Thruster-Pointing-Constrained Optimal Control for Satellite Servicing Using Indirect Optimization

Future space missions such as in-space assembly of telescopes and on-orbit servicing require rendezvous and proximity operations trajectories that avoid thruster-induced contamination of delicate components onboard the client spacecraft. We present a novel technique to incorporate a hard thruster pointing constraint into the indirect optimal control formulation and solve the problem using a single-shooting method. A thruster pointing constraint is an inequality constraint that imposes a limit on the angular range over which a spacecraft thruster is permitted to operate, thus mitigating plume contamination during rendezvous and proximity operations. Through novel incorporation of the constraint directly into the dynamic model, the problem can be easily solved with no a priori knowledge of the burn sequence or information about when the constraint is active or inactive. Our formulation is capable of handling a constant thruster pointing constraint as well as one that varies as a function of distance from the target spacecraft. Results are presented under Clohessy–Wiltshire dynamics; however, the method can be easily extended to handle nonlinear dynamic systems. As expected, we see an increase in fuel consumption with increasing constraint angle for the solution of problems with the same boundary conditions and time of flight. To validate our method, we compare the performance and results to those of a direct method, sequential convex optimization, utilizing the CVX MATLAB plug-in and the MOSEK solver. We found that our approach converged more easily and required no hand-tuning of parameters. It also converged to solutions that satisfy the pointing constraints to a stricter tolerance. We anticipate that our novel approach to generating thruster-pointing-constrained fuel-optimal trajectories will be enabling to a host of future servicing space missions.