Adaptive Leader–Follower Formation Control of Underactuated Surface Vehicles With Guaranteed Performance

This article studies the formation tracking control problem for a group of underactuated surface vehicles with guaranteed transient properties, including connectivity maintenance, collision avoidance, and tracking performance specifications. The formation is within the leader–follower control framework, in which every follower is controlled to track its leader and maintain a desired relative distance and bearing angle with respect to its leader such that the prescribed formation geometry is achieved based on local sensing capability. The onboard sensor systems are of limited range and angle of view, thus defining a cone of detectable region for every follower. Each follower can detect its leader, if and only if the relative distance and bearing angle keep always inside the predefined detectable region such that the connectivity between the follower and its leader is maintained over time. In addition to the consideration of connectivity maintenance, no collision between the follower and its leader is also considered. A transverse function control approach is introduced to overcome the difficulties caused by the off-diagonal system matrix and underactuation. The barrier Lyapunov function and adaptive backstepping procedure are incorporated into the formation control design to achieve the boundedness of the closed-loop systems with guaranteed transient performance. Collision avoidance and connectivity maintenance between every follower and its leader are also proven mathematically. Simulation studies are performed to show the effectiveness of the proposed control design technique.