Synchronization Motion Tracking Control of Multiple Underactuated Ships With Collision Avoidance

This paper presents a constructive method to design distributed controllers that force a group of N underactuated ships under sea loads to perform a desired synchronization motion tracking task and guarantee no collisions between the ships. First, an observer is designed to globally exponentially estimate the sea loads. Then, the ship dynamics is transformed to an almost spherical form. Smooth or p-times differentiable step functions are next introduced to ensure that the collision avoidance is only active when the ships are in their collision detection zones. For each ship, a dynamical variable is introduced to deal with relaxation of the reference path generation and difficulties caused by underactuation. The control design is based on the above developments, and Lyapunov and backstepping methods. The effectiveness of the proposed results is illustrated through simulations.