This paper presents the control of a quadruped walking robot, without feet, for a gallop gait. This gait is decomposed into two phases: a single supprot phase and a double support phase. Two control schemes are necessary to achieve the motion of the robot, depending on the current phase. For the single support phase, the system is underactuated: one variable is kept free without control. For the double support phase, the system is overactuated. This redundancy is used to satisfy contact force constraints during the motion. The reference trajectory is built with respect to physical constraints: sliding, impact and contact constraints on the leg tips. Also, the trajectory is defined to cope with changes on the free variable evolution.
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