Nonlinear sliding mode formation control for underactuated surface vessels

A sliding mode control law of formation control for multiple underactuated surface vessels is proposed. The three degrees of freedom dynamics model is considered. Since the sway axis is not directly actuated, the vessels are underactuated. The formation model is obtained based on the leader-following approach. The controller is designed by using Lyapunov´s direct method and sliding mode control technique. In the dynamics design, the first-order surface in terms of the surge motion tracking errors and the second-order surface in terms of sway motion tracking errors are introduced. The stability analysis of the sliding mode control law is taken based on Lyapunov theory. Numerical simulations are provided to validate the effectiveness of the proposed formation controller for underactuated surface vessels.