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针对非线性强非凸的滑翔飞行器轨迹规划问题，提出了一种高度定制化的序列凸优化方法。首先，分析了经典序列凸优化方法及用于求解凸子问题的二次锥规划内点法的迭代流程，评估了各关键步骤的计算效率；其次，根据序列凸优化相邻迭代的解间距，提出了一种限制内部迭代次数的改进二次锥规划内点法；然后，解析了稀疏对称矩阵的存储性质和LDLT分解过程，结合二阶锥规划中KKT矩阵的非零结构，实现了KKT矩阵的快速LDLT分解；最后，在滑翔飞行器轨迹规划仿真中，通过参数优化实现最小化内部迭代次数，并结合快速LDLT分解方法完成轨迹规划的蒙特卡洛仿真。结果表明：所提算法在保持求解精度的同时，计算效率上具有显著优势。
Abstract：A highly customized sequential convex optimization method is proposed for the nonlinear strongly nonconvex gliding vehicle trajectory planning problem. Firstly, the classical sequential convex optimization approach is analyzed, as well as the iterative process of the second-order cone programming(SOCP) interior-point method used to solve the convex subproblems, and the computational efficiency of each key step is evaluated. Secondly, an improved second-order cone programming interior point method limiting the number of internal iterations is proposed based on the solution spacing of adjacent iterations of the sequence convex optimization. Then, the storage properties of sparse symmetric matrices and the LDLT decomposition process are analyzed. Then, a fast LDLT decomposition method is developed by exploiting the sparsity pattern of the KKT matrix in SOCP. Finally, parameter optimization is employed to minimize internal iterations, and Monte Carlo simulations are conducted for glider trajectory planning using the proposed fast LDLT decomposition. The results show that the proposed algorithm has significant advantages in computational efficiency while maintaining the solution accuracy.
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基本信息:
DOI：10.13645/j.cnki.f.d.20250918.004
中图分类号:V249.1;V448.2
引用信息:
[1]徐梓淇,李文博,程林,等.基于定制化序列凸优化的滑翔飞行器快速轨迹规划[J].飞行力学,2025,43(06):8-13+21.DOI:10.13645/j.cnki.f.d.20250918.004.