Modeling and robust cooperative control of two one-link flexible arms considering bending and torsional vibrations

In this paper, we consider modeling and robust cooperative control of two one-link flexible arms with symmetric rigid end-effecters, of which the bending vibration and torsional vibration are coupled. By using the Hamilton´s principle and the Lagrange multiplier method dynamic equations of the cooperative flexible one-link arms grasping a rigid object are derived. As the obtained boundary conditions of the distributed parameter system are non-homogeneous, we introduce a change of variables to derive homogeneous boundary conditions. On the basis of the solution of an eigenvalue problem related to the distributed parameter system a finite dimensional modal model is derived. We design an optimal controller with low-pass property and a robust controller based on H^∞ control theory. Simulations have been carried out, and the performance of the controllers is compared