Robust formation control of marine craft using Lagrange multipliers

This paper presents a formation modelling scheme based on a set of inter-body constraint functions and Lagrangian multipliers. Formation control for a °eet of marine craft is achieved by stabilizing the auxiliary constraints such that the desired formation con¯guration appears. In the proposed framework we develop robust control laws for marine surface vessels to counteract unknown, slowly varying, environmental disturbances and measurement noise. Robustness with respect to time-delays in the communication channels are addressed by linearizing the system. Simulations of tugboats subject to environmental loads, measurement noise, and communication delays verify the theoretical results. Some future research directions and open problems are also discussed.