Issues in the design of passive controllers for flexible link robots

In this paper, issues in the design of passive controllers for flexible link robots are discussed. It is well known that, for the single flexible link manipulator, the mapping from the input torques to the joint velocities is passive whereas the mapping from the input torques to the derivative of net tip movements (the usual output chosen) is not. However, if an appropriate output variable is selected, the transfer function, can be made passive provided that the hub inertia seen by the flexible link is sufficiently small. Then, by the passivity theorem, using any strictly passive controller with finite gain will result in an L₂-stable system. However, for an an industrial robot, the effective hub inertia seen by the flexible link is usually large. Alternate approaches are examined for extending these passivity results to large hub inertias. Experimental results are presented for a 5-bar-linkage manipulator with the last link being flexible