Stepping in the direction of the fall: the next foot placement can be predicted from current upper body state in steady-state walking

Abstract

During human walking, perturbations to the upper body can be partly corrected by placing the foot appropriately on the next step. Here, we infer aspects of such foot placement dynamics using step-to-step variability over hundreds of steps of steady-state walking data. In particular, we infer dependence of the 'next' foot position on upper body state at different phases during the 'current' step. We show that a linear function of the hip position and velocity state (approximating the body center of mass state) during mid-stance explains over 80% of the next lateral foot position variance, consistent with (but not proving) lateral stabilization using foot placement. This linear function implies that a rightward pelvic deviation during a left stance results in a larger step width and smaller step length than average on the next foot placement. The absolute position on the treadmill does not add significant information about the next foot relative to current stance foot over that already available in the pelvis position and velocity. Such walking dynamics inference with steady-state data may allow diagnostics of stability and inform biomimetic exoskeleton or robot design.

Keywords: biomechanics; control; dynamics; foot placement; stability; walking.

Figure 1.

Describing walking motion with pelvis and foot positions. (a) The right-foot position at mid-stance relative to the previous left-foot stance position, shown for a single subject, for each of about 265 strides at 1 m s⁻¹ (blue dots), 1.2 m s⁻¹ (red) and 1.4 m s⁻¹ (black). (b) Human walking motion represented by pelvis position and two foot positions. (c) Mid-stance is defined as when the swing foot has the same fore–aft position as the pelvis. The stance foot position is assumed fixed at the foot position at mid-stance. (d) A schematic showing a deviation from the average pelvis trajectory and a corresponding change in the next stance foot position.

Figure 2.

Foot placement dynamics. (a) The estimated partial derivative J(0) of the foot position with respect to pelvis state at mid-stance P(0); box-plot shows mean across subjects and trials (red midline), standard deviation over all trials (boxes) and 95% interval (whiskers, 2.5 to 97.5 percentile). Colour shading indicates left to right transitions and grey indicates right to left. A negative sign (−) indicates display of the sign-reversed coefficients for some right to left transitions; red asterisks indicate coefficients statistically different from zero (p < 0.05). (b) Sensitivity of foot position on selected pelvis states at different phases ϕ; mean (thick solid line) ± s.d. (coloured band) are shown for left to right transitions; see the electronic supplementary material, figure S4. (c) Fraction of foot position variance explained by phase-dependent pelvis state (dark colours) or the phase-dependent swing foot state (light colours). (d) The sensitivity of the swing foot relative to the pelvis, in response to mid-stance pelvis deviations. In panels (b–d), red dashed (ϕ = 0.22) and solid (ϕ = 0.34) lines roughly indicate, respectively, moments just before heel-strike and just after push-off, with double stance between; solid lines and filled bands are for left to right transitions and dashed lines are for right to left transitions.