The surface of a minor body in space features a harsh terrain and microgravity. To explore such surfaces in detail, a robot with an appropriate moving mechanism is required. To this end, we proposed a robot that moves by gripping the surface like a rock climber. We focus on the robot's gait, where the motion of the idling arm generates the reaction force that acts on the gripper of the supporting arm. The reaction force needs to be controlled to maintain a grip without slipping. Therefore, we formulate a simultaneous control law that combines the tip position control of the idling arm with reactionless control by utilizing the reaction null-space. Moreover, the validity of the control law was confirmed by an experiment involving an air floating system under microgravity. Furthermore, a planar simulation clarified that the robot can move continuously on an irregular terrain.