This paper presents a method for formation control of marine surface craft inspired by Lagrangian mechanics. The desired formation configuration and response of the marine surface craft are given as a set of constraints in analytical mechanics. Thus, constraints forces arise and feedback from the constraint functions keeps the formation assembled. Since the constraint functions are designed for a desired effect, the forces can be interpreted as control laws. Examples of constraint functions that maintain a formation are presented. Furthermore, the same approach has been applied with no major modification to position control proposes for a single vessel. An extension to underactuated vessles is given. Simulations with nonlinear models of tugboats illustrate the proposed method versatility and its robustness with respect to environmental disturbances and time delays.
Ieee Journal of Oceanic Engineering, 2006, Vol 31, Issue 4, p. 922-934