Modeling and simulation of human gait in three dimensions with multibond graphs

Abstract

Multibond graphs are used to derive a model and equations for the simulation of human gait. A simple model consists of seven rigid bodies. The connections between the bodies are pin joints with only rotational degrees of freedom. Floor contact is approximated as a spherical joint to a body (earth) which has zero velocity. During contact, the connection point (center of support) shifts along the foot. The resultant of torques, caused by active (muscle) forces, are applied to the bodies via the joints. For the description of the kinematics and dynamics of the system, body-fixed coordinate frames are chosen. Euler parameters are used in the calculation of coordinate transformation. Due to the kinematic constraints between the bodies, the inertias are not causally independent. From the multibond graph a set of implicit differential and algebraic equations can be derived, which can be solved with an iterative numerical technique. To solve the closed kinematical loop during the double support phase, additional implicit equations can be formulated and solved with the same numerical technique. Different models are formulated for the different phases in gait in order to deal with the discontinuity caused by the floor contact. The model can be simulated when input data (resultant torques, center of support), parameter values and data on initial condition ( position and velocity) are available.