Optimization-based motion prediction of mechanical systems: sensitivity analysis

In this study, we derive sensitivity equations for the problem of optimization-based motion prediction of a mechanical system using the inverse recursive Lagrangian formulation. The simulation and sensitivity formulations are based on Denavit–Hartenberg transformation matrices. External forces and moments are taken into account in the formulation. The sensitivity information is needed in the optimization-based simulation process. The proposed formulation is demonstrated by calculating sensitivities for the optimal time trajectory planning problem of a two-link manipulator. In addition, sensitivities obtained using the proposed algorithm are compared to those obtained using the closed-form equations of motion. The two sensitivities match quite closely. The lifting motion of the two-link manipulator with external loads is also optimized by using the algorithm developed in this paper. More complex applications of the proposed formulation to digital human motion prediction are presented elsewhere.