Formation Control in the scope of the MORPH project. Part I: Theoretical Foundations★ ★

We address the subject of formation control of underwater vehicles, using either inter-vehicle relative position measurements or range-only measurements. The work is motivated by the MORPH project, aiming at the use of formations of vehicles with complementary capabilities to map the underwater environment in complex 3D environments. The main problem studied is that of driving a vehicle (follower) to an appropriately defined position with respect to another vehicle (leader), which moves along a trajectory that is unknown to the follower. This control task is divided into two steps. Firstly, a trajectory-tracking controller is designed so that a follower vehicle can track a specified virtual target. Secondly, we design path-generators that yield the position and velocity of the virtual target to be tracked, for both the relative position measurements and the range-only measurements scenarios. These path-generation strategies take into account desirable formation behaviour and typical maneuver geometries. Applications to the MORPH project are presented. Finally, results of simulations are shown.