 0.19 m/s was achieved.

Table 5.5 describes the used parameters values for this experiment.

β µ ωsw (rad s−1)12 100 10.47

Table 5.5: Parameter values used in tripod gait generation experiments.

The planned generated coxa jointsxi trajectories are illustrated in figure 5.23 as well as

the recordedxi trajectories from the servos.

−10

−5

0

5

10

xi (

o)

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10

−5

0

5

10

Time (s)

x~

i (o

)


Note that, as expected, three legs are in-phase at each time.Adjacent legs are half a

period(180o) lagged. L2 (solid red line), R1 (solid dark green line) and R3(dashed light

green line) trajectories are together in-phase as well as R2(light blue line), L1 (solid blue

line) and L3 (dashed purple line) trajectories.


Figure 5.24 shows each recordedxi trajectory from de coxa servos (dashed line) and we

can prove that is very closely to the generated onesxi (solid line) as we desire but with an

insignificant delay between them.

−10

0

10

L1

−10

0

10

R1

−10

0

10

L2

−10

0

10

R2

−10

0

10

L3

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10

0

10

Time (s)

R3

Figure 5.24: Recordedxi trajectories from the servos (dashed line) and generated coxa jointsxi tra-jectories (solid line) for tripod gait.

The feet sequence and the recordedxi trajectories from the coxa servos for each corre-

sponding leg are depicted in figure 5.25. This diagram demonstrates that each time three legs

are in contact with the ground (L1, L3, R2 and R1, R3, L2).

However, we can see that almost all legs, in small instants ofthe stance phase touch the

ground and come to lift resulting in a different duty factor compared with the real value. We

had to ’ignore’ the glitches in order to calculate the actualduty factor. As our controller

network is working open-loop this shows the need of closing the loop.

In next chapter will be discussed the switch between these three gaits using a simple

mechanism.


L1

L2

L3

R1

R2

R3

−10

0

10

x~1 (o)

−10

0

10

x~3 (o)

−10

0

10

x~5 (o)

−10

0

10

x~2 (o)

−10

0

10

x~4 (o)

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20−10

0

10

Time (s)

x~6 (o)

o

ST

ST

ST

ST

ST

ST

SW

SW

SW

SW

SW

SW

Figure 5.25: Achieved footfall sequence for Tripod gait. Below each feet sequence are depicted thecorresponding recordedxi trajectories from the coxa servos.

Chapter 6

Gait Transition

An objective of this work is to switch between the three implemented gaits. For this pur-

pose a modulatory drive signal,m, is used to regulate the activity of the CPGs where its

strength initiates, stops and switches among gaits, by adjusting the needed parameters of the

oscillators.

These parameters are the amplitudeµ, the frequencyωst of the stance phase and the gait

phases(θ ij). Both the value of the stance frequency and the gait phases can be expressed as

functions of the duty factorβ .

6.1 Gait Transition Mechanism

One aim of this work is to achieve gait transition between thethree implemented gaits. In

this work a modulatory drive signal,m, is used to regulate the activity of the CPGs. Its

strength initiates, stops and switches among gaits, by adjusting the needed parameters of the

oscillators. Bellow a lower threshold of the modulatory drive,mlow, the robot stops to move.

Them values were chosen arbitrarily as well as its range.

Different values of the drive signal mean different behaviors, that is, locomotion initia-

tion, speed change and gait change. These different behaviors correspond to adjustments of

the CPG parameters, namely: amplitude, stance frequency and coupling parameters.

6.2 Initiating/stopping locomotion

By modifying theµ parameter the system switches between a stable fixed point atxi = 0

(µ < 0) and a rhythmic movement(µ > 0), meaning theµ parameter sets whether or not

there are oscillations generated by the CPG. For am below mlow = 0.2 the oscillators are

shut down and the robot stops its movement.

84

6.3. DUTY FACTOR MODULATION 85

6.3 Duty factor modulation

In this work, the metachronal gait has a duty factor of(56), the ripple gait has a duty factor

of (34) and the tripod gait has a duty factor of(1

2). As the modulatory drive increases in

strength, the duty factor linearly decreases (from(56) until (1

2)). β is defined as a piecewise

linear function of the modulatory drivem,

β =

{−0.083m2+0.166m+0.749 ,mlow < m≤ 3

0.5,m≥ 3. (6.1)

6.4 Gait phases modulation

In order to modulate the gait phases we use the adaptive gait rule from [62]. This rule states

that: 1) in consecutive legs, each leg motion has 1−β phase shift fast to fore side leg; and

2) legs of the same girdle perform the step cycle 0.5 out of phase from each other.

The adaptive gait rule is defined as a function of the duty factor. The task of change the

robot walking speed means changing the duty factor, thus this gait rule must be changed as

the walking speed changes. This rule is used because it is very hard to change the leg phases

without stopping the robot and the adaptive gait rule simplifies this process allows achieve

the desired relative phases keeping its synchronized motion.

According to these indications,(θ ij) can be mathematically defined by

θ ij =

{(1−β )2π , adjacent legs

(0.5)π , contralateral legs. (6.2)

In fact we have presented the required relative phases for the network of oscillators based

on this rule in Table 5.1.

6.5 Experiments

In order to demonstrate the implementation of this model to perform the gait transition in the

hexapod robot, several experiments were realized. The aim of these experiments is demon-

strate the smoothness and performance on gait transition when interlimb phase relationships

are progressively adjusted following the previously presented solution. We expect a smoother

locomotion when the interlimb phase relationships are changed according to the proposed

rule.

86 CHAPTER 6. GAIT TRANSITION

An abrupt transition between the gaits it is used in the first experiment, and another

experiment uses a gradual transition between the differentgaits.

In the first experiment (Fig. 6.1) the robot walks forward during the first 20 s perform-

ing the metachronal gait(β = 56) (Fig. 6.1(b)) with an initial modulatory drivem (Top fig-

ure 6.1(a)) of 1 , then att = 20s themvalue is abruptly changed to 2 and the robot performs

the transition to the ripple gait(β = 34) (Fig. 6.1(c)). Finally at instantt = 40s, m drops to 3

forcing the robot to transit to the tripod gait(β = 12) (Fig. 6.1(d)). Thenµ is set to a negative

value and the oscillators stop the movement of the robot.

But in the second experiment (Fig. 6.2), the robot only stabilizes in the ripple gait at about

t = 45sand for tripod gait the hexapod stabilizes betweent = 85sandt = 90s. These facts

occur because the transition is realized in a gradual way thus taking more time.

During this first experiment the duty factor (Bottom figure 6.1(a)) is modulated according

to changes in modulatory drive signalm value, where we can verify that in the first 20 s the

duty factor value is56 because the robot is in metachronal gait, att = 20 s the robot transits

to ripple gait and the duty factor value is abruptly changed to 34. At t = 40 s as the robot

performs the transition to the tripod gait, the duty factor value is quickly changed to12.

In figure 6.1 are demonstrated the obtained results for the abrupt transition between the

gaits, where are presented the modulatory drive signal (m) and duty factor (Fig. 6.1(a)) as

well as recordedxi trajectories from the servos for robot coxa joints (Figures6.1(b), 6.1(c)

and 6.1(d)).

In the second experiment (Fig. 6.2), it is used a gradual transition between the different

gaits.

In this experiment (Fig. 6.2) the modulatory drive signalm (Top figure 6.2(a)) starts at 1

and during the first 20 s the robot performs the metachronal gait (β = 56) (Fig. 6.2(b)) , then

at t = 20s themvalue is gradually increased to 2 with the robot performing the transition to

the ripple gait(β = 34) and the figure 6.2(c) demonstrates the recordedxi trajectories from

the servos betweent = 40 s andt = 45 s when the robot finishes the transition. Ultimately

at instantt = 40 s, m is gradually changed to 3 allowing the robot to transit to thetripod gait

(β = 12) and in figure 6.2(d) we can see the recordedxi trajectories from the servos when

the robot is finishing the transition to tripod gait. Thenµ is set to a negative value and the

oscillators stop the movement of the robot.

6.5. EXPERIMENTS 87

1

2

3

m

0 10 20 30 40 500.5

0.75

0.8

Time (s)

β

20 40

(a)

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20

−5

0

5

Time(s)

x~

i (o)

(b)

35 35.5 36 36.5 37 37.5 38 38.5 39 39.5 40

−5

0

5

Time (s)

x~

i (o)

(c)

55 55.5 56 56.5 57 57.5 58 58.5 59 59.5 60 60.5

−5

0

5

Time (s)

x~

i (o)

(d)

Figure 6.1: Abrupt Transition. a) Top: Modulatory drive,m, is abruptly changed between the gaitstransition. a) Bottom: Duty factor modulation. b) Recordedxi trajectories from the servos betweent = 15sandt = 20 swhere the robot performs the metachronal gait. c) Recordedxi trajectories fromthe servos betweent = 35 s and t = 40 s when the robot finishes the transition to ripple gait. d)Recordedxi trajectories from the servos betweent = 55 s andt = 60 s when the robot finishes thetransition to tripod gait.

For this experiment the duty factor modulation according tochanges in modulatory drive

signalmvalue is presented in bottom figure 6.2(a), where we can see that in the first 20 s the

duty factor is56 because the robot is performing the metachronal gait, att = 20 s the robot


transits to ripple gait and consequently the duty factor is gradually decreased to34. Finally at

t = 40s the duty factor value is continuously modulated to12 because the robot is performing

the transition to tripod gait.

1

2

3

m

0 10 20 30 40 50 60 70 80 900.5

0.75

0.8

Time (s)

β

20 40

Tim

(a)

15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20

−5

0

5

Time (s)

x~

i (o)

(b)

40 40.5 41 41.5 42 42.5 43 43.5 44 44.5 45

−5

0

5

Time (s)

x~

i (o)

(c)

85 85.5 86 86.5 87 87.5 88 88.5 89 89.5 90

−5

0

5

Time (s)

x~

i (o)

(d)

Figure 6.2: Gradual Transition. a) Top: Modulatory drive,m, is gradually changed between the gaitstransition. a) Bottom: Duty factor modulation. b) Recordedxi trajectories from the servos betweent = 15sandt = 20 swhere the robot performs the metachronal gait. c) Recordedxi trajectories fromthe servos betweent = 40 s and t = 45 s when the robot finishes the transition to ripple gait. d)Recordedxi trajectories from the servos betweent = 85 s andt = 90 s when the robot finishes thetransition to tripod gait. In this situation the robot takesmore time to achieve the desired behaviors.

Next will be described another experiment with a different sequence of gait change. In

this experiment the gait transition not begin in metachronal gait and not finishes in tripod

6.5. EXPERIMENTS 89

gait but is performed in an alternated way.

In this experiment (Fig. 6.3) the modulatory drive signalm (Top figure 6.3(a)) starts at 3

and during the first 10 s the robot performs the tripod gait(β = 12) where in figure 6.3(b)) are

displayed the recordedxi trajectories from the servos for the first 5 s. Then att = 10 s them

value drops to 2 , forcing a quick change from tripod to ripple(β = 34) gait and figure 6.3(c)

demonstrates the recordedxi trajectories from the servos betweent = 10sandt = 15swhen

the robot starts the transition to ripple gait. In figure 6.3(d) are demonstrated the recordedxi

trajectories for final instants (betweent = 25 s andt = 30 s) of the transition to ripple gait.

Finally at instantt = 30 s, m is gradually reduced down to 1, (top fig. 6.3(a)). In fig-

ure 6.3(e) are shown the last moments of the transition to metachronal gait. Thenµ is set to

a negative value and the oscillators stop the movement of therobot.

The duty factor value during the gait transitions is demonstrated in the bottom of fig-

ure 6.3(a), where it is possible to verify that in the first 10 sthe duty factor value is12 because

the robot is in tripod gait, att = 10 s the robot makes the transition to ripple gait and the

duty factor value is abruptly changed to34 and remains in this value untilt = 30 s where the

hexapod switches to metachronal gait and the duty factor value is gradually increased to56.

In the last experiment we can verify that the robot changes its gait by simply adjusting

the modulatory drive signal value and consequently the dutyfactor. However this duty factor

is planned and would be interesting to analyze the real duty factor. With this aim we have

also measured touch sensors from the feet in order to verify the actual duty factor.

In figures 6.4, 6.5, 6.6 and 6.7 are demonstrated the feet sequence for the different instants

of the last experiment.

Analyzing, for example, the last instants (Fig. 6.7) of the experiment (i ∈ {1,2,3,4,5,6}),

following the figure 5.16 that demonstrates the resulting network of six coxa coupled Hopf

oscillators, the robot performs the transition to metachronal gait. We can see that R2 touches

and lifts during the stance phase resulting in a different duty factor compared with the real

value (SW indicates swing phase andST indicates the stance phase). In order to calculate

the actual duty factor we had to ’ignore’ the glitches that occurred. Our controller network

is working open-loop and this shows the need of closing the loop.


0

1

2

3

m

0 10 20 30 40 50 600.5

0.7

0.8

Time (s)

β

10

e (s)

30

(a)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−5

0

5

x~

i (o)

Time (s)

(b)

10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15

−5

0

5

Time (s)

x~

i (o)

(c)

25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30

−5

0

5

Time (s)

x~

i (o)

(d)

55 55.5 56 56.5 57 57.5 58 58.5 59 59.5 60

−5

0

5

Time (s)

x~

i (o)

(e)

Figure 6.3: a) Top: Modulatory drive,m, is abruptly changed to 2 att = 10 s when the robot is per-forming the transition between tripod gait and ripple gait.Fromt = 30s, m, is gradually decreased inorder to achieve the metachronal gait. a) Bottom: Duty factor modulation. b) Recordedxi trajectoriesfrom the servos betweent = 0 sandt = 5 swhen the robot is in tripod gait. c) Recordedxi trajectoriesfrom the servos betweent = 10 s andt = 15 swhere the robot is starting the transition to ripple gait.d) Recordedxi trajectories from the servos betweent = 25 s andt = 30 s when the robot is in fullripple gait. e) Recordedxi trajectories from the servos between 55sand 60swhen the robot is alreadyperforming the metachronal gait.

6.5. EXPERIMENTS 91

L1

L2

L3

R1

R2

R3

−10

0

10x~

1 (o)

−10

0

10

x~

3 (o)

−10

0

10

x~

5 (o)

−10

0

10

x~

2 (o)

−100

10

x~

4 (o)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−10

0

10

Time (s)

x~

6 (o)

SWST

11

SW

SW

SW

SW

SW

ST

ST

ST

ST

ST

Figure 6.4: Feet Sequence betweent = 0 s and t = 5 s. L1, L2, L3, R1, R2 andR3 demonstratethe readings from the touch sensors from these legs.x1, x2, x3, x4, x5 and x6 present the recordedtrajectories from coxa servos for the respective legs(L1,L2,L3,R1,R2 and R3).

L1

L2

L3

R1

R2

R3

−10

0

10

x~

1 (o)

−10

0

10

x~

3 (o)

−10

0

10

x~

5 (o)

−10

0

10

x~

2 (o)

−10

0

10

x~

4 (o)

10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15−10

0

10

Time (s)

x~

6 (o)

1111 11.511.5

SWST

SW

SW

SW

SW

SW

ST

ST

ST

ST

ST

Figure 6.5: Feet Sequence betweent = 10 s andt = 15 s. L1, L2, L3, R1, R2 andR3 demonstratethe readings from the touch sensors from these legs.x1, x2, x3, x4, x5 and x6 present the recordedtrajectories from coxa servos for the respective legs(L1,L2,L3,R1,R2 and R3).


L1

L2

L3

R1

R2

R3

−10

0

10

x~

1 (o)

−10

0

10

x~

3 (o)

−10

0

10

x~

5 (o)

−10

0

10

x~

2 (o)

−10

0

10

x~

4 (o)

25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30−10

0

10

Time (s)

x~

6 (o)

26.

SW

SW

SW

SW

SW

SW

ST

ST

ST

ST

ST

ST


L1

L2

L3

R1

R2

R3

−10

0

10

x~

1 (o)

−10

0

10

x~

3 (o)

−10

0

10

x~

5 (o)

−10

0

10

x~

2 (o)

−10

0

10

x~

4 (o)

55 55.5 56 56.5 57 57.5 58 58.5 59 59.5 60−10

0

10

Time (s)

x~

6 (o)

SW

SW

SW

SW ST

ST

ST

ST

ST

SW ST

SW


Next chapter will be proposed a lateral posture controller using the dynamical systems

approach and will be tested in different situations in whichthe hexapod robot is expected to

6.5. EXPERIMENTS 93

maintain balance. Moreover, a set of biological principlesbased mechanisms that improve

the hexapod locomotion will be also demonstrated and explained.

Chapter 7

Posture Control

In locomotion overall architecture of this work we also include a lateral posture mechanism

to compensate the robot lateral tilt which will be discussedin this chapter.

7.1 Lateral Posture Control

The overall architecture used in this work (fig. 5.4) also includes a lateral posture mechanism

that automatically corrects the body orientation of the robot in respect to lateral inclination.

Parallel to the network of CPGs, a lateral posture mechanismacts on the limbs to correct the

body’s orientation through the value of roll displacement of the body, correcting the posture

and adapting the locomotion on inclined terrains by generating discrete trajectories for the

femur and tibia. The lateral tilt of the robot is measured using accelerometers.

The main aim of this posture control is, by measuring the lateral tilt of the robot body,φ ,

we want to stretch the legs towards which the robot is tilted and fold the other legs (fig. 7.1),

thus reducing the robot lateral tilt and keeping the body parallel to the ground (in this case

a moveable platform). This aim is achieved modulating and adjusting the femur and tibia

joints values that are controlled by dynamical systems.

94

7.1. LATERAL POSTURE CONTROL 95

Hexapod Robot Front View

(a)

(b)

(c)

Figure 7.1: Lateral posture control. Process of stretch andfold the legs. a) Robot stretching the rightlegs and folding the left legs. b) Normal position of the robot. c) Robot stretching the left legs andfolding the right legs.

In our approach we compensate lateral displacement of the body by increasing or de-

creasing leg height on both sides, performed by changing theangles of the femur and tibia

joints. These angles are controlled by discrete movements,generated by a nonlinear dynam-

ical system designed to find the neutral point of lateral posture of the robot, reducing the roll

to a minimum. The dynamical system is given by

˙yo,i = ko, j ,i f (φ)+α(yo,i −Mo,i)e− (yo,i−Mo,i )

2

2σ2

+α(yo,i −Do,i)e− (yo,i−Do,i )

2

2σ2 , (7.1)

is applied to the femur (F) and tibia (T) joints (o = F,T) whereko, j ,i ( j =left,right andi,∈{L1,L2,L3,R1,R2,R3}) is a static gain, set symmetrically for the right and left legs.

Function f (φ) defines a dead zone for the robot’s roll angleφ (fig. 7.2).

96 CHAPTER 7. POSTURE CONTROL

f (φ)

φ00.2- 0.2

0.8 φ

Figure 7.2: Functionf (φ). When−0.2< φ > 0.2, f (φ) has the value zero and elsewheref (φ) hasthe value 0.8φ .

The limits of operation for the system are given by the valuesMi (maximum) andDi

(minimum). These values were chosen following the joints limits values of the real robot.

The correspondence between the system and the leg’s joint isdescribed by the scheme

presented in figure 7.3.

Femur

Tibia

Coxa

yFemur

yTibia

~ xCoxa

Figure 7.3: Posture control scheme where only the used structure to one leg of the hexapod is demon-strated since the procedure for the other legs is the same.

Only the coxa joints perform a rhythmic motion, provided by the six coupled CPGs. The

discrete movements are applied to the femur and tibia joints, changing the height of the leg,

reducing the lateral tilt to a minimum.

7.2. EXPERIMENTS 97

Table 7.1: Parameter values used in the posture control experiments.k j,i α σ MF,i DF,i MT,i DT,i

15 5000 0.1 100o −100o 160o −60o

7.2 Experiments

To demonstrate the role of the lateral posture control, we realize some experiments where

the simulated Chiara robot walks with a metachronal gait on the top of a moveable platform,

subject to different lateral inclinations, reacting to changes in its lateral tilt. The maximum

that the moveable platform could be inclined is 20◦. In Table 7.1 the chosen configuration

parameters are presented.

The robot must counteract the effects of the platform inclination on the robot body, reduc-

ing the sensed roll angle measured by accelerometers to values belonging to a small region

around zero as defined by the dead-zone.

For the first experiment the top panel of figure 7.4 shows the change of the platform

inclination in dashed red line. The robot walks forward during the first 10 s without any

lateral tilt change. Fromt = 10 s tot = 20 s, the platform is gradually inclined to the left up

to 7◦, while the robot remains walking. We can see that the robot successfully counteracts

the platform inclination, maintaining the body roll angle close to 0◦, counteracting the body’s

lateral tilt, stretching the left legs and folding the rightlegs.

Snapshots of the experiment are presented in figure 7.5, showing the inclination that

the robot is subjected and its reaction in order to maintain the body orientation. In fig-

ures 7.5(b), 7.5(c) and 7.5(d) we can visualize the robot stretching the left legs because the

platform is inclined to the left side and folding the right legs.

In figures 7.4(b) and 7.4(c) are demonstrated theyFemur and yTibia trajectories for the

left front leg (solid blue line) and right front leg (dashed red line) that while the platform is

inclined they compensate the robot lateral tilt in order to maintain the body roll angle close to

0◦, exhibiting symmetric trajectories, as expected. In figures 7.4(d) and 7.4(e) are presented

the yFemur and yTibia trajectories for the left front leg (solid blue line) and right front leg

(dashed red line) where as greater the lateral tiltφ change greater is the value of ˙yFemur and

yTibia trajectories.

Betweent = 20 s andt = 30 s the platform is gradually shifted to the right up to 15◦.

Again, the robot successfully maintains its lateral tilt near 0◦, this time, by stretching the


right legs and folding the left as we can see in figures 7.5(e),7.5(f), 7.5(g) and 7.5(h).

5 10 15 20 25 30 35

−10

−5

0

5

φro

bo

t, p

latf

. (° )

(a)

5 10 15 20 25 30 35

−20020

yF

(° )

(b)

5 10 15 20 25 30 35−20020

yT

(° )

(c)

5 10 15 20 25 30 35−20

0

20

y. F (

° )

(d)

5 10 15 20 25 30 35

−10

0

10

y. T (

° )

(e)

Time (s)

10

10

10

10

20

20

(d

(c

(b

20

20

(a

(e

30

30

30

30

Figure 7.4: Posture control experiments: a) Lateral tiltφ of the robot (solid blue line) and platforminclination (dashed red line). b)yFemur trajectories for the left front leg (solid blue line) and rightfront leg (dashed red line). c)yTibia trajectories for the left front leg (solid blue line) and right frontleg (dashed red line). d) ˙yFemur trajectories for the left front leg (solid blue line) and right front leg(dashed red line). e) ˙yTibia trajectories for the left front leg (solid blue line) and right front leg (dashedred line).

In figure 7.6 we study with more detail the first experiment during t = 20 s untilt = 30 s

in order to demonstrate the response of the system. The vertical dashed lines of the figure

indicate three important instants of time where the changesin lateral tilt of the robot are more

abrupt. In middle and bottom panels of the figure we can verifythat in this three instants

yFemur and yTibia have greater values because as greater the lateral tiltφ change, greater is

the value of these trajectories. This figure also shows that the time to compensate posture is

very low depending of servos features and following the limits of operation for the system.

7.2. EXPERIMENTS 99

(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 7.5: Robot behavior during the posture control in first experiment. a)t = 2 s. b)t = 10 s.c) t = 12 s. d)t = 16 s. e)t = 20 s. f)t = 26 s. g)t = 28 s. h)t = 30 s.

The aim of second experiment (fig. 7.7) is describe a different situation that the robot is

subjected. In this case the robots also walks forward duringthe first 10 s without any lateral

tilt change and fromt = 10 s tot = 20 s, the moveable platform is progressively inclined up

to 7◦ to the left side while the robot remains its normal walking.

In top panel of figure 7.7 we can see that the robot counteractsthe platform inclination,

maintaining the body roll angle close to 0◦, stretching the left legs and folding the right legs

as desired.


20 21 22 23 24 25 26 27 28 29 30

−10

−5

0

7

φro

bo

t, p

latf

. (° )

20 21 22 23 24 25 26 27 28 29 30

−20

−10

0

10

20

y. F (

° )

20 21 22 23 24 25 26 27 28 29 30

−10

0

10

y.

T (

° )

Time (s)

21

21

Figure 7.6: Posture control experiments: Top figure: Lateral tilt φ of the robot (solid blue line) andplatform inclination (dashed red line); Middle figure: ˙yFemur trajectories for the left front leg (solidblue line) and right front leg (dashed red line); Bottom figure: yTibia trajectories for the left front leg(solid blue line) and right front leg (dashed red line).

In figure 7.8 are presented some snapshots of the experiment where are demonstrated the

different reactions of the robot to maintain the balance when subjected to different inclina-

tions of the platform.

Betweent = 10 s and 20 s the platform is inclined to the left side, the robot reacts stretch-

ing the left legs and folding the right legs as we can verify infigures 7.8(a), 7.8(b) and 7.8(c).

While the platform is inclined the lateral tilt of the robot is compensated in order to maintain

the body roll angle close to 0◦. Figures 7.7(b) and 7.7(c) demonstrate the behavior ofyFemur

andyTibia trajectories for the left front leg (solid blue line) and right front leg (dashed red

line) that exhibit symmetric trajectories and compensate the robot lateral tilt.

Figures 7.7(d) and 7.7(e) present ˙yFemur andyTibia trajectories for the left front leg (solid

blue line) and right front leg (dashed red line). We can verify that the value of these tra-

jectories increases and decreases as the lateral tiltφ change is greater or less varying in a

proportion way.

7.2. EXPERIMENTS 101

5 10 15 20 25 30 35

0

5

10

φrobot, p

latf

. (° )

(a)

5 10 15 20 25 30 35

−200

20

yF

(° )

(b)

5 10 15 20 25 30 35−20

0

20

yT

(° )

(c)

5 10 15 20 25 30 35

−20

0

20

y. F (

° )

(d)

5 10 15 20 25 30 35−20

0

20

y. T (

° )

(e)

Time (s)

10

10

10

10

(e

20

(d

20

20

(b

20

20

(a

30

30

30

30


Fromt = 20 s tot = 22 s the moveable platform is inclined up to 5◦ to the right side and

the robot maintains its lateral tilt near 0◦ but in this case stretching the right legs and folding

the left legs as we can see in figures 7.8(d), 7.8(e) and 7.8(f).

Finally, betweent = 22 s tot = 30 s the platform is again inclined to the left side up to

15◦ and the robot again reacts successfully keeping its lateraltilt near 0◦, by stretching the

left legs and folding the right. In order to achieve a better analysis of this situation we can

visualize figures 7.8(g), 7.8(h) and 7.8(i) where while the platform leans to the left side, the

robot stretches the left legs and folds the right, as expected.

In third experiment the main goals are demonstrate the reaction of the robot when sub-

jected to an abrupt inclination of the moveable platform that sustains its body and verify the

time it takes to respond to the abrupt change as well its behavior during this situation.

During the first 10 s nothing happens in the robot behavior because it walks forward

without any change in platform inclination.


But, fromt = 10 s tot = 20 s, the moveable platform is gradually inclined up to 7◦ to the

left side. In figure 7.9(a) we can verify that the robot remains its normal walking counter-

acting the platform inclination, keeping the body roll angle close to 0◦ as desired, stretching

the left legs and folding the right legs. Some snapshots of this experiment are shown in fig-

ure 7.10 where are demonstrated the several reactions and behaviors of the robot to keep the

balance when subjected to different inclinations of the platform. In order to verify the behav-

ior of the robot betweent = 10 s andt = 20 s, we can see the figures 7.10(a), 7.10(b), 7.10(c)

and 7.10(d) where the robot reacts stretching the left legs and folding the right legs. Fig-

ures 7.9(b) and 7.9(c) demonstrate the behavior ofyFemur andyTibia trajectories for the left

front leg (solid blue line) and right front leg (dashed red line). These trajectories are sym-

metric and compensate the robot lateral tilt maintaining the body roll angle close to 0◦ while

the platform is inclined. Figures 7.9(d) and 7.9(e) presentyFemur andyTibia trajectories for

the left front leg (solid blue line) and right front leg (dashed red line) where we verify that

vary in a proportion way to the lateral tiltφ change.


(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i)

Figure 7.8: Robot behavior during the posture control in second experiment. a)t = 10 s. b)t = 15 s.c) t = 20 s. d)t = 21 s. e)t = 21.5 s. f) t = 22 s. g)t = 24 s. h)t = 27 s. i)t = 30 s.

At t = 20 s the moveable platform is abruptly inclined up to 7◦ to the right side and the

robot maintains its lateral tilt near 0◦.

From∼ t = 20.1 s to t = 30 s the platform is again inclined to the left side up to 15◦


and we verify that the robot maintains its lateral tilt near 0◦, by stretching the left legs and

folding the right as demonstrated in figures 7.10(e), 7.10(f), 7.10(g) and 7.10(h).

In figure 7.11 we can visualize and analyze with more detail the reaction of the robot

at t = 20 s when the platform is abruptly inclined. Top panel of thisfigure presents the

lateral tilt φ of the robot (solid blue line) and platform inclination (dashed red line), middle

panel demonstrates ˙yFemur trajectories for the left front leg (solid blue line) and right front

leg (dashed red line) and bottom panel shows the behavior of ˙yTibia trajectories for the left

front leg (solid blue line) and right front leg (dashed red line).

The two vertical dashed lines of the figure indicate the beginning and end of the robot

compensation to the abrupt change in platform inclination in order to keep its lateral tilt near

0◦. We can verify that the compensation begins att ≃ 20.04 s and ends att ≃ 20.08 s. So,

the robot takes about 0.04 s to respond to the abrupt inclination of the moveable platform.

5 15 25 350

5

10

φro

bo

t, p

latf

. (° )

(a)

5 10 15 20 25 35−50

0

50

yF

(° )

(b)

5 10 15 20 25 30 35−40−2002040

yT

(° )

(c)

5 10 15 20 25 30 35

−20

0

20

y. F (

° )

(d)

5 10 15 20 25 30 35

−20

0

20

y. T (

° )

(e)

Time (s)

10

10

10

10

20

20

(d

20

(c

(b

20

(a

(e)

Time (s)

30

30

30


.


(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 7.10: Robot behavior during the posture control in third experiment. a)t = 10 s. b)t = 15 s.c) t = 19 s. d)t = 20 s. e)t = 23 s. f)t = 26 s. g)t = 28 s. h)t = 30 s.

In the next chapter will presented the conclusions retired from the realization of this work,

through the discussion of the obtained results and comparing with the initial aims. Also, will

be addressed future proposals in order to continue innovating and improving the developed

work.


5 10 15 20 25 30 35

0

5

10

φro

bo

t, p

latf

. (° )

Time (s)

20 20.01 20.02 20.03 20.04 20.05 20.06 20.07 20.08 20.09 20.1−20

−10

0

10

20

20 20.01 20.02 20.03 20.04 20.05 20.06 20.07 20.08 20.09 20.1

−10

0

10

y. T (

° )

Time (s)

y. F (

° )

20.04

20.04 20.08

20.08

Response time to abrupt inclination

Figure 7.11: Posture control experiments: Top figure: Lateral tilt φ of the robot (solid blue line) andplatform inclination (dashed red line); Middle figure: ˙yFemur trajectories for the left front leg (solidblue line) and right front leg (dashed red line); Bottom figure: yTibia trajectories for the left front leg(solid blue line) and right front leg (dashed red line).

.

Chapter 8

Conclusions

The main goal of this work is, initially, start a detailed study of the type of existing hexapod

robots and the several models of bio-inspired controllers to reproduce their locomotion.

The first step was the choose of a real hexapod robot in order todevelop it simulation

model to perform the all desired tests. We describe the development of a hexapod robot

called Chiara in the Webots simulator.

The development of a simulation model allows us to equip eachrobot with a large number

of available sensors and actuators to program these robots,simulate them and optionally

transfer the resulting programs onto our real robots.

In this work we address the problem of generate the most common hexapodal gaits and

also smoothly switch among these according to changes in thewalking velocity to achieve

stable locomotion.

During this work we only address the three most common hexapodal gaits that are

metachronal gait (”wave gait”) specifying slow walking, ripple gait corresponding to a medium

speed gait and the fast speed tripod gait.


similarly to their biological counterparts, should take place continuously with both the duty

factor and the interlimb phase relationships properly adjusted.

The developed architecture is formulated in terms of nonlinear dynamical systems. The

locomotor controller is stratified in three layers, allowing to functionally separate the several

components, facilitating its development.

For the purpose of this work, a model for a CPG was proposed in order to generate the

required movements for each limb of the hexapod robot. It wasdesigned applying nonlinear

dynamical systems approach, which present several advantages which allowed to coordinate

107

108 CHAPTER 8. CONCLUSIONS

all the joints in a limb in order to perform the movements of a step . The movements of each

limb results of trajectories generated on-line in a modularway.

In the first layer (lower level) of this work, is proposed a coordinated network of CPGs

modeled by nonlinear oscillators that it is responsible to control the locomotion of a hexapod

robot for the most common gaits, with independent step phasedurations.

In order to smoothly switch among the different hexapodal gaits, it was also developed a

second layer, which sends the appropriate set of parametersto the first layers CPGs according

to the desired motor programs. These motor programs includeinitiation, regulation and stop

CPGs activity, therefore initiate a walking gait, switch among gaits and stop the locomotion.

This layer receives a modulatory signal that regulates the CPGs activity and its strength is

mapped onto different sets of the CPG parameters resulting in the different motor behaviours.

Further, in this work we also address the situation of loss ofrobot balance due to pertur-

bation situations.

Additionally, in order to solve this problematic we proposea lateral posture control based

on the use of dynamical systems.

The idea is to make it possible to correct the robot posture and keep its balance when

subjected to changes in its lateral tilt (roll). By measuring the roll angle of the robot, the

system uses this information in order to compensate the tiltchanges and reduce them near to

zero.

8.1 Results Discussion

The experiments results were all obtained in simulation environment using Webots simulator.

These results demonstrated that the proposed controller iscapable of successfully gener-

ate the most common hexapodal gaits.

Further, the results demonstrate that using a simple command, a drive signal, allows

velocity control and the switching between three differentgaits.

Results also show that the lateral posture controller is able to maintain the roll angle

around zero, even when the robot walks in planes with a lateral inclination.

To conclude, the objectives initially proposed for this thesis were successfully accom-

plished.

8.2. FUTURE WORK 109

8.2 Future Work

Future work includes to achieve more complex postural control. The aim is to provide all

the capacities to the hexapod robot in order to walk on uneventerrain with different kind of

obstacles such as holes, terrain elevations and rocks. Thisability will require more robustness

to the locomotion controller. Some work and research have been carried in order to solve

this problem using biological inspiration, [89], [123].

Other important aims to future work include to achieve omnidirectional locomotion; par-

tially injured legs; homing and learning in hexapod robots.

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