The condition for dynamic stability in humans walking with feedback control

Abstract

The walking human body is mechanically unstable. Loss of stability and falling is more likely in certain groups of people, such as older adults or people with neuromotor impairments, as well as in certain situations, such as when experiencing conflicting or distracting sensory inputs. Stability during walking is often characterized biomechanically, by measures based on body dynamics and the base of support. Neural control of upright stability, on the other hand, does not factor into commonly used stability measures. Here we analyze stability of human walking accounting for both biomechanics and neural control, using a modeling approach. We define a walking system as a combination of biomechanics, using the well known inverted pendulum model, and neural control, using a proportional-derivative controller for foot placement based on the state of the center of mass at midstance. We analyze this system formally and show that for any choice of system parameters there is always one periodic orbit. We then determine when this periodic orbit is stable, i.e. how the neural control gain values have to be chosen for stable walking. Following the formal analysis, we use this model to make predictions about neural control gains and compare these predictions with the literature and existing experimental data. The model predicts that control gains should increase with decreasing cadence. This finding appears in agreement with literature showing stronger effects of visual or vestibular manipulations at different walking speeds. Author summaryThe walking human body is mechanically unstable and humans frequently lose upright stability and fall while walking. Stability of human walking is usually analyzed from a biomechanical perspective. We argue that sensorimotor control is an essential aspect of walking stability. We model a walking system as a combination of inverted pendulum biomechanics and a neural feedback controller for foot placement and analyze the properties of this hybrid dynamical system. We find that there is always exactly one periodic orbit and derive a criterion for the asymptotic stability of this periodic orbit. This analytic criterion allows us to characterize the region in the parameter space where the walking system is stable. We use these theoretical results to analyze stability of human walking depending on different sensorimotor control gains. The model predicts that control gains should be larger for slower-paced walking, which is partially consistent with the available experimental data.