A PSO-enhanced Gauss pseudospectral method to solve trajectory planning for autonomous underwater vehicles

Wenyang Gan; Lixia Su; Zhenzhong Chu; Wenyang Gan; Lixia Su; Zhenzhong Chu

doi:10.3934/mbe.2023521

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 11713-11731. doi: 10.3934/mbe.2023521

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A PSO-enhanced Gauss pseudospectral method to solve trajectory planning for autonomous underwater vehicles

1.
Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China
2.
School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

Received: 05 March 2023 Revised: 05 April 2023 Accepted: 11 April 2023 Published: 08 May 2023

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.
- autonomous underwater vehicles,
- Gauss pseudospectral method,
- particle swarm optimization,
- trajectory optimization,
- optimal control
Citation: Wenyang Gan, Lixia Su, Zhenzhong Chu. A PSO-enhanced Gauss pseudospectral method to solve trajectory planning for autonomous underwater vehicles[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 11713-11731. doi: 10.3934/mbe.2023521

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Abstract

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.

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