Coordinated Path Following Control of Multiple Vehicles subject to Bidirectional Communication Constraints

The paper addresses the problem of making a set of vehicles follow a a set of given spatial paths at required speeds, while ensuring that they reach and maintain a desired formation pattern. Problems of this kind arise in a number of practical applications involving ground and underwater robots. The paper summarizes and brings together in a unified framework previous results obtained by the authors for wheeled robots and fully actuated underwater vehicles. The decentralized solution proposed does not require the concept of a leader and applies to a very general class of paths. Furthermore, it addresses explicitly the dynamics of the vehicles and the constraints imposed by the inter-vehicle bi-directional communications network. The theoretical machinery used brings together Lyapunov-based techniques and graph theory. With the set-up proposed, path following (in space) and inter-vehicle coordination (in time) can be viewed as essentially decoupled. Path following for each vehicle is formulated in terms of driving a conveniently defined generalized error vector to zero; vehicle coordination is achieved by adjusting the speed of each vehicle along its particular path, based on information on the position and speed of a number of neighboring vehicles, as determined by the communications topology adopted. The paper presents the problem formulation and summarizes its solution. Simulations with dynamics models of a wheeled robot and an underwater vehicle illustrate the efficacy of the solution proposed.