Non Linear Control of Four Wheel Omnidirectional Mobile Robot: Modeling, Simulation and Real-Time Implementation

Transcription

1 Non Linear Control of Four Wheel Omnidirectional Mobile Robot: Modeling, Simulation and Real-Time Implementation eer Alakshendra Research Scholar Robotics Lab Dr Shital S.Chiddarwar Supervisor Robotics Lab Department of Mechanical Engineering India-44000

2 Contents Introduction Objective How Matlab/Simulink helped us? Mathematical Modelling Controller Design Optimization Simulation Results Real Time Implementation (RTI) Conclusions Summary

3 Wheeled mobile robots Non holonomic : Controllable D.O.F < Total D.OF Direction of motion is restricted Holonomic : Controllable D.O.F = Total D.OF Direction of motion is not restricted. The robot can move in any direction. 3

4 Four wheel omnidirectional mobile robot (FWOMR) Omni-directional wheel platform is a holonomic system having 3 DOF in horizontal plane. Mecanum Wheel Direction of motion Motor 4

5 Applications of FWOMR Omni-directional wheel chair Omni fork lifter Warehouse Omni move lifter Omni robot Tokomak building 5

6 Objective Development of mathematical model of Mecanum wheeled mobile robot. Solution of highly non linear equations in less computational time. Development of a simulation environment. Development of robust controller for trajectory tracking of mobile robot in presence of matched and unmatched uncertainties. Real time implementation of proposed approach for trajectory tracking. 6

7 Work Flow Modeling Controller Design Optimization Real-Time Testing 7

8 Challenges faced Solving second order non linear differential equation. Estimating control design parameters. Building a simulation environment. Feedback data collection. Real time implementation on hardware. Solution Simulink Simulink Design Optimization Simscape Multibody Kinect Support package Arduino Support Package Robotics System Toolbox 8

9 Modeling Tool Used Simscape Multibody Simulink Simulink Design Optimization Robotics System Toolbox Arduino Support Package Kinect Support package 9

10 Kinematic Equation z x r x w b v. / z y r MW y w a v. / z y r MW y w a v. / z x r x w b v. 3 / 3 z x r x w b v. / 4 4 z x r x w b v. / z y r MW y w a v. / z y r MW y w a v. / ) /( ) /( ) /( ) /( 4 b a b a b a b a R w v v z y x cos( ) sin( ) 0 ( ) sin( ) cos( ) R ( ) T T q q q r r z P x y R x y q y q x r x r y 0

11 Dynamic equation x( t) f ( x) g( x) u( t) ( t, u( t)) Symbolic math toolbox

12 Solution of dynamic equation Equation of motion can be solved by either solving the derived equation using Simulink or by using Simscape Multibody. In Simscape Multibody, CAD file of the robot is imported to Matlab in the form of masses, inertias, sensors, joints etc. It also provides a 3D environment to visualize the system dynamics. To check the system dynamics, input voltage can be kept variable and it can be manually changed using Slider block available in the Dashboard library. Alternatively, Signal builder block can be used to build the input signal. Simscape Multibody

13 Second order sliding mode control error as t 0 s( t) k e( t) k e( t) k e( t) s( t) p d i st ( ) 0 u u u total equivalent switching u ( k B ) ( k e( t) k e( t) equivalent d 34 i 3 p 3 k ( x ( t) Ax( t) d 3 3 Bx( t) ) s( t) ) 3 3 u s( t) k sat( s( t) ) switching d 3 sw 3 k d k 0 0 d 0 k 0 d 0 0 k d k k sw p k 0 0 p 0 k 0 p 0 0 k p3 k 0 0 sw 0 k 0 sw 0 0 k sw3 k 0 0 i k 0 k 0 i i 0 0 k i Lyapunov stability criterion is satisfied 0 3

14 Second order sliding mode control in simulink Dynamics Input/output and uncertainties Controller 4

15 Simulink Design Optimization has been used to estimate the controller design parameters 5

16 Simulation results for complicated trajectory 6

17 Open loop testing 7

18 Close loop testing (Robotics System Toolbox) Node Node Kinect Matlab/Simulink program ROS Node IMU Matlab/Simulink program Simulink ROS OR Kinect ROS package IMU ROS package ROS Node 8

19 Close loop testing (Robotics System Toolbox) Subscriber Controller Publisher 9

20 Results for eight type trajectory 0

21 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.

22 Summary of the work and advantages of using Matlab Summary Advantages of using Matlab Control Law Dynamic Equation Kinematic Equation Open loop test using Arduino MEGA ADK Estimation of control design parameters Closed loop test using camera and IMU. Model based design Implementation of control strategy Ability to solve non linear equations Parameter estimation Real time implementation Better understanding of kinematic and dynamic model Implementation of control strategy Ability to perform number of simulation experiments

23 THANK YOU Q & A? 3