Spacecraft Trajectory Planning with Avoidance Constraints Using Mixed-Integer Linear Programming

Amethod for Ž nding fuel-optimal trajectories for spacecraft subjected to avoidance requirements is introduced. These include avoidance of collisions with obstacles or other vehicles and prevention of thruster plumes from one spacecraft impinging on another spacecraft. The necessary logical constraints for avoidance are appended to a fuel-optimizing linear programby including binary variables in the optimization. The resulting problem is a mixedinteger linear program (MILP) that can be solved using available software. The logical constraints can also be used to express the conŽ guration requirements for maneuvers where only the Ž nal relative alignment of the vehicles is important and the assignment of spacecraft within the  eet is not speciŽ ed. The collision avoidance, trajectory optimization, and  eet assignment problems can be combined into a single MILP to obtain the optimal solution for these maneuvers. The MILP problem formulation, including these various avoidance constraints, is presented, and then several examples of their application to spacecraft maneuvers, including reconŽ guration of a satellite formation and close inspection of the International Space Station by a microsatellite, are shown. These examples clearly show that the trajectory design methods presented are particularly well suited to proposed formation  ying missions that involve multiple vehicles operating in close proximity.