Abstract
In this paper, we present a continuous norm-regulation-based limit cycle control for vertical hoppers, inspired by the phased-locked controller for an anchored spring-mass-damper system. Our approach provides continuous real-time norm regulation during the stance phase, leading to faster convergent rate and larger disturbance rejection capability as compared to the conventional impulsive or continuous stance phase control approaches. We analytically proved that the proposed controller can asymptotically stabilize the vertical hopper to a desired limit cycle with an intermittent transition between the stance and flight phases. In addition, we also proved that the convergence of the controller can be preserved even with model parameter uncertainty. Simulations and experiments were conducted to demonstrate the effectiveness of the proposed controller.
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