Adaptive practical leader-following formation control of multiple nonholonomic wheeled mobile robots

This article investigates the leader-following formation control of multiple uncertain nonholonomic wheeled mobile robots. The leader trajectory can be any sufficiently smooth signal, either feasible or nonfeasible. This includes but not limited to a fixed point, a trimming trajectory, and the one that does not satisfy the nonholonomic constraint as robots in question do. To compensate for the effects that only a subset of follower robots has connected to the leader, we develop a distributed observer to estimate the leader's position and velocities. Using leader's estimated states, we convert formation errors into an augmented system with external oscillator states, which introduce an additional control variable and overcome the difficulties caused by underactuation. Subsequently, an adaptive tracking control law dealing with model uncertainties and stabilizing the augmented system is proposed, ensuring that formation errors are globally uniformly ultimately convergent to arbitrarily small balls near the origin. Simulation results are performed to validate the proposed control design.