Optimal Control for Spacecraft to Rendezvous with a Tumbling Satellite in a Close Range

One of the most challenging tasks for satellite on-orbit servicing is to rendezvous and capture a non-cooperative satellite such as a tumbling satellite. This paper presents an optimal control strategy for a servicing spacecraft to rendezvous (in close range) with a tumbling satellite. The strategy is to find an optimal trajectory which will guide the servicing spacecraft to approach the tumbling satellite such that the two vehicles will eventually have no relative rotation. Therefore, a subsequent docking or capture operation can be safely performed. Pontryagin´s maximum principle is applied in generation of the optimal approaching trajectory and the corresponding set of control force/torque profiles. A planar satellite chasing problem is presented as a case study, in which together with the maximum principle, the Lie algebras associated with the system are used to examine the existence of singular extremals for optimal control. Optimal trajectories for minimum fuel consumption are numerically simulated