Safe rendezvous scenario design for geostationary satellites with collocation constraints

Rendezvous on the geostationary orbit (GEO) is much more complex than that on the low earth orbit and has a higher critical requirement for safety performance. This paper presents a safe scenario design method for GEO rendezvous proximity missions where the safety constraint of a collocated satellite is considered. A recently proposed quantitative index considering trajectory uncertainty is introduced to analyze the safety performance of the scenario parameters including the V-bar keeping positions and the fly-by trajectory radius. Furthermore, an exhaustive analysis is performed to find the dangerous regions of the V-bar keeping positions and the appropriate semi-major axis of the fly-by ellipse, considering the safety requirements of both the target and the collocated satellite. A geometry method is then developed for designing a feasible and suboptimal safe rendezvous scenario. The method is tested by designing four rendezvous scenarios with $\pm$V-bar approach directions respectively in the situations with and without one collocated satellite. Safety performance and velocity increments of the scenarios are compared and a conclusion is reached that the collocated satellite has a significant influence on the scenario design.