Robotic studies have suggested a contribution of limit-cycle oscillation of the neuro-mechanical periphery to human walking by demonstrating stable bipedal robotic gaits with minimal actuation and control. As behavioral evidence of limit-cycle oscillation in human walking, we recently reported entrainment of human gaits to mechanical perturbations. We observed synchronization of human walking with mechanical perturbation only when the perturbation period was close to the original walking period. In addition, the entrainment was always accompanied by phase locking at the end of double-stance. A highly-simplified state-determined walker reproduced these salient features: 1) entrainment to periodic perturbations with a narrow basin of entrainment and 2) phase-locking at the end of double stance. Importantly, the model required neither supra-spinal control nor an intrinsic self-sustaining neural oscillator (like a rhythmic central pattern generator), which suggests that prominent features of human walking may stem from simple afferent feedback processes that produce limit-cycle oscillation of the neuro-mechanical periphery without significant involvement of the brain or rhythmic central pattern generators. One limitation of that model was that it entrained only to perturbations faster than the unperturbed walking period. In the study reported here, we modified the model to have two independent steps per stride. The revised model reproduced entrainment to perturbations both slower and faster than the unperturbed cadence, as observed experimentally in human walking.
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