Abstract
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.
Highlights
Time-optimal reorientation of a spacecraft is an open and interesting problem for the observation of multiple asteroids
For bang-bang solutions, the total number of switches varies with the reorientation angle and the moment of inertia
We find that the total number of switches is usually 5 or 6
Summary
Time-optimal reorientation of a spacecraft is an open and interesting problem for the observation of multiple asteroids. Studies about asteroids mainly focused on an individual asteroid, such as 25143 Itokawa (Binzel et al 2001), 433 Eros (Jiang and Baoyin 2016), 216 Kleopatra (Yu and Baoyin 2012; Jiang 2015). The early exploration missions mainly aimed at a single asteroid. The Hayabusa spacecraft was specially designed to explore the asteroid 25143 Itokawa (Fujiwara et al 2006). Scientists have turned more and more attention to the research of a class of asteroids, such as near-Earth asteroids (Zeng et al 2014; Bao et al 2015), Trojan asteroids (Liu and Schmidt 2018), and so on. The corresponding exploration missions have been proposed. Projects SODA (Shugarov et al 2018) and Universat-SOCRAT
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