A superellipsoid-plane model for simulating foot-ground contact during human gait

Musculoskeletal models and forward dynamics simulations of human movement often include foot-ground interactions, with the foot-ground contact forces often determined using a constitutive model that depends on material properties and contact kinematics. When using soft constraints to model the foot-ground interactions, the kinematics of the minimum distance between the foot and planar ground needs to be computed. Due to their geometric simplicity, a considerable number of studies have used point-plane elements to represent these interacting bodies, but few studies have provided comparisons between point contact elements and other geometrically based analytical solutions. The objective of this work was to develop a more general-purpose superellipsoid-plane contact model that can be used to determine the three-dimensional foot-ground contact forces. As an example application, the model was used in a forward dynamics simulation of human walking. Simulation results and execution times were compared with a point-like viscoelastic contact model. Both models produced realistic ground reaction forces and kinematics with similar computational efficiency. However, solving the equations of motion with the surface contact model was found to be more efficient (~18% faster), and on average numerically ~37% less stiff. The superellipsoid-plane elements are also more versatile than point-like elements in that they allow for volumetric contact during three-dimensional motions (e.g. rotating, rolling, and sliding). In addition, the superellipsoid-plane element is geometrically accurate and easily integrated within multibody simulation code. These advantages make the use of superellipsoid-plane contact models in musculoskeletal simulations an appealing alternative to point-like elements.