Composite computed torque control of robots with elastic motor transmission

The main problem in the control of robots with elastic transmissions between the actuators and the rigid links is caused by the number of control inputs being less than the number of degrees of freedom. This problem has been faced by a composite control law consisting of the conventional `rigid' computed torque controller for link-based trajectory tracking and a `flexible' computed torque part multiplicated with the inverse of the stiffness matrix for stabilization of the elastic deflections. The resultant control system resembles the so-called two-time scale sliding control technique of Slotine and Hong (1987), but in the authors approach the stiffnesses of the elastic motor transmissions do not have to be relatively large neither is there the restriction that there have to be as many motor inputs as elastic transmissions. The goal of the composite controller is that the individual link trajectories will follow the desired trajectories while the elastic-transmission forces/torques, which are not directly constrained by the output specifications, remain on a certain `manifold' due to the natural flexibility behavior of the system. The key concept is illustrated with simulation results of a translation-rotation robot with one torsional-elastic motor transmission