Optimal control of a space manipulator for detumbling of a target satellite

Robotic capture of a tumbling target-satellite means that the space robot´s hand and the target grapple point arrive at a rendezvous point with the same velocity and then the chase vehicle mechanically connects into the target using a grapple device. This paper is focused on optimal control of the space manipulator in the postcapture phase so as to bring the tumbling non-cooperative satellite to rest in minimum time while ensuring that the magnitude of the interaction torque between the manipulator and target remains below a prescribed value. First, we seek fast detumbling maneuvers of the target satellite subjected to the torque restriction. The theory of optimal control and Pontryagin´s principle are applied to obtain a closed-form solution for the optimal path planning problem, giving a great deal of insight: the vector of the interaction torque is aligned opposite to the direction of the instantaneous angular momentum vector. Second, a coordination control for combined system of the space robot and the target satellite, which acts as the manipulator payload, is developed so that the robot tracks the optimal path while regulating the attitude of the chase vehicle to a desired value. A preliminary illustrative example is appended.