The Effective Inertia of the Lower Limb During Locomotion

Accurate modelling of inertial properties of human lower limbs is of great interest to many tasks, from gait analysis in biomechanics to motion tracking and control in computer animation. Previous work typically simplified the human musculoskeletal structure as a chain of rigid capsules, with muscle mass lumped with body segments. Such simplifications lead to errors in the inertia matrix, and the error propagates to torque and pose estimates. In this study, we developed a data-driven model to represent the joint-space inertia of the lower-body of a human in motion. The model does not make any assumptions other than that the estimated inertia matrices must be symmetric and positive definite. We show that a joint-space inertia matrix, estimated from synchronized motion and ground force data following foot strikes, reveals inertial coupling, and that estimated inertia matrices are bilaterally symmetric and motion-type dependent. These are properties which a rigid, mass-lumped inertia matrix fails to entail. Moreover, we show that the data-driven model fits to data better than the articulated rigid body inertia model, and that when used for reconstructing lower body kinematics estimated inertia yields more accurate and stable motion.