基于自适应阈值伪谱法的空间机器人轨迹优化

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.