Abstract—This paper presents a reference generation technique for bounding quadruped locomotion. Synthesis of the reference is carried out by forming contact forces. Contact forces are planned with the aid of linear and angular momentum conservation and impulse laws. For the purpose of obtaining a stable and continuous bound gait, linear and angular momentum changes are set to be equal to zero over a full gait cycle. This condition allows the robot body to keep its initial dynamics at the end of the cycle, thus, producing a stable bound gait throughout the cycles. Periodicity in vertical linear velocity and angular velocity is obtained. These settings also result in almost constant horizontal body linear velocity. Suitable contact forces are produced with an optimization algorithm. Sequential Quadratic Programming (SQP) is utilized as an optimization solver. Linear and angular momentum laws and a non-slipping condition are applied as constraints of optimization. A full-dynamics simulation environment is employed to test the proposed reference generation algorithm. Results verify the validity of the proposed reference generation method for quadruped bounding.  
 
Index Terms—quadruped robot, legged robot locomotion, reference generation, force planning, simulation, optimization