Collision avoidance maneuver planning with robust optimization

In recent years, a growing number of space missions have emerged which are utilizing distributed systemsof satellites. This is accompanied by a rising level of interest in both the scientific and defense communitiesto develop mature systems and software for autonomous rendezvous and formation flying. An underlyingrequirement for these types of missions is the need to ensure safe, collision-free operations.The PRISMA mission, to be launched in 2009, will demonstrate Guidance, Navigation, and Controlstrategies for advanced autonomous formation flying between two spacecraft. The Swedish Space Corporation(SSC) is the prime contractor for the project which is funded by the Swedish National Space Board(SNSB). The safe guidance mode, based upon algorithms developed by Princeton Satellite Systems (PSS)under a CRADA, will be an integral part of the PRISMA mission. Its role is to plan a collision avoidancemaneuver if the relative distance is too small, and to continually plan relative station-keeping maneuvers tokeep the spacecraft on a safe relative trajectory.One important requirement of the safe guidance algorithms for PRISMA is that they guarantee reliableplans immediately, which led to the choice of completely deterministic methods. In this paper, we consideralternative numerical methods that are appropriate for the online computation of collision avoidance maneuvers.In particular, we discuss how to pose the original non-convex problem as a linear programming(LP) problem, using a combination of well-defined convex constraints. We go on to show how navigationuncertainty can be included in the LP formulation, enabling the efficient solution of robust, fuel optimal maneuvers.