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

Abstract 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.

[1]  J. MacKinnon,et al.  Estimation and inference in econometrics , 1994 .

[2]  Mikael Norrlöf,et al.  Closed-Loop Identification of an Industrial Robot Containing Flexibilities , 2003 .

[3]  Denny Oetomo,et al.  Neuro-adaptive motion control with velocity observer in operational space formulation , 2011 .

[4]  Ioan Doré Landau,et al.  Identification in closed loop: a powerful design tool (better design models, simpler controllers) , 2001 .

[5]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[6]  Jan Swevers,et al.  Dynamic model identification for industrial robots - Integrated experiment design and parameter estimation , 2007 .

[7]  Jan Swevers,et al.  Maximum Likelihood Identification of a Dynamic Robot Model: Implementation Issues , 2002, Int. J. Robotics Res..

[8]  Jeffrey M. Wooldridge,et al.  Introductory Econometrics: A Modern Approach , 1999 .

[9]  Wisama Khalil,et al.  Modeling, Identification and Control of Robots , 2003 .

[10]  P. Poignet,et al.  Robust dynamic experimental identification of robots with set membership uncertainty , 2005, IEEE/ASME Transactions on Mechatronics.

[11]  Maxime Gautier,et al.  A Generic Instrumental Variable Approach for Industrial Robot Identification , 2014, IEEE Transactions on Control Systems Technology.

[12]  P. Young,et al.  Optimal instrumental variable method for closed-loop identification , 2011 .

[13]  Alexandre Janot,et al.  An instrumental variable approach for rigid industrial robots identification , 2014 .

[14]  Maarten Steinbuch,et al.  Modeling and identification for high-performance robot control: an RRR-robotic arm case study , 2004, IEEE Transactions on Control Systems Technology.

[15]  J. Hausman.  Specification tests in econometrics , 1978 .

[16]  M. Gautier.  Numerical calculation of the base inertial parameters of robots , 1991, J. Field Robotics.

[17]  Liuping Wang,et al.  Identification of Continuous-time Models from Sampled Data , 2008 .

[18]  Graham C. Goodwin,et al.  On the Optimality of Open and Closed Loop Experiments in System Identification , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[19]  Maxime Gautier,et al.  A Durbin-Wu-Hausman test for industrial robots identification , 2013, 2013 IEEE International Conference on Robotics and Automation.

[20]  Koichi Osuka,et al.  Base parameters of manipulator dynamic models , 1990, IEEE Trans. Robotics Autom..

[21]  Maxime Gautier,et al.  New criteria of exciting trajectories for robot identification , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[22]  Antonio Visioli,et al.  Optimized Dynamic Calibration of a SCARA Robot , 2002 .

[23]  Peter C. Young,et al.  Recursive Estimation and Time-Series Analysis: An Introduction , 1984 .

[24]  Graham C. Goodwin,et al.  Choosing Between Open- and Closed-Loop Experiments in Linear System Identification , 2007, IEEE Transactions on Automatic Control.

[25]  Maxime Gautier,et al.  A New Closed-Loop Output Error Method for Parameter Identification of Robot Dynamics , 2010, IEEE Transactions on Control Systems Technology.

[26]  Fengfeng Xi.  Effect of non-geometric errors on manipulator inertial calibration , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[27]  J. De Schutter,et al.  Dynamic Model Identification for Industrial Robots , 2007, IEEE Control Systems.

[28]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[29]  Antonella Ferrara,et al.  MIMO Closed Loop Identification of an Industrial Robot , 2011, IEEE Transactions on Control Systems Technology.

[30]  Jun Nakanishi,et al.  A Bayesian Approach to Nonlinear Parameter Identification for Rigid Body Dynamics , 2006, Robotics: Science and Systems.

[31]  M. Gautier,et al.  Exciting Trajectories for the Identification of Base Inertial Parameters of Robots , 1992 .

[32]  P. Poignet,et al.  Extended Kalman filtering and weighted least squares dynamic identification of robot , 2000 .

[33]  Yoky Matsuoka,et al.  Modeling and System Identification of a Life-Size Brake-Actuated Manipulator , 2009, IEEE Transactions on Robotics.

[34]  Svante Gunnarsson,et al.  Estimation of Nonlinear Effects in Frequency Domain Identification of Industrial Robots , 2008, IEEE Transactions on Instrumentation and Measurement.