Multi Lyapunov Function Theorem Applied to a Mobile Robot Tracking a Trajectory in Presence of Obstacles

In this paper, a reactive control architecture based on hybrid systems (continuous/discrete) is used to control a unicycle mobile robot tracking a given trajectory while avoiding obstacles. The main motivation of using hybrid systems is the possibility to define the overall control scheme as a combination of several elementary controllers (trajectory tracking, obstacle avoidance) that stability can be easily proved. However, there is a serious risk of oscillatory switching or even instability caused by random switch between these two elementary controllers. The contribution of this paper is to use the multiple Lyapunov functions (MLF) theorem to prove the global stability of a trajectory tracking task in presence of obstacles. To satisfy the MLF conditions, we propose to introduce a third controller in the architecture of control: the go-to-goal controller. Its role is to satisfy the second and the most difficult condition of MLF in a finite time. The approach is validated by numerical simulation.