This paper focuses on the guidance of a robot manipulator to capture a tumbling satellite and then bring it to state of rest (detumbling). First, a coordination control for combined system of the space robot and the target satellite, which acts as the manipulator payload, is presented so that the robot tracks the optimal path while regulating the attitude of the chase vehicle to a desired value. Subsequently, two optimal trajectories for the pre-and post-capture phases are designed. In the pre-capturing phase, the manipulator maneuvers are optimized by minimizing a cost function which 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 postgrasping phase, the manipulator dumps the initial velocity of the tumbling satellite in minimum time subject to the constraint that the magnitude of the torque applied to the satellite remains below a safe value. Simulation and experimental results are appended.