A revised Durbin-Wu-Hausman test for industrial robot identification

• The Durbin-Wu-Hausman-test extended to identification of industrial robots.
• The Revised DWH-test based on general statistical assumptions.
• Validation/invalidation of the instruments constructed by the user.
• Validation/invalidation of the LS estimates.
• Experimental validation on a 6-DOF industrial robot.

This paper addresses the topic of robot identification. The usual identification method makes use of the inverse dynamic model (IDM) and the least squares (LS) technique while robot is tracking exciting trajectories. Assuming an appropriate bandpass filtering, good results can be obtained. However, the users are in doubt whether the columns of the observation matrix (the regressors) are uncorrelated (exogenous) or correlated (endogenous) with the error terms. The exogeneity condition is rarely verified in a formal way whereas it is a fundamental condition to obtain unbiased LS estimates. In Econometrics, the Durbin-Wu-Hausman test (DWH-test) is a formal statistic for investigating whether the regressors are exogenous or endogenous. However, the DWH-test cannot be straightforwardly used for robot identification because it is assumed that the set of instruments is valid. In this paper, a Revised DWH-test suitable for robot identification is proposed. The revised DWH-test validates/invalidates the instruments chosen by the user and validates the exogeneity assumption through the calculation of the QR factorization of the augmented observation matrix combined with a F-test if required. The experimental results obtained with a 6 degrees-of-freedom (DOF) industrial robot validate the proposed statistic.