基于自适应阈值伪谱法的空间机器人轨迹优化

Adaptive threshold pseudo-spectral method for space robot trajectory optimization

摘要:

为解决传统Radau伪谱法在轨迹优化求解效率与轨迹解可行性之间存在的矛盾,本文提出一种基于自适应阈值的分段升阶伪谱法,用于提升非线性优化问题的求解精度,加快收敛速度。该方法通过动态比较迭代过程中的误差矩阵极大值与标准时间步长,在误差超过自适应阈值的区间设置新分段点,并在误差小于偏差阈值的分段内增加配点数,这种策略对轨迹解的平滑/非平滑区间进行针对性优化,从而以较少的分段数和配点数达成轨迹规划目标。相比于传统Radau伪谱法,自适应分段升阶方法能够以较少迭代轮次收敛到期望结果,实现数值精度与求解效率的有效平衡。为验证算法性能,本研究基于自由飞行空间机器人非合作目标捕获场景进行了对比仿真实验。实验结果表明,本文提出的自适应分段升阶方法,在求解耗时和轨迹解的末端精度方面均优于对比方法,显示出更好的综合表现。

Abstract:

To address the trade-off between solution efficiency and trajectory feasibility in traditional Radau Pseudo-spectral Method (RPM) for trajectory optimization, this paper proposes an adaptive threshold-based segmented polynomial-degree elevation pseudo-spectral method (AT-RPM). This approach aims to enhance nonlinear optimization accuracy and accelerate convergence. By dynamically comparing the maximum value of the error matrix with a standard time step during iterative process, the method establishes new segment points in intervals where the error exceeds an adaptive threshold. Furthermore, the number of collocation points within segments is also increased when the error falls below a deviation threshold. This strategy selectively optimizes both smooth and non-smooth regions of the trajectory solution, thereby enabling achievement of trajectory planning goals with fewer segments and collocation points. Compared with the traditional Radau Pseudo-spectral Method, AT-RPM can converge to the desired result in fewer iteration rounds, effectively balancing numerical accuracy and solution efficiency. To validate performance, comparative simulation experiments have been conducted in a non-cooperative target capture scenario involving a free-flying space robot. The results indicate that the proposed method outperforms the existing approaches in both computation time and terminal accuracy, demonstrating superior overall performance.