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Feedforward Control of Flexible Link Systems using Parallel solution Scheme

In this paper, a parallel solution scheme of inverse dynamics is revised and applied to flexible link systems where elastic deformation and vibration normally occur in constituting links. The scheme is considered to be valid for link systems with elastic members, as the calculation process of the scheme is based upon a finite element approach. It evaluates the analysed model in absolute Cartesian coordinates with the equation of motion expressed in dimension of force. The calculated nodal forces are converted into joint torques 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 the calculation seamless in application to any type of link system regardless of its boundary conditions or stiffness values. In this paper, the scheme is revised and the calculation time is shortened by applying Bernoulli-Euler beam elements, and it is then combined with a kinematics solution scheme that calculates target trajectories for flexible models. The calculation flow of inverse dynamics is shown for a five-link system, and some feedforward control experiments are carried out on a two-link system with different stiffness links. The accuracies of trajectories and torque values are verified by applying the system to a sensorless, model-based vibration control. The trajectories and torque values are confirmed to be highly accurate compared with the actual data for feedforward control, and the validity of the approach is verified.