This paper presents a comparative study of six common pseudospectral (PS) methods for solving optimal spacecraft attitude control problems. The problems of minimum time, minimum control effort, and the linear combination thereof are considered here, for a rest-to-rest spacecraft slew maneuver. In this study, three traditional PS methods (Gauss, Legendre, and Chebyshev) and three variations of the novel Birkhoff PS method (Legendre–Gauss, Legendre–Gauss–Lobatto, and Chebyshev–Gauss–Lobatto) are used. The Wilcoxon rank sum test is used to perform statistical analysis to compare results between traditional and Birkhoff PS results. Accuracy, computational efficiency, and robustness to initial conditions are used as performance metrics for each PS method. The results show that for all three optimal control problems, the Birkhoff Legendre–Gauss method is more accurate than the traditional Gauss PS method. Furthermore, the results show that the Birkhoff variants could in some cases find the minimum cost using fewer iterations compared with traditional PS methods. The Birkhoff PS methods also are less susceptible to initial guesses for solutions that could cause the results to reach infeasible points or become trapped in local minimums.

本文介绍了解决航天器最优姿态控制问题的六种常见伪谱 (PS) 方法的比较研究。对于静止到静止的航天器回转机动，这里考虑了最短时间、最小控制工作及其线性组合的问题。在本研究中，使用了三种传统的 PS 方法（Gauss、Legendre 和 Chebyshev）和新型 Birkhoff PS 方法的三种变体（Legendre-Gauss、Legendre-Gauss-Lobatto 和 Chebyshev-Gauss-Lobatto）。Wilcoxon 秩和检验用于执行统计分析以比较传统和 Birkhoff PS 结果之间的结果。准确性、计算效率和对初始条件的鲁棒性被用作每种 PS 方法的性能指标。结果表明，对于所有三个最优控制问题，Birkhoff Legendre-Gauss 方法比传统的 Gauss PS 方法更准确。此外，结果表明，与传统 PS 方法相比，Birkhoff 变体在某些情况下可以使用更少的迭代找到最低成本。Birkhoff PS 方法也不太容易受到初始猜测解的影响，这可能导致结果达到不可行点或陷入局部最小值。