Multi-objective control in human walking: insight gained through simultaneous degradation of energetic and motor regulation systems

Abstract

Minimization of metabolic energy is considered a fundamental principle of human locomotion, as demonstrated by an alignment between the preferred walking speed (PWS) and the speed incurring the lowest metabolic cost of transport. We aimed to (i) simultaneously disrupt metabolic cost and an alternate acute task requirement, namely speed error regulation, and (ii) assess whether the PWS could be explained on the basis of either optimality criterion in this new performance and energetic landscape. Healthy adults (N = 21) walked on an instrumented treadmill under normal conditions and, while negotiating a continuous gait perturbation, imposed leg-length asymmetry. Oxygen consumption, motion capture data and ground reaction forces were continuously recorded for each condition at speeds ranging from 0.6 to 1.8 m s^-1, including the PWS. Both metabolic and speed regulation measures were disrupted by the perturbation (p < 0.05). Perturbed PWS selection did not exhibit energetic prioritization (although we find some indication of energy minimization after motor adaptation). Similarly, PWS selection did not support prioritization of speed error regulation, which was found to be independent of speed in both conditions. It appears that, during acute exposure to a mechanical gait perturbation of imposed leg-length asymmetry, humans minimize neither energetic cost nor speed regulation errors. Despite the abundance of evidence pointing to energy minimization during normal, steady-state gait, this may not extend acutely to perturbed gait. Understanding how the nervous system acutely controls gait perturbations requires further research that embraces multi-objective control paradigms.

Keywords: energetics; locomotion; motor regulation; multi-objective control; prioritization.

Figure 1.

Custom-made platform shoe with an approximately 100 mm additional foam sole. The width of the base was reinforced for safety, providing an additional 20 mm around the middle third of the shoe, with a natural gradient progressing to the most anterior and posterior aspects in a manner such that no additional length was added. (Online version in colour.)

Figure 2.

Components of a GEM analysis. Combinations of stride lengths (L) and times (T) that achieve the desired speed fall directly on the GEM (grey dashed line; L = vT, where v is the treadmill speed). Values fluctuating tangential to the GEM are considered to be deviating in the goal-equivalent direction and do not affect the task goal (i.e. maintaining constant speed). Values fluctuating perpendicular to the GEM are considered to be deviating in the goal-relevant direction and are responsible for poorer performance in relation to the speed-maintenance goal. The eigenvectors of a linear map fitted to the sequence of stride lengths and stride times give the direction of strong stability (light (blue) arrow; ${\mathit{v}}_{\mathrm{SS}}$) and weak stability (dark (blue) arrow; ${\mathit{v}}_{\mathrm{WS}}$). Whereas the weakly stable direction is expected to be nearly tangent to the GEM, and hence is not important to speed regulation, the strongly stable direction can drive fluctuations onto the GEM, and hence is an indication of the strength of motor regulation during walking. (Online version in colour.)

Figure 3.

Group (mean; N = 21) speed versus COT during normal (dark/black), and perturbed walking (leg-length asymmetry; light/red). The PWS from each condition is denoted by a triangle. Error bars represent speed (horizontal) and COT (vertical) standard deviations. 95% confidence intervals for the quadratic curve minimums are displayed (transparent red and black bars). (Online version in colour.)

Figure 4.

Group (mean; N = 21) speed versus strength of speed error correction, as quantified by the strongly stable eigenvalue (λ_SS) of inter-stride fluctuations for normal walking (dark/black), and perturbed walking (leg-length asymmetry; light/red). The PWS from each condition is denoted by a triangle. Error bars represent speed (horizontal) and COT (vertical) standard deviations. Values closer to zero represent stronger regulation, while increasingly negative values indicate greater over-correction. For comparison, optimal regulation corresponds to values that are exactly zero. (Online version in colour.)

Figure 5.

A typical illustration of the GEM and fluctuation eigenstructure produced for a single subject (N = 1) walking at their preferred walking speed during both normal (dark/black; 1.22 m s⁻¹) and perturbed walking (one flat, one platform shoe; light/red; 0.94 m s⁻¹). The direction of strongly stable eigenvectors is indicated by a light (blue) arrow, while the direction of weakly stable eigenvectors is indicated by a dark (blue) arrow. Eigenvalues (λ_SS, λ_WS) are presented near their associated eigenvector. (Online version in colour.)