Penalty-function guidance for multiple satellite cluster formation

Distributed systems with a cluster of multiple artificial satellites have been considered to be beneficial for telecommunications1,2 and other science missions.3 Therefore, advanced operations of a cluster formation have a crucial role on such space applications. Clustering of two satellites has already been studied by analyzing just one relative orbit of the Clohessy-Wiltshire (CW) rotating coordinate frame (see Ref. 4). Near-miss avoidance imposes more complex constraints as a cluster is composed of more satellites. It is probable that one satellite escaping from another satellite encounters other satellites if near-miss avoidance strategy between all of the satellites in close proximity is not fully considered. One solution is to accelerate the respective satellites as if they have virtual repulsion. Such potential fields have been formulated and imposed on the state-variable space to form an equidistant constellation around the Earth5 and a cluster center,6 respectively. Other solutions have been also proposed: graph theory for switching the roles of leaders and followers7 and mixed-integer linear programming.