Non-collision coordination for surface vessels with elliptical shape

In this paper, we address the problem of cooperation and collision avoidance for multiple surface vessels with disturbances. The surface vessels are regarded as elliptical agents with nonlinear dynamics. We design control laws that guarantee cooperation as well as collision-free maneuvers. We show, using a two-step proof, that the avoidance part of the control laws guarantees safety of the agents independently of the coordinating part. Then, we establish an ultimate bound on the avoidance term. The obtained theoretical results are illustrated through numerical examples.