Adaptive PID formation control of nonholonomic robots without leaderʹs velocity information

This paper proposes an adaptive proportional integral derivative (PID) algorithm to solve a formation control problem in the leader–follower framework where the leader robotʹs velocities are unknown for the follower robots. The main idea is first to design some proper ideal control law for the formation system to obtain a required performance, and then to propose the adaptive PID methodology to approach the ideal controller. As a result, the formation is achieved with much more enhanced robust formation performance. The stability of the closed-loop system is theoretically proved by Lyapunov method. Both numerical simulations and physical vehicle experiments are presented to verify the effectiveness of the proposed adaptive PID algorithm.