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In order to create a three-dimensional running robot, we study a control method called variable constraint control, which can realize various kinds of gaits. In this research, we have developed a quadruped robot, which simulates dynamic walking and running motions of a cheetah. Next, we have realized a motion pattern for a quadruped robot, which is expressed as differential equations of characteristic values of the robot. Experimental results show that a quadruped robot is produced which has a bounce gaits.