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Robust constrained formation tracking control of underactuated underwater vehicles (UUVs) fleet in 3-D space is a challenging but practical problem. To address this problem, this article develops a novel consensus-based optimal coordination protocol and a robust controller, which adopts a hierarchical architecture. On the top layer, the spherical coordinate transform is introduced to tackle the nonholonomic constraint, and then a distributed optimal motion coordination strategy is developed. As a result, the optimal formation tracking of UUVs fleet can be achieved, and the constraints are fulfilled. To realize the generated optimal commands better and, meanwhile, deal with the underactuation, at the lower-level control loop a neurodynamics-based robust backstepping controller is designed, and in particular, the issue of &#x201C;explosion of terms&#x201D; appearing in conventional backstepping-based controllers is avoided and control activities are improved. The stability of the overall UUVs formation system is established to ensure that all the states of the UUVs are uniformly ultimately bounded in the presence of unknown disturbances. Finally, extensive simulation comparisons are made to illustrate the superiority and effectiveness of the derived optimal formation tracking protocol.

Distributed Neurodynamics-Based Backstepping Optimal Control for Robust Constrained Consensus of Underactuated Underwater Vehicles Fleet