Robust constrained formation tracking control of underactuated underwater vehicles (UUVs) fleet in three-dimensional space is a challenging but practical problem. To address this problem, this paper 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 "explosion of terms" 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.

翻译：三维空间中欠驱动水下无人潜航器编队的鲁棒约束编队跟踪控制是一个具有挑战性且实际意义的问题。为此，本文提出了一种新颖的基于一致性的最优协调协议及鲁棒控制器，采用分层架构。在顶层，引入球坐标变换以处理非完整约束，进而开发了一种分布式最优运动协调策略。该策略可实现水下无人潜航器编队的最优编队跟踪，并满足各项约束。为更好地实现生成的最优指令，同时应对欠驱动问题，下层控制回路设计了一种基于神经动力学的鲁棒反步控制器，该控制器尤其避免了传统反步控制器中出现的"项爆炸"问题，并提升了控制效能。通过建立整体水下无人潜航器编队系统的稳定性分析，确保了在未知扰动下所有水下无人潜航器状态一致最终有界。最后，通过广泛仿真对比验证了所推导的最优编队跟踪协议的有效性与优越性。