Lyapunov Stability of a Nonholonomic Car-like Robotic System

Abstract

This paper shows how the Lyapunov method can be used to generate continuous time-invariant control laws that, to some extent, simultaneously solve the multi-task problem of navigation, steering, and point and posture stabilizations of nonholonomic car-like mobile robots. Even though the proposed method does not guarantee asymptotic stability, it provides a starting point for looking at the difficult problem of posture stability - essentially the problem of parking a car-like vehicle - without the use of discontinuous or time-varying control laws, which are currently the only laws capable of circumventing the well-known Brockett Theorem on the stabilization of nonholonomic systems and providing complete solutions to point and posture stabilities .