Guaranteed Tracking Controller for Wheeled Mobile Robot Based on Flatness and Interval Observer

Amine Abadi,Adnen El Amraoui,Nacim Ramdani,Hassen Mekki

doi:10.1109/cdc40024.2019.9029479

Abstract

This paper proposes a guaranteed tracking controller for a Wheeled Mobile Robot (WMR) based on the differential flatness theory and the interval observer. Using the flatness property, it is possible to transform the non linear WMR model into a canonical Brunovsky form, for which it is easier to create a state feedback controller. Since, in most real applications, the WMR is subjected to uncertainties such as slip, disturbance and noise, control algorithms must be modified to take into account those uncertainties. Therefore, based on the information of the upper and lower limits of the initial condition and all the uncertainties, an interval observer that generates an envelope enclosing every feasible state trajectory is developed. After that, based on the center of the obtained interval observer, a new control law is proposed to guarantee the tracking performance of the WMR despite the existence of un-measurable states and bounded uncertainties. The closed-loop stability of the system is proven analytically using the Lyapunov theorem. A lot of numerical simulation is realized in order to demonstrate the efficiency of the suggested guaranteed tracking control scheme.

Highlights

In the last decade, special attention has been paid to mobile robots in view of their particular structure, automatic programming and practical challenges
The differential flatness property introduced by Fliess [1] has proven to be a good tool to ameliorate the trajectory planning and to create tracking controllers for linear and nonlinear systems
A reference trajectory is generated for the Wheeled Mobile Robot (WMR) perm√itting its movement from the initial stat√e X(0) = [0, 0, 2, 45]T to the final state X(5) = [4, 7, 2, 45]T

Summary

INTRODUCTION

Special attention has been paid to mobile robots in view of their particular structure, automatic programming and practical challenges. With flatness, all the state and control inputs of the system can be written as a function of the flat outputs and their derivatives. This property allows us to eliminate the utilization of the complex integration process. By permitting an accurate linearization of the system’s dynamical model, it can be possible to avoid utilizing the linear models with limited validity in the controller design.

WHEELED-ROBOT MOBILE MODEL

FLATNESS-BASED TRACKING CONTROL

UNCERTAIN KINEMATIC MODEL

INTERVAL OBSERVER DESIGN

GUARANTEED TRACKING CONTROL

SIMULATION AND RESULTS

Simulation 1

Simulation 2

VIII. CONCLUSION