The surface of an asteroid features an irregular terrain and microgravity. Therefore, robotic exploration in an asteroid requires the adoption of an appropriate locomotion strategy. Moreover, an exploration robot is expected to be capable of moving to an area of scientific interest. In response to this, we have proposed a ground grip robot that moves by gripping the surface like a rock climber. By gripping the surface, the robot can prevent unintended flotation and rotation while propelling itself across the surface. When the idling arm is moved while the supporting arm's gripper is attached to the surface, all of the reaction forces act on the gripper. If the gripping force is to be exceeded, however, the robot could come adrift from the surface. In this paper, therefore, we propose a motion control method that does not act the reaction force on the gripper by utilizing the reaction null-space. Additionally, the tip position trajectory is generated as an ellipse to enable smooth movement and eliminate any frictional force. This control law was validated by a planar dynamic simulation. The simulation model assumes a dual-armed robot with three degrees of freedom (DOF) in each arm, while the uneven surface is simulated under certain conditions. As a result, the robot was able to move continuously with reactionless motion and the propriety of the control law was confirmed.