Robotics (Locomotion)

Winter 1393

Bonab University

Locomotion “Movement or the ability to move”

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Locomotion

Locomotion mechanisms used in biological

systems:

-Successful in harsh environments

-Inspired most engineered locomotion

systems

Exception: wheels

However,

Our walking ~= rolling polygon

Locomotion – Can we copy nature?

• Extremely difficult because:• Mechanical complexity is achieved by: Structural replication

(cell division) like: millipede

• Man-made structure: fabrication=individual

• Miniaturization : extremely difficult

• Nature’s energy storage and activation (torque, response time,

And conversion efficiency) unachievable

Example: insects (robust)

Such limitations locomotion choice:• Wheeled (simpler, suitable for flat ground)

• Small # of legs ( higher DOFs mechanical complexity)

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Locomotion

Locomotion -- efficiency

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Locomotion

• on flat surfaces wheeled locomotion 1-2 orders of magnitude more efficient than legged locomotion• Example: railway with rolling friction = ideal

But, as the ground gets softer !!

• Legged locomotion = only point contacts

A biped walking system

~= by a rolling polygon,

with sides = d to the

span of the step.

As the step size

decreases

circle/wheel

Locomotion -- efficiency

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Locomotion

• Efficiency of wheeled locomotion depends on:• Environment (specially on ground)

• Flatness

• Hardness

• Efficiency of legged locomotion depends on:• Mass (that robot needs to support at all parts of gait)

• Leg

• Body

• So, it’s clear why• nature chooses legged rough/unstructured env.

(insect vertical variation > 10 it’s height)

• Human environments = engineered, smooth surfaces so, choice= wheeled

• Recently, for more natural outdoor environments hybrid

General Considerations (all forms of mobile robot locomotion)

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Locomotion

• Locomotion vs. Manipulation both study:• Actuators generate interaction forces

• Mechanisms desired kinematic & dynamic properties

• Key issues for locomotion:• stability

- number and geometry of contact points

- center of gravity

- static/dynamic stability

- inclination of terrain

• characteristics of contact- contact point/path size and shape

- angle of contact

- friction

• type of environment- structure

- medium, (e.g. water, air, soft or hard ground)

Legged Mobile Robots

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Locomotion:

Legged

• Legged locomotion = a series of point contacts between the robot & ground

• Advantages: • Adaptability

• Maneuverability in rough terrain

• Quality of the ground: does not matter

• Cross holes so long as its reach exceeds the width

• Potential to manipulate objects in the environment with great skill, e.g.

• Disadvantages:• power and mechanical complexity (Leg, which may include several DoF, must be capable of

sustaining part/whole weight)

• high maneuverability = forces in different directions (if leg has enough DoFs)

Example of

manipulation:

Dung beetle

Leg configurations and stability

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• Some biologically successful legged systems• Large animals (reptiles, mammals): 4-legs

• Insects >= 6-legs

• Some mammals perfected for 2-leg locom.

Humans can even jump on 1-leg (balance)

Price = complex active control

In contrast: 3-legged static stability

(stool : balance without motion, passive)

• Robot: static walk (need to lift legs) = need 6-legs

(a tripod of legs in touch with ground at all times)

• Insects/spiders, Mammals, Human

Arrangement of the legs of various animals

Static walking with six legs

Standing/walking after birth is more difficult

6-legs 4-legs 2-legs

Locomotion:

Legged

Video demonstrating

tripod walk

Variety of successful legs: from very simple to complicated

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• Complexity of individual legs• Caterpillar (1-DoF)

• Hydraulic pressure extends leg

• Release in pressure + single tensile muscle retracts leg

• Complex overall locomotion

• Two robotic legs (with 3-DoFs):

• Human leg: (> 7 major DoFs)• Further actuation at toes

• > 15 muscle groups, 8-complex joints

leg is extended using hydraulic pressure

Locomotion:

Legged

Variety of successful legs: Example

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• 3-DoF cockroach leg

Locomotion:

Legged

http://www.manoonpong.com/AMOSWD06.html

Leg DoFs needed to Move

• At least 2-DoFs needed• Lift

• Swing forward

• More common is adding 1-dof for adding complex maneuvers

• 4th is in recent walking robots at ankle

• In general: adding dof = increase maneuverability

• Range of terrains

• Different gaits

• Main disadvantage: Added energy, control, and mass

• And leg coordination / gait control

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2-types of gaits in a 4-legged

robot, static walking is

impossible:

Locomotion:

Legged

Possible gaits

• Gait: a sequence of lift and release events for the individual legs.

• For a mobile robot with k legs:

1. lift right leg;

2. lift left leg;

3. release right leg;

4. release left leg;

5. lift both legs together;

6. release both legs together.

• K=6:

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Locomotion:

Legged

Examples of walking robots: One-legged

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• No high-volume industrial application (legged), but important research

• 1-leg • Minimizes mass

• No leg coordination

• Maximizes advantage of legged motion (1 contact point vs. whole track)

So, suitable for the roughest terrain

Hopper running start cross a gap > its stride

Multilegged can’t run limited to gap = its reach

• Major challenge: balance• Not only static walk = impossible

• Static stability while stationary = impossible

• Active balance:1-Change centre of gravity, 2-Corrective forces

Locomotion:

Legged

Examples of walking robots: One-legged

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• Raibert hopper (well-known single legged hopping robot)

• Actuators: hydraulic (large off-board pump)

• Continuous corrections (body attitude, velocity)

• By adjusting leg angle

Locomotion:

Legged

Not very energy efficient

Examples of walking robots: One-legged

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• 2D single bow leg hopper• More energy efficient

• Hydraulic actuator bow leg

(85% of landing energy is returned, means:

Stable hopping with 15%)

• 1 battery set 20 minutes of hop

• controls velocity by changing the angle

of the leg to the body at the hip

• An important aspect in hopping robots:

Duality: mechanics vs. controls• Mechanical design can help simplify control

• Dynamic stability with more passivity

Locomotion:

Legged

The 2D single bow leg hopper from CMU

Video: Robots from MIT’s Leg Lab

• Past 10 years: many successful bipedal robots demonstrated:• Walking-run

• Jumping

• Up-down stairs

• Even aerial tricks

• In the commercial sector:• Honda

• Sony

• They both designed:• Servos for small power joints

• Great: power/weight (small & strong)

• Intelligent (with sensors, so compliant actuation)

Examples of walking robots: 2-legged

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Locomotion:

Legged

significant advances highly capable 2-leg robots

SonyHonda

• Result of research begun in 1997

• Objective: motion/ communication entertainment

(dancing & singing)

• 38 DOF

• 7 microphones fine sound localization

• Person recognition (image)

• Stereo map reconstruction

• Speech recognition (limited)

• For this goal, Sony spent considerable effort designing

a motion prototyping application system to enable engineers to

script dances in a straightforward manner

Examples of walking robots: 2-legged (Sony SDR-4X II)

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Locomotion:

Legged

NAO – biped robot video

• Long history Asimo P2

• Much larger than Sony SDR-4X

• Practical mobility in the human world of stairs

• The first robot that famously (biomimetic): stair up/down

• Goal: not entertainment, but human aids in society

• Height ~= humans operate in their world

(say, control light switches)

important feature (2-leg robots): anthropomorphic shape

• Can have same approximate dimensions as humans

• Makes them excellent vehicles for research in human-robot interaction

Examples of walking robots: 2-legged (Honda P2)

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Locomotion:

Legged

• WABIAN-2R developed at Waseda University in Japan• designed to emulate human motion (even to dance like a human)

• DOF= leg:6x2, foot:1x2(passive), waist:2, trunk:2, arm:7x2, hand:3x2,

Neck:3

• Spring flamingo of MIT:• Springs in series with leg actuators =

More elastic gait

• Combined with kneecaps

• Very biomimetic

• 2-leg robots:• can only be statically stable within

some limits

• must perform continuous

balance-correcting even when

standing still

Examples of walking robots: 2-legged

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Locomotion:

Legged

• Standing still = passively stable, walking remains challenging (CoG needs to be actively shifted during gait)

• Sony invested several $million on AIBO:

Examples of walking robots: 4-legged

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Locomotion:

Legged

Sony produced:• A new robot operating system that is near real-time

• New geared servomotors:

• Sufficiently high torque to support the robot

• Yet back drivable for safety

• A color vision system -> AIBO can chase a brightly

colored ball

• function for 1-hour -> recharging

• > 60,000 units sold in the first year

• ~ $1500

• 4-leg: the potential to serve as effective artifacts for research in human-robot interaction:• As a pet (might develop an emotional relationship)

• They can emulate learning and maturation (AIBO does)

Examples of walking robots: 4-legged (AIBO, artificial dog from Sony)

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Locomotion:

Legged

• Extremely popular for their static stability in walking

So, less control complexity

• In most cases, each leg has 3DOF:• hip flexion, knee flexion, & hip abduction

Examples of walking robots: 6-legged (hexapods)

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Locomotion:

Legged

Lauron II, a hexapod platform developed at

the University of Karlsruhe, GermanyPlustech developed the first application-

driven walking robot

• Genghis is a commercially available hobby robot• has six legs, each 2DOF provided by hobby servos

(hip flexion - hip abduction)

• Such robots has less maneuverability in rough

terrain but performs quite well on flat ground.

• Straightforward arrangement of servomotors,

straight legs -> easily built

• Insects (the most successful locomoting creatures

on earth), excel at traversing all forms of terrain

with 6-legs, even upside down.

• The gap of capability (insects-robots) is still huge• Not lack of DOF in robots

• Insects combine few active DOFs with passive structures (microscopic barbs, textured pads) -> grip strength

Examples of walking robots: 6-legged (hexapods)

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Locomotion:

Legged

Genghis, one of the most famous walking robots

from MIT, uses hobby servomotors as its actuators

Wheeled Mobile robots

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• Wheeled locomotion: the design space• Wheel design

• Wheel geometry

• Stability

• Maneuverability

• Controllability

• Wheeled locomotion: case studies• Synchro drive

• Omnidirectional drive (locomotion)

• with three spherical wheels

• with four Swedish wheels

• with four castor wheels and eight motors

• Tracked slip/skid locomotion

• Walking wheels

Locomotion:

Wheeled

Uranus

from CMU

Nomad X4000

Has 4 castor

Wheels all

-steered

-driven

Wheeled Mobile robots: Design space - wheel design

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• 4 basic wheel types (large effect on the overall kinematics)

(a) Standard wheel 2DOF; rotation around the (motorized) wheel axle

and the contact point

b) castor wheel: 2DOF; rotation around an offset steering joint

c) Swedish wheel: 3DOF; rotation around the (motorized) wheel axle,

around the rollers, and around the contact point

(d) Ball or spherical

Locomotion:

Wheeled

Highly directional

steering

Wheeled Mobile robots: Design space - wheel geometry

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Choice of wheel • Types

• Arrangement, or wheel geometry

• Why not common car configuration (Ackerman)?

Locomotion:

Wheeled

strongly linked affects:• Maneuverability

• Controllability

• Stability

Wheeled Mobile robots: Design space - wheel geometry

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Locomotion:

Wheeled

Wheeled Mobile robots: Design space - wheel geometry

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Locomotion:

Wheeled

Wheeled Mobile robots: Design space - Stability

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• Minimum # wheel for stability?• Surprisingly, 2 (CoM below axle)

• But wheel diameter = impractically large

• Dynamics (high enough torque) can also cause instability

• Conventionally, static (Not dynamic) stability requires

3-wheels• CoG be contained in the triangle of contacts

• Otherwise it needs controller to be stabilized

• Stability further improves by adding wheels• But we’ll need flexible suspension on uneven terrain

Locomotion:

Wheeled

Cye does vacuum and deliveries

Wheeled Mobile robots: Design space - Maneuverability

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• Maneuverability: Overall DoF that robot can manipulate:• Mobility

• Steerability

• Omnidirectional Robot?• Can move at any time in any direction on the ground plane (x,y)

• Regardless of robot’s orientation around it’s vertical axix

• requires wheels to move in more than just 1-direction

• So, usually employ powered Swedish (Mecanum) or

spherical wheels

Locomotion:

Wheeled

Wheeled Mobile robots: Design space - Maneuverability

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• Examples of robot direction based on wheels’ rotation:

Locomotion:

Wheeled

Uranus: uses four Swedish wheels to rotate and

translate independently and without constraints

Wheeled Mobile robots: Design space - Maneuverability

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• A disadvantage for Swedish/spherical wheels:• Limited ground clearance (mechanical limitations)

• A solution: 4-castor wheels:• All actively translated

• All actively steered -> truly omnidirectional (although robot moves with this steering)

• Other classes of robots are highly popular: • High maneuverability slightly inferior to Omnidirectional:

• Motion in any direction:• May require initial rotation

• If a circular robot with rotation axis at the centre, footprint also won’t change

• The simplest is 2-wheel differential drive

• 1-2 more contact points for improved stability

• Ackerman config. (lower maneuverability)

• Turning diameter > car

• Moving sideways very difficult

• advantage: its directionality ->

very good lateral stability in high-speed turns (popular)

Locomotion:

Wheeled

Wheeled Mobile robots: Design space - Controllability

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• Controllability vs. Maneuverability (inverse correlation)

• E.g., 4-castor wheel -> significant processing (desired rotational/translational velocities -> individual wheel commands)

• Omnidirectional designs greater DOF at the wheel (the Swedish wheel has a set of free rollers) -> accumulation of slippage ->

• reduce dead-reckoning accuracy

• increase the design complexity

• For specific direction of travel:

• Ackerman: just lock the steering

• 2-wheel diff. drive : Challenging for the 2 motors to have the same velocity profile

• Variations between wheels, motors, environmental differences

• Uranus: even more difficult

• Summary: no ideal configuration maximizes

Locomotion:

Wheeled

• Stability

• Maneuverability

• Controllability

-> Design based on: Application

Wheeled Mobile robots: Case studies

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• 1-Synchro drive:• Popular for indoor applications

• Only 2-motors

• Translation motor

• Steering motor

• No direct way of reorienting the chassis

• It drifts with time (uneven tire slippage)

• Rotational dead reckoning problem

• Can add extra motor for this purpose

• Dead reckoning: True omnidirectional < Synch. < Ackerman

• Closest wheel starts spinning first (single belt for translation)

Locomotion:

Wheeled

Omnidirectional, but orientation of chassis is not controllable

B21r: sold with such capability

Wheeled Mobile robots: Case studies

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• 2-Omnidirectional drive:• Complete maneuverability = high interest

• In any direction (x,y,θ) holonomic (Every DoF is controllable)

a) With 3 spherical wheels

• Suspended by 3 contact points (2 bearing, 1 by wheel connected to motor axle)

• Simple design, but limited to flat surfaces & small loads

b) With 4 Swedish wheels (or with 3 90o wheel because we have 3 DoF in the plane)

• One motor for each wheel

• Direction & relative speed of each motor omnidirectionality

• Even can simultaneously rotate around its vertical axis

• One application: Mobile manipulator (gross motion by robot chassis)

c) With 4 castor wheels & 8 motors

• Requires precise synchronization and coordination for

Precise motion (x,y,θ)

Locomotion:

Wheeled

XR4000 from

Nomadic

Wheeled Mobile robots: Case studies

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• 3-Tracked slip/skid locomotion:• Assumption in wheel configurations: wheels are not

allowed to skid

• Alternatively: reorient the robot by spinning wheels that

are facing the same direction

• at different speeds

• in opposite directions

• Example: army tank, Nanokhod

• Large ground contact patches better:

• maneuverability in loose terrains

• traction

• Disadvantage: changing orientation (=skidding turn)

• Most of the track must slide

• Exact centre of turn is difficult to predict

• Dead reckoning: inaccurate

• Power efficiency: good on loose train, bad otherwise

Locomotion:

Wheeled

Walking wheels

• Walking robots:• best maneuverability in rough terrain

• Inefficient on flat ground & need sophisticated control

• Hybrid solutions: combining• adaptability of legs

• efficiency of wheels

• Example:• Shrimp: 6 motorized wheels

• Front-back motors are steered

• 4 on the side help steering by

speed control

• Personal rover

• Actively shifts CoM

• By identifying the terrain

• Then moving the boom

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Shrimp, an all-terrain robot with

outstanding passive climbing abilities (EPFL)

Supplement

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Locomotion

Extra explanation – Mecanum Wheel

Figure 2 provides a top view of a (rectangular) vehicle featuring four Mecanum

wheels, along with its attached coordinate system (x,y), the origin of which is assumed to be the geometrical centre of the rectangle; the wheels are identifed by the numbers 1 : : : 4, starting from the right-bottom corner (i.e., from the

right-rear wheel of the vehicle) and proceeding in the counter-clockwise direction. The angular velocities w1:::4 are designed positive for translational motion in the forward direction (increasing y).

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Extra explanation – Mecanum Wheel

• The driving (motor) force (thrust) ~Fi acting on wheel iof the vehicle (chosen to be wheel 2), along with its decomposition into one force ( ~Fi;p) parallel to the rotational axis of the roller (which is in contact with the ground at that moment) and one in the transverse direction ( ~Fi;t), are shown in Fig. 3. The angle between the transverse direction and the rotational plane of the wheel is denoted as α [0,π ). (The quantity sin α is also known as the efficiency of the wheel'.) Since the rollers rotate freely around their axle, there is no traction along the transverse direction; therefore, the force ~Fi;t can safely be ignored when studying the motion of the vehicle. The relation between Fi;p

• and Fi (indicating the corresponding moduli of the two vectors) reads as:

• Fi;p = Fi sin α.

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The rollers shown are assumed to be those

corresponding to the lower part of the wheel,

part of which is in contact with the ground.

Extra explanation – Mecanum Wheel

• Finally, the only relevant force, Fi,p, may be decomposed into forces along the axes of the attached coordinate system (see Fig. 4). The geometry dictates that Fi,x = Fi,p cos α= Fi sin αcos α and Fi,y = Fi,p sin α = Fi sin2 α .

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The rollers shown are assumed to be those

corresponding to the lower part of the wheel,

part of which is in contact with the ground.

Control scheme for mobile robots

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Locomotion

Main bodies of knowledge associated

with mobile robotics