non linear control of four wheel omnidirectional mobile robot: modeling, simulation ... · non...

Non Linear Control of Four Wheel Omnidirectional Mobile Robot:

Modeling, Simulation and Real-Time Implementation

Department of Mechanical EngineeringVisvesvaraya National Institute of Technology, Nagpur

India-440010

Veer AlakshendraResearch ScholarRobotics Lab

Dr Shital S.ChiddarwarSupervisorRobotics Lab

Contents

• Introduction

• Objective

• How Matlab/Simulink helped us?

• Mathematical Modelling

• Controller Design

• Optimization

• Simulation Results

• Real Time Implementation (RTI)

• Conclusions

• Summary

2Visvesvaraya National Institute of Technology, Nagpur

3

Wheeled mobile robots

Non holonomic : Controllable D.O.F < Total D.OF

Holonomic : Controllable D.O.F = Total D.OF

Visvesvaraya National Institute of Technology, Nagpur

Direction of motion is restricted

Direction of motion is not restricted. The robot can move in any direction.

1

2

Introduction Objective How Matlab helped us Mathematical Modelling Controller Design Optimization Simulation Results RTI

Four wheel omnidirectional mobile robot (FWOMR)

• Omni-directional wheel platform is a holonomic systemhaving 3 DOF in horizontal plane.

Motor

Direction of

motion

Mecanum Wheel



Applications of FWOMR

Omni-directional wheel chair Omni fork lifter

Omni move lifter Omni robot


Warehouse

Tokomak building



Objective

Development of mathematical model ofMecanum wheeled mobile robot.Solution of highly non linear equations inless computational time.Development of a simulation environment.Development of robust controller fortrajectory tracking of mobile robot inpresence of matched and unmatcheduncertainties.Real time implementation of proposedapproach for trajectory tracking.


7

Work Flow

Modeling

Controller Design

Optimization

Real-Time Testing



Challenges faced


Solution

Solving second order non linear differential equation.Estimating control design parameters.Building a simulation environment.Feedback data collection.Real time implementation on hardware.

SimscapeMultibody

Simulink

Simulink Design Optimization

Kinect Support package

ArduinoSupport Package

Robotics System Toolbox


9

Modeling Tool Used


SimulinkSimscape Multibody

Simulink Design Optimization

Kinect Support package

Arduino Support Package

Robotics System Toolbox


Kinematic Equation

zxrx wbvVV .2/22

zyrMWy wavVVV .2/111


zxrx wbvVV .2/33 zxrx wbvVV .2/44

zxrx wbvVV .2/11



3

3

2

1

)/(1)/(1)/(1)/(1

1111

1111

4

babababa

R

w

v

v

z

y

x cos( ) sin( ) 0

( ) sin( ) cos( ) 0

0 0 1

R

( )T T

q q q r r zP x y R x y

qy

qx

rx

ry



11

Dynamic equation


))(,()()()()( tuttuxgxftx

Symbolic math toolbox


12

Solution of dynamic equation

Visvesvaraya National Institute of Technology, NagpurVisvesvaraya National Institute of Technology, Nagpur

Simscape Multibody

Equation of motion can be solved by either solving the derivedequation using Simulink or by using Simscape Multibody.

In Simscape Multibody , CAD file of the robot is imported toMatlab in the form of masses, inertias, sensors, joints etc. It alsoprovides a 3D environment to visualize the system dynamics.

To check the system dynamics, input voltage can be kept variableand it can be manually changed using Slider block available inthe Dashboard library.

Alternatively, Signal builder block can be used to build the inputsignal.


Second order sliding mode control0error as t

( ) 0s t

( ) ( ) ( ) ( ) ( )p d i

s t k e t k e t k e t s t

total equivalent switchingu u u

1

3 4 3 1 3 1

3 1 3 1

3 1 3 1

3 1 3 1

( ) ( ( ) ( )

( ( ) ( )

( ) ) ( ) )

( ) ( ( ) )

equivalent d i p

d d

switching sw

u k B k e t k e t

k x t Ax t

Bx t s t

u s t k sat s t

1

2

3

0 0

0 0

0 0

d

d d

d

k

k k

k

1

2

3

0 0

0 0

0 0

p

p p

p

k

k k

k

1

2

3

0 0

0 0

0 0

i

i i

i

k

k k

k

1

2

3

0 0

0 0

0 0

1

2

3

0 0

0 0

0 0

sw

sw sw

sw

k

k k

k

1

2

3

0 0

0 0

0 0

Lyapunov stability

criterion is satisfied

0V




Second order sliding mode control in simulinkDynamics

ControllerInput/output and uncertainties



Simulink Design Optimization has been used to estimate the controller

design parameters



Simulation results for complicated trajectoryIntroduction Objective How Matlab helped us Mathematical Modelling Controller Design Optimization Simulation Results RTI

17

Open loop testing



18

Simulink

IMU ROS package

Kinect ROS package

IMU Matlab/Simulink

program

Kinect Matlab/Simulink

program

ROS

ROS

OR

ROS

Node Node

Node

Node

Close loop testing (Robotics System Toolbox)



19

Subscriber PublisherController

Close loop testing (Robotics System Toolbox)



20

Results for eight type trajectory



Conclusions

• Solution of non linear dynamic equation including orientation of mobile robot.

• Successful tracking of desired trajectory in presence of matched and unmatched uncertainties.

• Smooth and chattering free control input.

• Successful real time implementation.


Summary of the work and advantages of using Matlab


Kinematic Equation

Dynamic Equation

Control Law

Estimation of control design parameters

Open loop test using Arduino MEGA ADK

Closed loop test using camera and IMU. Better

understanding of kinematic and dynamic model

Implementation of control strategy

Ability to perform number of simulation

experiments

Ability to solve non linear equations

Parameter estimation

Model based design

Implementation of control strategy

Real time implementation

Summary Advantages of using Matlab

THANK YOU


Q & A?

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