Developing Equations of Motion for a Planar Biped Walker with Nonuniform Foot Shape

Foot shape can strongly influence performance and efficiency in bipedal gait, playing a critical role in both human and robot walking. While flat feet and circular feet are common in human models, a more general shape may better capture the effective foot shape of humans, leading to an improved simulation-experimental match. The key challenge in modeling a biped with a nonuniform foot shape is locating the ankle as the foot rolls forward so that the equations of motion can be derived. This work develops a method to find the equations of motion for a planar biped whose foot shape can be modeled as any convex, continuously differentiable function. The method is demonstrated using a six-link, planar biped model with nonuniform, curved feet. Using nonlinear constrained optimization, valid gaits were identified for foot shapes parameterized by circular, elliptical, and polynomial functions. The resulting gaits were compared to experimental spatiotemporal and kinematic walking data from one human subject. The polynomial model both best approximated the subject’s foot shape and best matched the experimental spatiotemporal behavior and stance ankle angle trajectory, confirming the viability of the method for both simulating gait and matching human walking.