Trajectory Planning of Autonomous Underwater Vehicles Based on Gauss Pseudospectral Method

This paper aims to address the obstacle avoidance problem of autonomous underwater vehicles (AUVs) in complex environments by proposing a trajectory planning method based on the Gauss pseudospectral method (GPM). According to the kinematics and dynamics constraints, and the obstacle avoidance requirement in AUV navigation, a multi-constraint trajectory planning model is established. The model takes energy consumption and sailing time as optimization objectives. The optimal control problem is transformed into a nonlinear programming problem by the GPM. The trajectory satisfying the optimization objective can be obtained by solving the problem with a sequential quadratic programming (SQP) algorithm. For the optimization of calculation parameters, the cubic spline interpolation method is proposed to generate initial value. Finally, through comparison with the linear fitting method, the rapidity of the solution of the cubic spline interpolation method is verified. The simulation results show that the cubic spline interpolation method improves the operation performance by 49.35% compared with the linear fitting method, which verifies the effectiveness of the cubic spline interpolation method in solving the optimal control problem.