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

Arthur Richards, Tom Schouwenaars, Jonathan P. How, and Eric Feron

AIAA JGCD, Vol. 25, No. 4, July - August 2002.

This paper introduces a method for finding fuel-optimal trajectories for spacecraft subject to avoidance requirements. These include avoidance of collisions with obstacles or other vehicles and prevention of thruster plumes from one spacecraft impinging upon another spacecraft or obstacle. The necessary logical constraints for avoidance are appended to a fuel-optimizing linear program by including binary variables in the optimization. The resulting problem is a \emph{mixed-integer linear program} (MILP) that can be solved using available software. The logical constraints can also be used to express the configuration requirements for maneuvers where only the final relative alignment of the vehicles is important, and the assignment of spacecraft within the fleet is not specified. The collision avoidance, trajectory optimization, and fleet assignment problems are combined into a single MILP to obtain the optimal solution for these maneuvers. The paper presents the MILP problem formulation, including these various avoidance constraints, and then shows several examples of their application to spacecraft maneuvers, including reconfiguration of a satellite formation and close inspection of the International Space Station by a microsatellite. These examples clearly show that the trajectory design methods presented in this paper are particularly well suited for proposed formation flying missions that involve multiple vehicles operating in close proximity.

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Professor Jonathan P. How
jhow@mit.edu

Arthur Richards

11/5/02