Distributed Formation Control of Second-order System with Input Saturation and Obstacle Avoidance

This paper studies the formation control of second-order systems with obstacle avoidance. The control input is subject to a priori saturation constraint. Two distributed for-mation protocols are proposed. The first one considers the issue of formation with a group reference velocity under undirected graphs. The second one deals with the case that only a subset of systems have access to the leader's information under directed graphs, and the upper bound of the protocol is independent of the number of its neighbors. Explicit Lyapunov functions are constructed to prove the formation properties of the resultant closed-loop system. An algorithm based on the improved artificial potential field is developed to avoid obstacles in the formation process. Numerical simulations are presented to illustrate the effectiveness of the theoretic results.