3D hybrid formation control of an underwater robot swarm: Switching topologies, unmeasurable velocities, and system constraints

This paper addresses formation control of underactuated autonomous underwater vehicles in three-dimensional space, using a hybrid protocol that combines aspects of centralized and decentralized control with constraints that are particular to underwater vehicles, including switching topologies, unmeasurable velocities, and system constraints. Using a distributed leader–follower model, the hybrid formation protocol does not require velocity sensing, access to global information, or static and connected topologies. To handle switching jointly connected networks—that is, to tolerate temporary disconnections—a distributed observer is designed for followers to cooperatively estimate leader states using local measurements and local interactions. On this basis, a compound formation control strategy is proposed to achieve geometric convergence. Firstly, cascaded extended state observers are developed to recover the unmeasurable velocities and unknown dynamic uncertainties induced by internal model uncertainty and external disturbances. Secondly, an improved three-dimensional line-of-sight guidance law at the kinematic level is used to address the underactuated configuration and the nonzero attack and sideslip angles. Thirdly, to overcome potential instability as a result of system constraints, including velocity constraints and input saturations, two adaptive compensators in the dynamic controller are used to address the negative effects of truncation. Using the proposed approach, the estimation errors and formation tracking errors are proved to be uniformly and ultimately bounded. Additionally, the numerical simulation results verify the performance of the approach and demonstrate improvement over both distributed and centralized state-of-the-art approaches.