Abstract—For generating a translational motion of a robot in a horizontal plane or under microgravity, it is possible to utilize an impact force between the end-effector and a surface such as a wall and the ground. In this paper, we consider a legged robot consisting of four links that pushes a certain surface to obtain a translational momentum in a horizontal plane. The motion that maximizes the momentum is searched for, under the condition that the torque consumption during it is the same, by numerical optimization. The optimization results indicate that the motion with an impact force that is caused by hitting the surface is advantageous in increasing the translational momentum.  
 
Index Terms—motion planning, differential evolution, impact force