Inverse dynamics based control system for a three-degree-of-freedom flexible arm

This article describes a new control scheme designed for a three-degree-of-freedom flexible arm. This arm has been built with light links, has most of its mass concentrated at the tip, and uses a special mechanical configuration to approximately decouple tip motions in spherical coordinates. This configuration facilitates the dynamic modeling and control of the arm. A compliance matrix can be used to model the oscillations of the structure. A consequence of this simple dynamic is that minimum sensing effort is required (only direct motor and tip measurements), and the use of complex observers is avoided because the state of the system can be very easily obtained from these measurements. A two-nested control-loop scheme is used to control the tip position by using joint position and tip acceleration feedbacks. The stability of the controlled system is analytically proven in the case of perfect dynamic modeling. Then, an analysis of stability in the case of modeling errors is carried out, and conditions for local stability are derived. Experimental results are presented for the cases of perturbation control and trajectory tracking. Comparative results between controlled and noncontrolled tip responses are also shown.