Backstepping-based direct adaptive fuzzy formation control of uncertain mobile robots

The Leader/Follower formation control of mobile robots with uncertain dynamical models is investigated in this paper and adaptive shape tracking and trajectory tracking controllers are developed for the follower and leader, respectively. Firstly, a kinematic shape tracking controller is presented for the follower based on the formation equation, then the shape tracking error equation is derived with backstepping technology and a direct adaptive dynamical shape tracking controller is constructed by using fuzzy systems (FSs) to approximate the uncertainties. Furthermore, an adaptive trajectory tracking controller is also presented for the leader. It is proved that both shape tracking errors of the follower and adaptive parameters of the FSs are uniformly ultimately bounded (UUB), while the tracking error of the leader tends to zero asymptotically. Numerical simulations demonstrate the effectiveness of the proposed control strategies.