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Some of the unique properties associated with running with curved legs or feet (as opposed to point-contact feet) are examined in this work, including the rolling contact motion, the change of the leg's effective stiffness and rest length, the shift of the effective flexion point along the leg, and the compliant-vaulting motions over its tiptoe during stance. To examine these factors, a novel torque-driven reduced-order dynamical model with a clock-based control scheme and with a simple motor model is developed (named as torque-driven and damped half-circle-leg model (TD-HCL)). The controller parameters are optimized for running efficiency and forward speed using a direct search method, and the results are compared to those of other existing dynamical models such as the torque-driven and damped spring-loaded-inverted-pendulum (TD-SLIP) model, the torque-driven and damped two-segment-leg (TD-TSL) model, and the TD-SLIP with a rolling foot (TD-SLIP-RF) model. The results show that running with rolling is more efficient and more stable than running with legs that involve pin joint contact model. This work begins to explain why autonomous robots using curved legs run efficiently and robustly. New curved legs are designed and manufactured in order to validate these results.

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