Abstract To observe multiple asteroids in a short time, the time-optimal reorientation is investigated here for the rest-to-rest reorientation of a generic rigid spacecraft. First, the problem is formulated and solved using the hp-adaptive pseudospectral method. It is found that there exist not merely bang-bang but also singular solutions for the problem. Then, the bang-bang and singular solutions are discussed by various cases. The results reveal that the optimal solution is essentially a balance between the larger torque, the shorter angular path and the less moment of inertia. For bang-bang solutions, the total number of switches varies with the reorientation angle and the moment of inertia. The number of switches is usually 5 or 6 and does not exceed 8. For singular solutions, either one and two controls singular are possible. The singular optimal solution is probably optimal for the slender rod-like spacecraft. Finally, an analytical estimation method is proposed for determining the range of the optimal time. The results of the simulations indicate that the proposed method is real-time and highly accurate. All formulas of this paper are derived in canonical units and therefore apply to any rigid spacecraft.

中文翻译：

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用于观测多颗小行星的时间最优航天器重新定向

摘要 为了在短时间内观测多颗小行星，本文研究了通用刚性航天器的静止到静止重定向的时间最优重定向。首先，使用 hp 自适应伪谱方法来制定和解决问题。发现该问题不仅存在bang-bang，而且存在单一解决方案。然后，通过各种案例讨论了 bang-bang 和奇异解。结果表明，最佳解决方案本质上是在更大的扭矩、更短的角路径和更小的转动惯量之间取得平衡。对于 bang-bang 解决方案，开关总数随重定向角度和转动惯量而变化。开关的数量通常为 5 个或 6 个，并且不超过 8 个。对于单一解决方案，一个或两个控制单一是可能的。对于细长的棒状航天器来说，奇异最优解可能是最优的。最后，提出了一种确定最佳时间范围的解析估计方法。仿真结果表明，该方法具有实时性和高精度。本文的所有公式均以规范单位导出，因此适用于任何刚性航天器。