Abstract The problem of obtaining long term relative orbit configurations for spacecraft clusters with realistic operational considerations such as safety, station keeping and inter-spacecraft distances is addressed. Two different approaches are developed for station keeping and safety objectives. In the first approach, relative orbit configurations, or relative TLEs, are found minimizing deviations from reference mean orbit which would maximize the station-keeping objective. In second one, relative configurations are found from a reference initial condition by minimizing probability of collision, hence maximizing the safety objective, between the spacecraft in the cluster which are propagated numerically through a high precision orbit propagator. For the design optimization, a derivative free algorithm is proposed. Effectiveness of the approaches is demonstrated through simulations. Using this design framework, several configurations can be found by exploring the limits of the clusters in terms of spacecraft number, distance bounds and probabilities of collision for long time intervals.

中文翻译：

---

异构航天器群长期安全相对轨道设计

摘要 解决了在安全、站位保持和航天器间距离等实际操作考虑下获得航天器集群的长期相对轨道配置的问题。为保持站点和安全目标开发了两种不同的方法。在第一种方法中，发现相对轨道配置或相对 TLE 最小化与参考平均轨道的偏差，这将最大化站保持目标。在第二个中，通过最小化碰撞概率从参考初始条件中找到相对配置，从而最大化集群中航天器之间的安全目标，这些航天器通过高精度轨道传播器进行数值传播。对于设计优化，提出了一种无导数算法。通过模拟证明了这些方法的有效性。使用这个设计框架，可以通过探索集群在航天器数量、距离界限和长时间间隔碰撞概率方面的限制来找到几种配置。