End-Point Control of a Two-Link Manipulator with a Very Flexible Forearm: Issues and Experiments

An important consideration when designing a control system is where to place sensors. For mechanical manipulators, a logical sensor location is at the manipulator end-point where tasks are performed. Unfortunately, when bending flexibility exists between an end-point sensor and a joint actuator, stability and performance are achieved only through a sophisticated control design. Some of the issues involved in utilizing end-point sensing for two-link flexible manipulators are addressed in this paper. First, a modelling technique is presented that properly represents the foreshortening of a flexible link undergoing deflections, as are the resulting terms that appear in the equations of motion. An example illustrates how this technique corrects a simulation that otherwise incorrectly predicts that the manipulator end-point will exceed workspace limits. Next, in order to realize fully the advantages of the assumed-modes modelling method, mode shapes are selected that allow a low-order model to be used effectively for simulation and control purposes. Then, a nonlinear controller, incorporating state feedback and a constant gain extended Kalman filter driven by end-point measurements, is designed and compared to a conventional proportional-plus-derivative controller that uses collocated sensors. Finally, the results are presented from implementing these controllers on the experimental Stanford Multi-Link Flexible Manipulator configured with a rigid upper arm and a very flexible forearm.