Collision avoidance guidance for formation-flying applications

Several proposed space science missions require deployment of a number of spacecraft to form a single functional unit or a formation flying spacecraft. There are many applications of a formation flying spacecraft; variable baseline optical space interferometry is one of them. These missions require frequent formation reconfigurations where the relative spacecraft positions must be changed. Spacecraft-to-spacecraft separations can range from a few meters to several kilometers during such formation reconfigurations. It is mission critical to avoid collisions between spacecraft as they move in space. In this paper we present an optimal formation pathplanning approach which is suitable for implementation on-board, on a single spacecraft. The optimal collisionavoidance problem is formulated as a parameter optimization problem where the translation paths taken by each spacecraft are parameterized as high order splines. This parameterization results in an optimization problem whose size is proportional to the number of spacecraft in the formation. An iterative algorithm to solve the problem on-board is proposed. Properties of optimal control are also identified. Examples are given for representative formation reconfigurations for the cases of a two spacecraft formation (the Space Technology-3 mission) and five spacecraft formation (the Terrestrial Planet Finder mission).