Coordinated path-following control of multiple underactuated autonomous vehicles in the presence of communication failures

This paper addresses the problem of steering a group of underactuated autonomous vehicles along given spatial paths, while holding a desired inter-vehicle formation pattern. For a general class of vehicles moving in either two or three-dimensional space, we show how Lyapunov-based techniques and graph theory can be brought together to yield a decentralized control structure where the dynamics of the cooperating vehicles and the constraints imposed by the topology of the inter-vehicle communications network are explicitly taken into account. Path-following for each vehicle amounts to reducing an appropriately defined geometric error to a small neighborhood of the origin. Vehicle coordination is achieved by adjusting the speed of each vehicle along its path according to information on the positions of a subset of the other vehicles, as determined by the communications topology adopted. The system obtained by putting together the path-following and vehicle coordination strategies adopted takes a cascade form, where the former subsystem is input-to-state stable (ISS) with the error variables of the latter as inputs. Convergence and stability of the overall system are proved formally. The results are also extended to solve the problem of temporary communication failures. Using the concept of "brief instabilities" we show that for a given maximum failure rate, the coordinated path following system is stable and the errors converge to a small neighborhood of the origin. We illustrate our design procedure for underwater vehicles moving in three-dimensional space. Simulations results are presented and discussed