Scaling and Local Marker Coordinates Determination of Musculoskeletal Systems

In this paper, we introduce a new general method for estimation of kinematic parameters for a musculoskeletal model from motion capture data. We shall determine parameters that are constant over the whole sampling period in addition to the time-dependent system coordinates. Being able to do this is critical in situations where local joint coordinates, local marker coordinates or the overall scaling of the rigid multi-body model are not known precisely a priori. Even for small-scale mechanical systems, this yields a large-scale optimization problem with the system coordinates at each sample and the constant parameters as unknowns. We show that, due to the special structure of the linearized Karush-Kuhn-Tucker (KKT) conditions for this problem, it is possible to find a local minimizer efficiently.

We demonstrate the usability of the method on a scaling problem for an 18 degrees of freedom (DOF) 3D model of gait with the motion prescribed from a real motion capture experiment.