Issues in the design of passive controllers for flexible-link robots

In this article, issues in the design of passive controllers for a class of multilink manipulators with the last link flexible 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 cart be made passive, provided that the hub inertia seen by a flexible link is sufficiently small. Then, by the Passivity theorem, using any strictly passive controller with finite gain will result in an L-2-stable system. However, for a multilink industrial robot, the effective hub inertia seen by the flexible link is usually large. In addition, the dynamic equations are highly nonlinear. Approaches are examined for extending these passivity results to multilink manipulators. Experimental results are presented for a five-bar-linkage manipulator with the last link being flexible.