Metabolically efficient walking assistance using optimized timed forces at the waist

Abstract

The metabolic rate of walking can be reduced by applying a constant forward force at the center of mass. It has been shown that the metabolically optimal constant force magnitude minimizes propulsion ground reaction force at the expense of increased braking. This led to the hypothesis that selectively assisting propulsion could lead to greater benefits. We used a robotic waist tether to evaluate the effects of forward forces with different timings and magnitudes. Here, we show that it is possible to reduce the metabolic rate of healthy participants by 48% with a greater efficiency ratio of metabolic cost reduction per unit of net aiding work compared with other assistive robots. This result was obtained using a sinusoidal force profile with peak timing during the middle of the double support. The same timing could also reduce the metabolic rate in patients with peripheral artery disease. A model explains that the optimal force profile accelerates the center of mass into the inverted pendulum movement during single support. Contrary to the hypothesis, the optimal force timing did not entirely coincide with propulsion. Within the field of wearable robotics, there is a trend to use devices to mimic biological torque or force profiles. Such bioinspired actuation can have relevant benefits; however, our results demonstrate that this is not necessarily optimal for reducing metabolic rate.

Fig. 1.. Experimental conditions and simulation model.

(A) Photograph of the robotic waist-tether setup. A cable robot (HuMoTech, Pittsburgh, PA, USA) applied force profiles to a waist belt. To avoid the tether going slack during portions of the step cycle, a constant backward force was simulated by inclining the treadmill (17, 18) by a 2.8° angle. The reported aiding forces are the forces measured with a load cell minus the parallel component of gravity. (B) Schematic of the force profile conditions. We used the cable robot to apply Sinusoidal Force conditions, Constant Force conditions, and a Zero Force condition. (C) Simple pendulum model. We modeled an inverted pendulum (3, 19) with the mean mass and leg length of our participants. This model was used to simulate different aiding force timings and magnitudes. For each condition, we identified the initial COM velocity required to match the experimental step time and the velocity at the end of single support. Based on COM velocity, we estimated the metabolic rate (visualized as colored surfaces) of the trailing and leading legs during the step-to-step transition and the support leg during single support (15). The metabolic rate of the step-to-step transition was estimated by dividing the redirection work rate that the legs have to produce (3) by the assumed efficiencies (20).

Fig. 2.. Effects of force profiles on metabolic rate.

(A) Net aiding forces and corresponding metabolic rate reductions. Lines represent the means of the participants for the Sinusoidal Force conditions and the best Constant Force condition. The color scale indicates metabolic rate reduction. Thick lines indicate the highest and lowest reductions. We applied the same profile during left and right steps; therefore, we plotted profiles versus step instead of stride time. (B) Effect of peak timing on metabolic rate. Dots and error bars represent means and SEMs of participants for conditions with different timings but approximately the same duration and net aiding work rate as the condition with the highest reduction. Solid line represents the mixed-effects model fitted on all Sinusoidal Force conditions (15) evaluated at the mean magnitude of dots. Dotted line represents the estimation from the simple pendulum simulated over the feasible range. (C) Effect of net aiding work rate on metabolic rate. Dots and error bars represent means and SEMs for conditions with different net aiding work rates within a timing range of ± 6% from the optimum (15.1%). Circles and the dashed line represent Constant Force conditions. Independent variables of (B) and (C) were selected from different candidate metrics (15). P-values of reductions in metabolic rate versus Zero Force condition were smaller than 0.05 for all conditions (paired t test with Holm-Šidák correction, n = 10).

Fig. 3.. Effects of timing on GRF and COM velocity.

(A) Effect of timing on bilateral parallel GRF. The tether does not act unilaterally on one leg; therefore, we chose to analyze the bilateral GRF instead of the unilateral GRF. Colored lines represent the means of participants from conditions with similar actuation magnitudes and approximately the same net aiding work rate as the best condition from Fig. 2B but with different timings. The GRFs of the colored conditions appear offset because of the net aiding force that is not shown here. Gray lines represent all other conditions. Bar plots represent the average propulsion GRF averaged over the entire step duration. The thick line marks the condition that showed the highest metabolic rate reduction. (B) Comparison of bilateral parallel GRF between the condition with the highest reduction in metabolic rate (thick blue line), best Constant Force condition (dashed blue line), and Zero Force condition (black line). (C) Effect of timing on the resultant COM velocity. Bar plots represent the magnitude of the COM velocity vector at the beginning and end of single support. Horizontal lines represent the actuation periods. The condition with the highest reduction in metabolic rate (dark blue bar) has the lowest COM velocity at the end of single support, the highest COM velocity at the beginning of single support, and thus the highest acceleration during double support. (D) Comparison of COM velocity between the condition with the highest reduction in metabolic rate (thick blue line), best Constant Force condition (dashed blue line), and Zero Force condition (black line). * means P-value of effect of peak timing < 0.05. ^# means P-value of paired t test versus Best Constant Force condition < 0.05. (n = 10).

Fig. 4.. Hypothesis and underlying mechanism.

(A) Hypothesized best timing of a Sinusoidal Force condition. The plot shows the mean net aiding force (solid line) and the bipedal sum of the parallel GRF (dashed line) from the participants in the Sinusoidal Force condition where the net aiding force matches closest to the bipedal propulsion timing, plotted versus step time. (B) Best timing result. Condition with the highest reduction in metabolic rate. (C) Explanation based on COM velocity effect. Plot showing the mean COM velocity of all participants of the conditions with the hypothesized best timing and the highest metabolic rate reduction. (D) Simple pendulum model. Stick figures show the higher COM acceleration at the beginning of the step and lower COM velocity at the end of the step in the condition with early peak timing compared to the condition with late peak timing. The pendulum model predicts that the higher initial acceleration and lower final velocity will result in lower positive and negative leg work rates required to redirect the COM. (n = 10).

Fig. 5.. Literature comparison within the field of wearable robotics.

(A) Studies with linear assistance strategies (constant and non-constant tethers, and downhill walking) compared to the mean trend of 10 participants from our study. (B) Studies with exoskeletons and prostheses compared to our study. Reductions in metabolic rate compared to a Zero Force or no assistance condition versus net aiding work rate. The black line represents the effect of magnitude of conditions from the present study within 6% of the optimum peak timing (Fig. 2C). Colored lines represent trends from actuation magnitude parameter sweeps (, , , –14, 16). Circles represent results from studies that do not use actuation magnitude sweep protocols (6, 9, 15, 22, 23).