A fast optimization method based on the Gauss pseudospectral method (GPM) and particle swarm optimization (PSO) is studied for trajectory optimization of obstacle-avoidance navigation of autonomous underwater vehicles (AUVs). A multi-constraint trajectory planning model is established according to the dynamic constraints, boundary constraints, and path constraints. The trajectory optimization problem is converted into a non-linear programming (NLP) problem by means of the GPM, which is solved by the sequential quadratic programming (SQP) algorithm. Aiming at the initial values dependence of the SQP algorithm, a method combining PSO pre-planning with the GPM is proposed. The pre-planned trajectory points are configured on the Legendre-Gauss (LG) points of the GPM by fitting as the initial values for the SQP calculated trajectory planning problem. After simulation analysis, the convergence speed of the optimal solution can be accelerated by using the pretreated initial values. Compared to the linear interpolation and the cubic spline interpolation, the PSO pre-planning method improves computational efficiency by 82.3% and 88.6%, which verifies the effectiveness of the PSO-GPM to solve the trajectory optimization problem.
Keywords: Gauss pseudospectral method; autonomous underwater vehicles; optimal control; particle swarm optimization; trajectory optimization.