Rigidity Based Time-Varying Formation Tracking Control for Autonomous Underwater Vehicles with Switching Topologies

This paper addresses the problem of time-varying formation tracking control problem of multiply autonomous underwater vehicles (AUVs) using switching graph topologies. Different from the previous work, the states of the followers form a predefined time-varying formation while tracking the state of the leader. We introduce distance-based control laws for the multi-AUV formation, using a single-integrator agent model, the control laws are only a function of the relative distance of AUVs in an infinitesimally and minimally rigid graph, and either the desired velocity of the formation or the target's relative position to the leader and absolute velocity. Then an algorithm to design the policy with switching undirected topologies is presented, according to practical requirements, the configuration of formation can be chosen as arbitrary shape and the corresponding convergence time is allowed to be pre-estimated or preset, where the team of AUVs can translate and rotate as a virtual rigid body in 2D, so the formation size and/or geometric shape can vary in time. Thirdly, Strict stability analysis indicates that the designed formation control law can make AUVs achieve the predefined time-varying formation. Finally, a numerical simulation example with six followers and one leader is given to demonstrate that the AUVs formation control based on the backstepping control with this new structural method is stable and convergent.