Obstacle avoidance in multi-vehicle coordinated motion via stabilization of time-varying sets

In this paper, we review the recent results on stability and control for time-varying sets of nonlinear time-varying dynamical systems and utilize them for the problem of multi-vehicle coordinated motion in the context of obstacle avoidance where obstacles are approximated and enclosed by elliptic shapes. Specifically, we design distributed controllers for individual vehicles moving in a specified formation in the presence of such obstacles. The obstacle avoidance algorithm that we propose is based on transitional trajectories which are denned by a set of ordinary differential equations that exhibit a stable elliptical limit cycle. The control framework is implemented on the system of double integrators and is shown to globally exponentially stabilize moving formation of the agents in pursuit of a leader while ensuring obstacle avoidance.