This paper discusses on the control law for variable geometry truss(VGT) as space manipulator, which is required to capture space debris. The end of truss is constrained to move periodically. The motion is simulated to synchronize trajectory of malfunctioned satellite, which is usually spinning or tumbling. Control law is also required to reduce energy consumption because of limited resources in space. The control law is derived from the locally optimal condition of minimum energy problem with periodic constraints. The simulation results show that the proposed controller has good ability to reduce the energy consumption by repeating motions.