Feed-forward control of link mechanisms under various boundary conditions by using a parallel solution scheme

We describe a parallel solution scheme for inverse dynamics, and its application to feedforward control of link mechanisms under various boundary conditions. The conditions include such cases as open- and closed-loops, and even one that continuously changes its form from an open- to a closed-loop. The dynamic equations conducted by generally used schemes such as the Newton-Euler method or the Lagrangian method, include interdependent variables between the constituting links which make it highly complicated to derive inverse dynamics of the closed-loop link mechanisms, or of the continuously transforming ones. The proposed scheme is developed by using the finite element method (FEM), and evaluates the entire system as a continuum. The system is subdivided into finite elements, and the nodal forces are evaluated by equations of motion in a matrix form. The joint torque in the system is then calculated by converting the obtained nodal forces. Therefore, information from the entire system can be handled in parallel, which makes it seamless in application to open/closed-loop or continuously transforming mechanisms. The control results of link mechanisms under various boundary conditions reveal the possibility of using the proposed solution scheme for feedforward control, independent of the system configuration of link mechanisms.