Nonlinearity measurements via auto-tune test in robotics

In robotics actuators and manipulators are usually described by highly nonlinear models. Also for a manipulator dynamics with respect to a given equilibrium pOint, the linearized model must be considered along with some nonlinearity in order to get a significative global model. By assuming that a static nonlinear element is in series with a dynamic element we have a Hammerstein (Wiener) model if the nonlinearity precedes (follows) the linear dynamic part. In this paper a nonlinear auto-tuning by relay-feedback is used for the determination of both the linear part and the static nonlinearity of the model. In the conventional auto-tune test developed by Astrom-Hagglund a relay is placed in the loop and from the resulting limit cycle the critical gain and the critical frequency are measured. The non linear auto-tune method makes use of many relay-feedback tests with different relay amplitudes and different known dynamic elements inserted in the loop. By a suitable modification of the relay characteristics it is possible to compute points of the nonlinear characteristic. The effectiveness of this technique is demonstrated on a simulated example: the stiffness control of a simple robotic manipulator.