A Parallel Solution Scheme of Inverse Dynamics for Flexible Manipulators

In this paper, we describe a parallel solution scheme of inverse dynamics, and its application to flexible manipulators where elastic deformation and vibration normally occur in constituting link members. The scheme is developed by using the Finite Element Method (FEM), which evaluates the analyzed model in absolute Cartesian coordinates, with the equation of motion expressed in dimension of force. The calculated nodal forces are converted into joint torques by using a matrix form equation divided into terms of force, transformation between coordinates, and length. Therefore, information from the entire system can be handled in parallel, which makes it seamless in application to any type of link system regardless of its stiffness value. The proposed scheme is combined with a kinematics solution scheme also developed by using the FEM, which conducts target trajectories for flexible manipulators. Numerical tests are carried out on simple link systems to verify the validity of the proposed scheme.