This paper addresses the computation of Delta-V-optimal, safe, relative orbit reconfigurations for satellite formations in a centralized fashion. The formations under consideration comprise an uncontrolled chief spacecraft flying with an arbitrary number, N, of deputy satellites, where each deputy is equipped with a single electric thruster. Indeed, this represents a technological solution that is becoming widely employed by the producers of small-satellite platforms. While adopting a single electric thruster does reduce the required power, weight, and size of the orbit control system, it comes at the cost of rendering the satellite under-actuated. In this setting, the satellite can provide a desired thrust vector only after an attitude maneuver is carried out to redirect the thruster nozzle opposite to the desired thrust direction. In order to further extend the applicability range of such under-actuated platforms, guidance strategies are developed to support different reconfiguration scenarios for N-satellite formations. This paper starts from a classical non-convex quadratically constrained trajectory optimization formulation, which passes through multiple simplifications and approximations to arrive to two novel convex formulations, namely a second-order cone programming formulation, and a linear programming one. Out of five guidance formulations proposed in this article, the most promising three were compared through an extensive benchmark analysis that is applied to fifteen of the most widely-used solvers. This benchmark experiment provides information about the key distinctions between the different problem formulations, and under which conditions each one of them can be recommended.

中文翻译：

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Delta-V 最优集中式制导策略，用于欠驱动 N 卫星编队


本文以集中方式解决了卫星编队的 Delta-V 最优、安全、相对轨道重配置的计算。正在考虑的编队包括一个不受控制的主航天器，该飞船由任意数量的副卫星 N 飞行，每个副卫星都配备了一个电动推进器。事实上，这代表了一种技术解决方案，正在被小型卫星平台的生产商广泛采用。虽然采用单个电动推进器确实降低了轨道控制系统所需的功率、重量和尺寸，但代价是使卫星驱动不足。在这种情况下，只有在执行姿态机动以将推进器喷嘴重定向至与所需推力方向相反的方向后，卫星才能提供所需的推力矢量。为了进一步扩展这种欠驱动平台的适用范围，开发了制导策略以支持 N 卫星编队的不同重新配置场景。本文从一个经典的非凸二次方约束轨迹优化公式入手，经过多次简化和近似，得出两个新颖的凸公式，即二阶圆锥规划公式和线性规划公式。在本文提出的 5 个指导公式中，最有前途的 3 个通过广泛的基准分析进行了比较，该分析应用于 15 个最广泛使用的求解器。此基准实验提供有关不同问题表述之间的主要区别的信息，以及在哪些条件下可以推荐每个问题表述。