Fault Detection based on Orthotopic Set Membership Identification for Robot Manipulators Vasso Reppa ∗ Anthony Tzes ∗ ∗ Department of Electrical and Computer Engineering, University of Patras, Rio, Achaia, 26500, Greece (Tel: +30-2610-997293; e-mail: (reppa,tzes@ece.upatras.gr). Abstract: In this article a fault detection algorithm for capturing structural and/or sensor failures in robot manipulators is presented. The robot dynamics is linearizable with respect to a certain parameter. Using this linearizable representation, common faults in robot arms, such as failures of actuators or faulty sensor measurements, can be identified as variations encountered in the parameter vector. The proposed algorithm uses an Orthotopic Set Membership Identifier that defines the feasible parameter set and the parameters’ bounds, within which the Weighted Recursive Least Square parameter estimate resides. An Uncertainty Output Predictor that generates the future region of faultless system operation. A fault is detected, when one of the following criteria below is validated: a) the WRLS parameter estimate resides out of the parameters’s bounds, b) there is a sudden increase in the volume of the feasible set and c) the system’s output is not within the predicted interval. Simulation studies are offered to test this fault detection methodology, customized to a two-link robot arm. 1. INTRODUCTION From a general point of view, the fault diagnosis problem is concerned with the detection of time instants where there is a significant difference in the nominal system’s behavior. The next step is the detection of the reason of the fault occurrence. In case of robot manipulators, De Luca et al. [2005] determine a fault as the unexpected behavior observed in its torques, when a technical failure occurs. Dixon et al. [2000], Shin et al. [1999] report a Fault Detection Scheme targeting failures of actuators or active bias to a sensor measurement etc. Similarly, a false operation in its workspace, because of accidental collision with unknown obstacles or manipulating an unknown load has been reported in De Luca et al. [2005] and Spong [2001], respectively. The classical statistical methodology for fault detection is based on a fault indicator, or residual, which is computed via a specific model and observation, and defines a fault symptom De Luca et al. [2003], Yen et al. [2000], Green- wood [2005], Zhang et al. [2004]. This method is applied mostly in case of sensor failures in robot manipulators. On the other hand, the deterministic methodology for fault detection concerns set-membership approach, which takes into account a priori knowledge of model uncertainties and measurement errors Adrot et al. [2002], Milanese et al. [2003], Fagarasan et al. [2004], Ploix et al. [2001]. The goal of the set-membership approach is the characterization of a set of all parameter vectors that are consistent with the data, model structure and bounded noise errors, called fea- sible parameter set. In most techniques, the system output must be linearizable with respect to parameter vector. The benefit of the second methodology is the utilization of the parameter’s intervals that arise from polytopes Chischi et al. [1998], Ingimundarson et al. [2005], bounding the feasible parameter set. ⋆ This work was partially supported by University of Patras’ K. Karatheodoris research initiative program In this paper, a Fault Detection (FD) algorithm based on the interactive relation of an Orthotopic Set Membership Identifier (OSMI) and an Uncertainty Output Predictor is presented. The OSMI uses two geometric approaches: the ellipsoid Cheung et al. [1993], Fogel et al. [1982], Milanese et al. [1982], for the characterization of the feasible parameter set and the orthotope Le et al. [1997], Tzes et al. [1999], bounding the ellipsoid, for the computation of parameters’ bounds. The center of both the ellipsoid and the orthotope is the Weighted Recursive Least Square (WRLS)parameter estimate, and its volume reflects the parameter uncertainties, being induced from the bounded noise error. The vertices of the orthotope represent the parameter interval Walter et al. [1990], Fagarasan et al. [2001]. The bounds of the parameter interval are the inputs to the Uncertainty Iput/Output Predictor that generates the limited region of proper system operation. Finally, the fault detection is accomplished, when: a) the WRLS estimate of the parameter vector does not reside within the computed bounds, or b) the volume of the ellipsoid is suddenly increased Reppa et al. [2007] and c) the systems output is not within the predicted limited region Reppa et al. [2006]. This paper is structured in the following manner. The non linear system dynamics of a robot arm and the inherent assumptions that must be satisfied for the proper application of the FD-methodology are presented in the next section. The mathematical preliminaries of the OSMI is detailed in section 3, followed by the simulation studies and the conclusive remarks. 2. PROBLEM STATEMENT The dynamic equation of an m-link robot manipulator is given from the Euler-Lagrange theory as: M (q)¨ q + C(q, ˙ q)+ G(q)= τ (1) Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-11, 2008 978-1-1234-7890-2/08/$20.00 © 2008 IFAC 7344 10.3182/20080706-5-KR-1001.1510