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Control of forward velocity for a simplified planar hopping robot

A simplified lossless model of the Raibert planar hopper is introduced for the purpose of analytically studying the control of forward velocity. A closed-form return map describing the robot's state at the next hop as a function of that at the current hop is derived. The Raibert forward velocity controller is introduced and the fixed points of the closed loop system are characterized as well as the stability of these points. A new control law inspired by this analysis is introduced and compared with the Raibert control law.