A Durbin-Wu-Hausman test for industrial robots identification

This paper deals with the topic of industrial robots identification. The usual identification method is based on the use of the inverse dynamic model (IDM) and least squares (LS) technique. Good results can be obtained provided that a well-tuned bandpass filtering is used. However, we are always in doubt if regressors are exogenous i.e. statistically uncorrelated with error terms. Surprisingly, in papers dealing with identification of real-world systems, exogeneity assumption is never verified whereas it is a fundamental condition to obtain unbiased estimates. In Econometrics, the Durbin-Wu-Hausman test (DWH-test) is a theoretical method for investigating whether regressors are exogenous or not. The DWH-test makes of the Two Stage Lesat Squares estimator (2SLS) and an augmented LS regression. However, this test cannot be used as is for robots identification: instruments set is supposed to be valid and restrictive statistical assumptions are made while they are quite implausible in practice. In this paper, we aim at bridging the gap between Econometrics and Control engineering practices by introducing a revisited version relevant for robots identification. An experimental validation performed on a 2 degrees of freedom (DOF) robot shows the effectiveness and the usefulness of this revisited DWH-test.