To study autonomous control of a space robot, the authors developed their Advanced Space Robot Testbed with Redundant Arms (ASTRA). Berthing a satellite moving in space is a difficult and dangerous task when done manually. This paper describes a robot which berthed a mockup satellite moving and rotating in zero gravity. Features of the robot include autonomous approach to a moving target satellite using visual satellite motion estimation, using real-time visual tracking control to track satellite handles with two robot arms, and grasping the satellite handles with minimum mechanical shock using a flexible wrist mechanism and impedance control. The authors ran their satellite berthing experiment on the ASTRA to check its performance.>