  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.
