The energy losses due to impact between a hopping robot and a non-rigid foundation makes it challenging to maintain a desired apex height of the center-of mass. We consider an ankle-knee-hip robot hopping on an elastic foundation and a viscoelastic foundation with inertia. A continuous backstepping controller is designed to control the energy level and internal dynamics of the hopper to reach the desired apex height. For a viscoelastic foundation, the same controller results in steady state error and this error is eliminated using a discrete-time controller with integral action. Simulation results are presented to demonstrate the efficacy of the controller.

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