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This paper discusses on the control law for space manipulator. Space debris problem is significant for the future space development. It is desired for space manipulator to capture and retrieve large space debris such as disable satellite. Most disable satellites are spinning because controller is malfunction. Before capturing the satellite, the controller of manipulator satisfies that the end-effecter synchronizes the motion of disable satellite. The controller is also required to reduce energy consumption. Optimal periodic controller changes the attitude of manipulator to minimize the energy consumption after repeating the periodic motion. Stability and optimality of the controller is shown analytically.
