Distributed Kinematic Guidance Law for Containment Maneuvering of Underactuated Autonomous Surface Vehicles

This paper presents a distributed kinematic guidance law for containment maneuvering of a fleet of underactuated autonomous surface vehicles guided by multiple virtual leaders. The communication graph among virtual leaders is undirected. The communication graph among followers is directed, and there exists a directed path from each virtual leader to each follower. The information flow between the leader and the follower who has access to the leader is undirected. The distributed kinematic guidance law is developed on the basis of a constant bearing guidance principle and a containment maneuvering scheme. Then, two kinds of path update laws are presented based on the containment maneuvering error. By using the proposed distributed guidance law, the underactuated marine vehicles are able to track a convex hull spanned by multiple virtual leaders moving along parameterized paths. Compared with existing results, a key feature of the proposed distributed guidance law is that it can be applied to underactuated surface vehicles. Finally, the globally uniformly asymptotically stable and locally uniformly exponentially stable of the closed-loop system is proven by resorting to Lyapunov theory and graph theory.