  This paper presents a method for guiding a robot manipulator to capture and
bring a tumbling satellite to a state of rest. The proposed approach includes
developing a coordination control for the combined system of the space robot
and the target satellite, where the satellite acts as the manipulator payload.
This control ensures that the robot tracks the optimal path while regulating
the attitude of the chase vehicle to a desired value. Two optimal trajectories
are then designed for the pre- and post-capture phases. In the pre-capturing
phase, the manipulator manoeuvres are optimized by minimizing a cost function
that includes the time of travel and the weighted norms of the end-effector
velocity and acceleration, subject to the constraint that the robot
end-effector and a grapple fixture on the satellite arrive at the rendezvous
point with the same velocity. In the post-grasping phase, the manipulator dumps
the initial velocity of the tumbling satellite in minimum time while ensuring
that the magnitude of the torque applied to the satellite remains below a safe
value. Overall, this method offers a promising solution for effectively
capturing and bringing tumbling satellites to a state of rest.
