Lyapunov Global Stability for a Reactive Mobile Robot Navigation in Presence of Obstacles

This paper deals with the navigation of a mobile robot in unknown environment. The robot has to reach a final target while avoiding obstacles. It is proposed to break the task complexity by dividing it into a set of basic tasks: Attraction to a target and obstacle avoidance. Each basic task is accomplished through the corresponding elementary controller. The activation of one controller for another is done according to the priority task. To ensure the overall stability of the control system, especially at the switch moments, properties of hybrid systems are used. Hybrid systems allow switching between continuous states in presence of discrete events. In this paper, it is proposed to act on the gain of the proposed control law. The aim is to ensure the convergence of a common Lyapunov function to all the controllers. This ensures the stability of the overall control. Simulation results confirm the theoretical study.