For the one-legged robot, a modified SLIP model is studied in this paper and dynamical characteristics of flight phase, impact phase and stance phase in hopping gait are analyzed. A hybrid dynamics correspond to these phases are derived by Newton-Euler Recursive Approach. Through dynamics, the gait planning of stable hopping and different forwarding velocities transition are mathematically described. Based on the Serial Elastic Actuator (SEA) mounted in joints, one formulation of system actuated force/torque is proposed from the point of energy injection. Then a planning procedure of the stable hopping and transition between different forwarding velocities are described respectively by this formulation. Feasibilities of the proposed gait planning method in this paper are verified by simulations.
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