Defining Kinematic Chains for Musculoskeletal Optimal Control Simulations via Automatic Differentiation - Penner, Johann; Leyendecker, Sigrid (Proceedings of the 6th International Digital Human Modeling Symposium, 2020)
Many digital human model applications are based on optimal control simulations of the musculoskeletal system. These simulations usually involve the derivatives of the underlying kinematic and dynamic model, which are in general not easy to derive analytically. In the direct transcription method DMOCC, we use the discrete Euler-Lagrange equations together with a discrete null space matrix and a nodal reparametrization, which are embedded into a constrained optimization problem. The abstract and formalizable structure of this method offers many possibilities for automation. Therefore, we use the CasADi nonlinear optimization and algorithmic differentiation tool to automatically derive the discrete Euler-Lagrange equation and a valid discrete null space matrix. This allows us an efficient and easy implementation of the DMOCC method for large multibody systems.<br