Fig 1.
Overground walking experiment setup.
We measured the preferred walking speed of walking for subjects with unilateral amputation wearing a Jaipur foot passive prosthetic leg in two conditions: a) walking a range of short distances, starting and stopping each bout at rest and b) walking in circles of different radii, both clockwise and anti-clockwise. These experiments have been previously performed in subjects without amputation [17, 52].
Fig 2.
a) Jaipur foot prosthesis has a skin colored cosmesis that simulates a barefoot appearance. b) Key components of the Jaipur foot prosthesis are shown. The interface between the various components have various rubber compounds for bonding and durability [77]. See [77, 78] for cross-sectional photographs, and [77] for more constructional details and measured mechanical properties.
Table 1.
Walking speed measurements over distance or time.
Table 2.
Subject information.
Table 3.
Energy cost model coefficients.
Fig 3.
Decrease in preferred walking speed with distance walked for subjects with amputation.
a) Subjects with amputation showed a decrease in average preferred walking speed for short distances. b) The rate of change in preferred walking speed with distance for the subjects with unilateral amputation is shown over a regime where both the subject-averaged data and the model fit are well-fit by linear trends (R2 value greater than 95%).
Table 4.
Speed reduction while walking for short bouts or in circles.
Fig 4.
Minimization of total metabolic cost captures slower short-distance walking speeds.
The total cost of the walking a short distance includes a term due to constant-speed cost and a changing-speed cost. We find that minimizing this total cost predicts the observed trends in changing preferred walking speed with distance for subjects with or without amputation. The error bars for human data represent standard errors, and the filled bands represent the set of all speeds within 1% of the energy optimal energy cost. The best fit cost coefficients obtained via inverse optimization shown in Table 5 are used here. The overall qualitative trends of smaller speeds for shorter distances remain as long as the steady walking cost coefficients a0 and a2, and the changing speed coefficient achange are positive.
Table 5.
Cost coefficients from inverse optimization.
Fig 5.
Preferred walking speeds for circle walking.
a) The preferred walking speed for all the subjects with unilateral amputation showed a decrease with radius of the circle walked. b) Subjects with amputation, when pooled together, did not show a significant difference in preferred walking speed when walking with the prosthesis-leg inside versus outside the circle. c) Subjects with above-knee amputation show a greater walking speed on average when the prosthesis leg is outside the circle.
Fig 6.
Optimal walking speeds for circle walking.
Minimizing the energy cost of walking in a circle predicts slower walking for smaller circles. Error bars indicate one standard error about the mean, and these are generally within the set of all speeds within 1% of the optimal energy costs (the shaded bands shown). The cost coefficients used here are obtained via inverse optimization and shown in Table 5. This qualitative trend of lower speeds for smaller circles is predicted as long as the steady energy cost coefficients a0 and a2, and the turning cost coefficient aturn are positive. At R → ∞ (Inf), the path is a straight line and the human speed data reported is for the longest bout performed (23 m).