This paper deals with the impulsive formation control of spacecraft in the presence of constraints on the position vector and time. Determining a set of path constraints can increase the safety and reliability in an impulsive relative motion of spacecraft. Specially, the feasibility problem of the position norm constraints is considered in this paper. Under assumptions, it is proved that if a position vector be reachable, then the reach time and the corresponding time of impulses are unique. The trajectory boundedness of the spacecraft between adjacent impulses are analyzed using the Gerschgorin and the Rayleigh–Ritz theorems as well as a finite form of the Jensen's inequality. Some boundaries are introduced regarding the Jordan–Brouwer separation theorem which are useful in checking the satisfaction of a constraint. Two numerical examples (approximate circular formation keeping and collision-free maneuver) are solved in order to show the applications and visualize the results.

中文翻译：

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路径约束下航天器的脉冲编队控制

本文研究了存在位置矢量和时间约束的航天器脉冲编队控制。确定一组路径约束可以提高航天器脉冲相对运动的安全性和可靠性。特别地，本文考虑了位置范数约束的可行性问题。在假设条件下，证明如果一个位置向量是可达的，那么到达时间和对应的脉冲时间是唯一的。使用 Gerschgorin 和 Rayleigh-Ritz 定理以及 Jensen 不等式的有限形式来分析相邻脉冲之间航天器的轨迹有界性。介绍了有关 Jordan-Brouwer 分离定理的一些边界，这些边界对于检查约束的满足很有用。