Optimal control for final approach of rendezvous with non-cooperative target

This paper considers the final approach of rendezvous problem for servicing satellite to capture a tumbling satellite with external forces/torques as control inputs. The main purpose is to design an optimal control law to ensure a servicing satellite with the least fuel consumption. It is formulated as a constrained optimal control problem, where specific requirements of this final approach problem are all incorporated in the problem formulation. Then, by utilizing the specific features of the problem, this final approach of rendezvous problem is transformed into an equivalent standard optimal control problem subject to continuous state inequality constraints. A computational method is developed, based on the control parametrization in conjunction with a time scaling transform and the constraint transcription method, to design an optimal controller for this new constrained optimal control problem. Numerical results are presented for illustration.