Cooperative trajectory planning and trajectory tracking control for multiple surface vessels system

In this paper, we investigate the cooperative trajectory planning and trajectory tracking control for multiple surface vessels system. For the cooperative trajectory planning issue of the outer-loop kinematic model, we establish the states/control constraints model, the cooperation constraints model and cost function model. The cooperative trajectory planning issue is transformed into a nonlinear multi-constrained optimal control problem with individual constraints and cooperative constraints, where the hp-adaptive pseudospectral method is introduced to solve the optimal control problem. To achieve the optimal trajectory tracking, the small perturbation linearization and the LQR technique are utilized to obtain the practical closed-loop controller. For the inner-loop dynamic model, the attitude controller is designed to track the outer-loop command signal. Finally, we give a simulation example, and the results show that the cooperative trajectory can be obtained and the optimal trajectory tracking can be achieved.