A model of task-level human stepping regulation yields semistable walking

A simple lateral dynamic walker, with swing leg dynamics and three adjustable input parameters, is used to study how motor regulation affects frontal-plane stepping. Motivated by experimental observations and phenomenological models, we imposed task-level multi-objective regulation targeting the walker's optimal lateral foot placement at each step. The regulator prioritizes achieving step width and lateral body position goals to varying degrees by choosing a mixture parameter. Our model thus integrates a lateral mechanical template, which captures the fundamental mechanics of frontal-plane walking, with a lateral motor regulation template, an empirically verified model of how humans manipulate lateral foot placements in a goal-directed manner. The model captures experimentally observed stepping fluctuation statistics and demonstrates how linear empirical models of stepping dynamics can emerge from first-principles nonlinear mechanics. We find that task-level regulation gives rise to a goal-equivalent manifold in the system's extended state space of mechanical states and inputs, a subset of which contains a continuum of period-1 gaits forming a semistable set: perturbations off of any of its gaits result in transients that return to the set, though typically to different gaits.