Figure 1.
Experimental protocols and theoretical models. (a) Subject walking with oscillating speeds on a constant-speed treadmill, walking faster and slower than the belt, moving between two prescribed positions. A longitudinal bungee cord (never to be made taut) constrains the rear-most position and a bungee cord perpendicular to sagittal plane (not shown, never to be touched) constrains the forward-most position. (b) Sacral marker fore–aft velocities, original and smoothed. (c) A nine-step periodic inverted pendulum walking motion, with five steps faster and four steps slower than the mean speed. Initial and final stance-leg directions are shown for each step (red and blue). Details of one step-to-step transition are shown; downward velocity at the end of one step is redirected by push-off and heel-strike impulses. (d) Measuring preferred walking speeds as a function of bout distance D; subjects start and stop at rest. (e) An idealized bout: human travels the whole distance D at single speed vopt, starting and stopping instantaneously.