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Practical stabilization of a mobile robot using saturated control

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Abstract

CDC2006_Evers.dvi Practical stabilization of a mobile robot using saturated control Willem-Jan Evers and Henk Nijmeijer Department of Mechanical Engineering Technische Universiteit Eindhoven Eindhoven, The Netherlands Email: [email protected], [email protected] Abstract— This paper presents a new, practically stabilizing, hybrid control algorithm for a unicycle type of mobile robot. The design of this algorithm is based on a set of performance requirements and it is tested numerically and experimentally. The resulting controller is compared to three other recently developed controllers, considering (a limited amount of) mea- surement and input time-delays, model deviations, parameter uncertainty and measurement noise. I. INTRODUCTION In recent years, a lot of interest has been devoted to the (point) stabilization of dynamical systems with nonholo- nomic constraints. The main difficulty lies, as pointed out by Brockett [1], in the fact that the problem cannot be solved by continuous differentiable, time invariant, feedback laws. As a result, a wide range of solutions has been presented over the years. In [6] an extensive survey is given of the developments in this field. The solutions are divided into open-loop control (see for example: [2], [5] and [16]) and closed-loop control (see for example: [3], [4], [7], [10], [11], [14] and [15]). Furthermore, they are generally specified on the dynamics of a wheeled mobile robot or its chained form equivalent. Despite this wide range of solutions though, it remains unclear which one to use, on an experimental setup, for optimal results. Even more, most of the given solutions have only been tested numerically. The general focus of these papers lies on proving the obtained type of stability: exponential-, asymptotic-, or in some cases practical stability. However, the type of convergence is a mathematical issue that may have little importance on a practical setup. Or to quote [8], a slow asymptotic convergence rate does not mean that the sys

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