Gan Wenyang, Su Lixia, Chu Zhenzhong
Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China.
School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China.
Math Biosci Eng. 2023 May 8;20(7):11713-11731. doi: 10.3934/mbe.2023521.
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.
研究了一种基于高斯伪谱法（GPM）和粒子群优化算法（PSO）的快速优化方法，用于自主水下航行器（AUV）避障导航的轨迹优化。根据动态约束、边界约束和路径约束建立了多约束轨迹规划模型。利用高斯伪谱法将轨迹优化问题转化为非线性规划（NLP）问题，采用序列二次规划（SQP）算法求解。针对SQP算法对初始值的依赖性，提出了一种将PSO预规划与高斯伪谱法相结合的方法。通过拟合将预规划的轨迹点配置在高斯伪谱法的勒让德-高斯（LG）点上，作为SQP计算轨迹规划问题的初始值。经过仿真分析，使用预处理后的初始值可以加快最优解的收敛速度。与线性插值和三次样条插值相比，PSO预规划方法的计算效率提高了82.3%和88.6%，验证了PSO-GPM求解轨迹优化问题的有效性。
