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The effects of foot geometric properties on the gait of planar bipeds walking under HZD-based control

It has been hypothesized by many that foot design can influence gait. This idea was investigated in both simulation and hardware for the five-link, planar biped ERNIE controlled under the Hybrid Zero Dynamics paradigm. The effects of walking speed, foot radius, and foot center of curvature location on gait efficiency and kinematics were investigated in a full factorial study of gaits optimized using a work-based objective function. In most cases, the simulation correctly predicted the trends observed in hardware, indicating that simulation can be used for foot design. As expected, increasing walking speed decreased the energetic efficiency. The dominant effect of speed on joint kinematics was to alter the timing of the peak hip flexion. Increasing foot radius up to the length of the shank improved the energetic efficiency and increased the range of motion of the hip and knee joints. Shifting the foot center of curvature location forward altered the energetic efficiency in a manner that interacted with changes in foot radius. The energetically optimal foot center of curvature location was coincident with the shank for a large foot radius and shifted far in front of the shank for a small foot radius. In all cases, the forward shift increased the range of motion of the hip and knee joints. Therefore, a robot designer can achieve similar energetic benefits across a range of speeds with either a larger radius foot or a smaller radius foot whose center of curvature is located forward of the shank.