A Simple State-Determined Model Reproduces Entrainment and Phase-Locking of Human Walking

Abstract

Theoretical studies and robotic experiments have shown that asymptotically stable periodic walking may emerge from nonlinear limit-cycle oscillators in the neuro-mechanical periphery. We recently reported entrainment of human gait to periodic mechanical perturbations with two essential features: 1) entrainment occurred only when the perturbation period was close to the original (preferred) walking period, and 2) entrainment was always accompanied by phase locking so that the perturbation occurred at the end of the double-stance phase. In this study, we show that a highly-simplified state-determined walking model can reproduce several salient nonlinear limit-cycle behaviors of human walking: 1) periodic gait that is 2) asymptotically stable; 3) entrainment to periodic mechanical perturbations only when the perturbation period is close to the model's unperturbed period; and 4) phase-locking to locate the perturbation at the end of double stance. Importantly, this model requires neither supra-spinal control nor an intrinsic self-sustaining neural oscillator such as a rhythmic central pattern generator. Our results suggest that several prominent limit-cycle features of human walking may stem from simple afferent feedback processes without significant involvement of supra-spinal control or a self-sustaining oscillatory neural network.

The critical phase for visual control of human walking over complex terrain

“…Fourteen subjects [5 females, 9 males; mean age = 18.7 (18)(19)(20)(21) years] participated in experiment 1, 18 subjects [7 females, 11 males; mean age = 19.1 (18)(19)(20)(21) years] participated in experiment 2, and 12 subjects [5 females, 7 males; mean age = 20.0 (18)(19)(20)(21)(22) years] participated in experiment 3. Data from two subjects in experiment 1 were excluded because their average stepping accuracy across all conditions was more than 2 SDs from the mean.…”

“…As such, a small forward perturbation applied to the COM at midstep increases the speed of the COM, which in turn increases the collision loss so the additional energy that is injected into the system by the perturbation will be dissipated at collision (15). Although the basin of attraction for bipedal gait may be relatively shallow, spinal-level reflex pathways (3) may serve to facilitate gait-restorative responses that take advantage of this passive stability (18)(19)(20). † Active Control of Walking These insights imply that certain desirable characteristics of movement, such as coordination, efficiency, and stability, can emerge without active (i.e., perceptually guided) control.…”

Interlimb Coordination During Step-to-Step Transition and Gait Performance

“…Consistent with mathematical models, the energy dissipation due to non-elastic foot-ground interaction during the heel strike may be an essential element of legged locomotion rather than an accidental imperfection (Ahn & Hogan, 2012). It may not only provide indispensable sensory cues from foot contact of the leading leg (reflecting cutaneous input or load -related afferents) to coordinate locomotor patterns, but may also be a key mechanical factor that determines the stability of locomotion (Ahn & Hogan, 2012) as medio-lateral stability is mainly ensured by foot placement ('stepping strategy') (Hof, Vermerris, & Gjaltema, 2010). The importance of double support phase is also linked to the relation between postural stability, interlimb coordination and the metabolic cost of walking (Donelan, Shipman, Kram, & Kuo, 2004;Holt, Jeng, Ratcliffe, & Hamill, 1995;Krasovsky et al, 2012).…”

“…According to motor control theories, the system adjusts muscle activation thresholds of the trailing limb to guarantee dynamic gait stability (Feldman, Krasovsky, Baniña, Lamontagne, & Levin, 2011). Consistent with mathematical models, the energy dissipation due to non-elastic foot-ground interaction during the heel strike may be an essential element of legged locomotion rather than an accidental imperfection (Ahn & Hogan, 2012). It may not only provide indispensable sensory cues from foot contact of the leading leg (reflecting cutaneous input or load -related afferents) to coordinate locomotor patterns, but may also be a key mechanical factor that determines the stability of locomotion (Ahn & Hogan, 2012) as medio-lateral stability is mainly ensured by foot placement ('stepping strategy') (Hof, Vermerris, & Gjaltema, 2010).…”

A Control Framework for Anthropomorphic Biped Walking Based on Stabilizing Feedforward Trajectories

“…Taga proposed a control paradigm for walking based on the entrainment of neural oscillators (famously known as Central Pattern Generation - CPG) [22], which has been the basis of numerous works on locomotion control ever since [23]. Although the role of CPG in human walking remains a point of contention [24], Ahn and Hogan showed that the frequency of walking in healthy subjects adapts itself to rhythmic pulses from an external actuator on the ankle [25]. The small basin of entrainment observed in their experiments can be attributed to characteristics of a stable nonlinear oscillator underlying human walking.…”