Adaptive Leader–Follower Formation Control of Underactuated Surface Vessels Under Asymmetric Range and Bearing Constraints

This paper deals with the problem of leader-follower formation control for a group of underactuated surface vessels with partially known control input functions. In the proposed scheme, the problem is formulated as an adaptive feedback control problem for aLine-Of-Sight (LOS) based formation configuration of a leader and a follower. To account for LOS and bearing angle time-varying constraints, asymmetric barrier Lyapunov functions are incorporated with the control design. Furthermore, in order to alleviate required velocity information on the leader, a reconstruction module is designed to estimate the vector velocity of this leader. This reconstruction is accomplished in finite time with zero error, which allows the injection of accurate estimation into the formation controller. The controller is then developed within the framework of the backstepping technique, with the parametric uncertainties and the unknown gains being estimated by a novel structure identifier. The overall closed-loop system, is proved to be semiglobally uniformly ultimately bounded by Lyapunov stability theory. Furthermore, we show under the proposed control scheme that the constraints requirement on the LOS range and bearing angle tracking errors are not violated during the formation process. Finally, the effectiveness and the robustness of the proposed strategy are exhibited through simulations.