In prior work, a minimal mathematical model of bipedal walking was developed to investigate the experimentally observed entrainment behavior of human locomotion. While that model reproduced several salient properties of human walking, it failed to entrain to periodic perturbations with period longer than preferred walking period. To overcome that limitation, we introduced afferent feedback in the form of leading leg angle control that depended on the energetics of previous steps. The model response to periodic perturbations was again studied in simulation, testing several perturbation periods and initial perturbation phases. This revised model captured important aspects of human locomotion that had been previously observed experimentally: a finite basin of entrainment to both shorter and longer perturbation periods. Regardless of the (random) phases of the step cycle at which perturbations were initiated, all entrained simulations phase-locked with the torque pulses at the end of double stance. However, more than twice as many steps were required to entrain to longer perturbations. The results achieved with this revised walking model emphasize the importance of the oscillatory dynamics of bipedal locomotion and highlight possible applications of gait entrainment as a method for permissive motor guidance in the field of assistive and rehabilitation robotics.

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