Diagnosis in Robotic Systems
\n1410 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 8, NO. 6, NOVEMBER 1997
\nNeural-Network-Based Robust Fault
\nDiagnosis in Robotic Systems
\nArun T. Vemuri, Member, IEEE, and Marios M. Polycarpou, Member, IEEE
\nAbstract\u2014Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have
\nproposed fault diagnosis architectures for robotic manipulators
\nusing the model-based analytical redundancy approach. One of
\nthe key issues in the design of such fault diagnosis schemes is
\nthe effect of modeling uncertainties on their performance. This
\npaper investigates the problem of fault diagnosis in rigid-link
\nrobotic manipulators with modeling uncertainties. A learning
\narchitecture with sigmoidal neural networks is used to monitor
\nthe robotic system for any off-nominal behavior due to faults. The
\nrobustness and stability properties of the fault diagnosis scheme
\nare rigorously established. Simulation examples are presented
\nto illustrate the ability of the neural-network-based robust fault
\ndiagnosis scheme to detect and accommodate faults in a two-link
\nrobotic manipulator.
\nIndex Terms\u2014 Adaptive law, analytical redundancy, fault accommodation, fault diagnosis, learning architecture, nonlinear
\nfault diagnosis, neural networks, robotic systems, robust fault
\ndiagnosis.
\nI. INTRODUCTION
\nROBOTIC systems are integral components of many com- plex engineering systems including manufacturing processes [1] and space-based systems [2]. Stricter operational
\nand productivity requirements in such systems are resulting in
\nrobotic manipulators working near their design limits for much
\nof the time. This may often lead to robotic system failures
\nwhich are typically characterized by critical changes in the
\nrobotic system parameters or even by nonlinear changes in the
\ninherent dynamics of the manipulator. Robotic system failures
\ncan potentially result not only in the loss of productivity
\nbut also can lead to unsafe operation of the system. In
\ngeneral, modern control systems which are designed to handle
\nsmall perturbations that may arise under \u201cnormal\u201d operating conditions (in the \u201clinear\u201d regime) cannot accommodate
\nabnormal behavior due to faults. Hence automated health
\nmonitoring of robotic systems and effective accommodation
\nof any faults play a crucial role in the operation of modern
\nrobotic systems and especially autonomous and intelligent
\nrobotic manipulators.
\nThe design and analysis of fault diagnosis (FD) architectures
\nfor robotic systems using the model-based analytical redundancy approach has received considerable attention [2]\u2013[4].
\nManuscript received April 14, 1996; revised September 23, 1996, February
\n20, 1997, and August 17, 1997.
\nA. T. Vemuri is with the Department of Engine and Vehicle Research,
\nSouthwest Research Institute, San Antonio, TX 78238-5166 USA.
\nM. M. Polycarpou is with the Department of Electrical and Computer
\nEngineering, University of Cincinnati, Cincinnati, OH 45221-0030 USA.
\nPublisher Item Identifier S 1045-9227(97)08093-4.
\nIn this approach, quantitative nominal models of the robotic
\nsystem together with sensory measurements are used to provide estimates of measured and\/or unmeasured variables. The
\ndeviations between estimated and measured signals provide
\na residual vector which can be utilized to detect and isolate
\nsystem failures. In general, a fault is declared if a measure of
\nthe residual vector exceeds a certain threshold value. An alternative to analytical redundancy is the hardware redundancy
\napproach, where additional physical instrumentation is used to
\nprovide the necessary redundancy [5].
\nThe appeal of model-based FD schemes lies in the fact that
\nthe redundancy required for detecting faults is created using
\npowerful information processing techniques without the need
\nof additional physical instrumentation in the system. However,
\nthe model-based FD approach relies on the key assumption that
\na mathematical characterization of the manipulator is known a
\npriori. In practice, this assumption is usually not valid since it
\nis difficult to obtain the necessary modeling accuracy required
\nfor the construction of reliable analytical redundancy-based
\nFD architectures. Unavoidable modeling uncertainties, which
\narise due to modeling errors, time variations, measurement
\nnoise, and external disturbances, deteriorate the performance
\nof FD schemes by causing false alarms. This necessitates
\nthe development of FD algorithms which have the ability
\nto detect manipulator failures in the presence of modeling
\nuncertainties. Such algorithms are referred to as robust fault
\ndiagnosis schemes.
\nThe construction of robust FD architectures for robotic
\nmanipulators has been investigated to a limited extent. In
\n[6], Schneider and Frank use threshold adaptation based on
\nfuzzy logic to improve robustness of state-space model-based
\nFD architectures. Time-varying state-dependent thresholds are
\nused in [7] to achieve robustness in parity relations based
\nFD schemes for remote robots. These studies rely on two
\nkey assumptions: 1) the nominal model of the system is
\nlinear and 2) the failures are modeled as external additive
\ninputs (functions of time). Although it is convenient from an
\nanalytical viewpoint to study the FD problem in a linear system
\nframework, the dynamics of robotic systems are inherently
\nnonlinear. Furthermore, most practical failures are nonlinear
\nfunctions of the state and input.
\nThis paper presents a learning methodology for robust fault
\ndiagnosis in rigid-link robotic manipulators, which is based on
\na nonlinear nominal model of the manipulator and nonlinear
\ndeviation faults. The modeling uncertainties are assumed to be
\nbounded while the faults are modeled as nonlinear functions
\nof the measured variables. The principal idea behind this
\n1045\u20139227\/97$10.00 \uf8e9 1997 IEEE
\nAuthorized licensed use limited to: WRIGHT STATE UNIVERSITY. Downloaded on December 28, 2008 at 09:49 from IEEE Xplore. Restrictions apply.
\nVEMURI AND POLYCARPOU: ROBUST FAULT DIAGNOSIS IN ROBOTIC SYSTEMS 1411
\napproach is to monitor the plant for any off-nominal system
\nbehavior (which could be either due to faults or uncertainties)
\nutilizing a sigmoidal neural network. By using the knowledge
\nof the bound on the uncertainty we develop a systematic
\nprocedure, based on neuro-control techniques, for identifying
\nthe effects of system failures in the presence of modeling
\nuncertainties. The neural network not only is used to detect
\nthe occurrence of the fault but it also provides a postfault
\nmodel of the robotic manipulator. This postfault model can
\nbe effectively used to isolate and identify the fault and, if
\npossible, for accommodation of the failure.
\nThe fault diagnosis scheme described in this paper is rigorously analyzed for robustness and stability. Specifically, the
\nrobustness result addresses the FD system performance in the
\npresence of modeling uncertainties prior to the occurrence of
\nany faults while the stability property characterizes the FD
\nsystem performance after the occurrence of the fault.
\nThe organization of this paper is as follows: In Section II,
\nthe robot dynamics and its control law are described, and
\nthe fault diagnosis problem is formulated. In Section III,
\nthe neural-network-based robust fault diagnosis scheme is
\ndescribed. The analytical properties of the robust FD algorithm are established in Section IV. Simulation examples
\nillustrating the performance of the FD algorithm on a two-link
\nrobotic manipulator with modeling uncertainties are presented
\nin Section V. Section VI has some concluding remarks.
\nII. PROBLEM FORMULATION<\/p>\n
Consider a robotic manipulator described by\tmodel a much larger class of failures [in the framework of
\n(4)] is the need to approximate unknown nonlinear functions.
\nAssignmentTutorOnline<\/p>\n
(1)
\nand software simulation tools have rendered possible the use
\nwhere are vectors of joint positions, velocities
\nand accelerations, respectively, is the input torque
\nof on-line approximators such as sigmoidal neural networks
\nfor constructing and analyzing nonlinear models [12], [13].
\nvector, is the inertia matrix (whose inverse\tIn light of the above, the objective of this paper is to
\nexists [8], [9]), is a matrix containing the
\ncentripetal and Coriolis terms, is the gravity vector,
\nis a vector containing the unknown static and
\ndynamic friction terms, and is a vector representing<\/p>\n
unknown additive bounded disturbances and noise. The term
\nis a vector which represents the fault in the
\nrobot manipulator, represents the time profile of
\nthe fault, and is the time of occurrence of the fault.
\nThe control objective of the robotic system (1) is to follow
\na desired trajectory. A number of techniques are available in
\nthe literature for deriving position control laws for robotic
\nmanipulators in the presence of modeling uncertainties and in
\nthe absence of faults (i.e., ) [8], [10], [11]. Without any
\nloss of generality, in this paper we use the computed-torque
\nmethod to obtain a trajectory-tracking controller for the robotic
\nmanipulator described by (1). The controller derived using this
\nmethod relies on the position and velocity measurements of\tA1) The failure is abrupt and occurs at some unknown time
\ni.e., the time-profile of the failure is given by
\neach link and the nominal model given by\t(2)\tIII. FAULT DIAGNOSIS ARCHITECTURE
\nIn this section, we describe a robust nonlinear fault diagnosis
\nif
\nif
\nA2) The robotic system states remain bounded after the
\noccurrence of a fault; i.e., .
\nA3) The modeling uncertainty is bounded; i.e.,
\nwhere is a known constant and is
\nsome compact domain of interest.
\nThe structure of the computed torque controller is described by
\n(3)
\nwhere is the desired trajectory, is the tracking
\nerror, is an diagonal matrix of damping gains,
\nis an diagonal matrix of position gains. If the robot
\ndynamics are known exactly, then these matrices can be chosen
\nso that the control law leads to an exponentially convergent
\ntracking error [8], [9].
\nIn the remaining portion of the paper, since the above
\ncomputed torque control law is a function of and only,
\nwe represent the robotic manipulator model (1) as
\n(4)
\nwhere . Note that the friction and the
\ndisturbance terms in (4) are assumed to represent the modeling
\nuncertainties in the system.
\nA fault in the robotic system changes the dynamics of the
\nmanipulator in an unpredictable way. An accurate description
\nof fault conditions, most often, requires nonlinear modeling of
\nfaults, which is what is described by in (4). The nonlinear
\nmodeling capability is reflected in allowing the deviation
\ndue to faults to be a nonlinear function of the joint positions
\nand velocities. It is important to note that the fault formulation
\ndescribed by (4) allows nonadditive types of faults. For
\nexample, if the matrix changes to due to a fault
\nat time then this can be represented by letting
\nWe refer to FD schemes that
\nare based on such nonlinearly modeled faults as nonlinear FD
\nschemes. The price that one has to pay for the potential to
\nHowever, recent advances in both hardware implementation
\ndevelop a robust nonlinear fault diagnosis architecture with
\nguaranteed robustness and stability properties for the robotic
\nsystem described by (4). We make the following assumptions
\nthroughout the paper.
\narchitecture for detecting system faults in robotic manipulators described by (4). We begin by observing that in the
\nabsence of modeling uncertainties any off-nominal behavior
\nAuthorized licensed use limited to: WRIGHT STATE UNIVERSITY. Downloaded on December 28, 2008 at 09:49 from IEEE Xplore. Restrictions apply.
\n1412 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 8, NO. 6, NOVEMBER 1997
\nobserved from input\u2013output measurements can be attributed
\nto a fault in the robotic system. Thus, the process of fault
\ndetection in the absence of modeling uncertainties can be
\nachieved by approximating, on-line, the unknown function
\n[14]\u2013[16]. However, in the presence of modeling
\nuncertainties, the difference in the dynamics could be either
\ndue to faults or due to modeling uncertainties. Therefore, a
\nkey question is: how does one identify the effects of a fault in
\nthe presence of modeling uncertainties? In the special case that
\nthe modeling uncertainties have certain known characteristics
\nthat distinguish them from faults, then any off-nominal system
\nbehavior provided by the neural network can be classified
\n(for example, via pattern and signal classification methods) as
\nbeing due to either faults or modeling uncertainties. However,
\nin most practical manipulators, both faults and modeling uncertainties are unknown a priori. Hence the issue of robustness
\nis very important.
\nFrank [17] describes a robust fault detection algorithm
\nwhich, while providing an on-line estimate of the uncertainty
\nlevel, deals exclusively with the detection of faults. In the context of fault diagnosis, in addition to detecting the occurrence
\nof a fault, it would be useful to obtain an approximation of
\nthe fault function. In this paper, we develop a robust fault
\ndiagnosis algorithm for detecting faults in the presence of
\nmodeling uncertainties that satisfy the bounding condition A3.
\nAn estimate of the fault function is obtained provided that the
\nratio between the fault function magnitude and the modeling
\nuncertainty level is sufficiently large. Note that Assumption
\nA3 allows the derivation of a robust fault diagnosis algorithm
\nwhich is based on bounded unstructured uncertainty.
\nA. Nonlinear Estimation Model
\nA key objective of this paper is to design a fault diagnosis
\narchitecture for the robotic manipulator described by (4) using
\nthe approximation properties of sigmoidal neural networks. In
\nthis section, the construction of a neural-network-based nonlinear estimation model is described. Utilizing this estimation
\nmodel, a learning algorithm for updating the parameters of the
\nneural network so that it approximates any off-nominal behavior due to faults, in the presence of modeling uncertainties that
\nsatisfy Assumption A3, is described in the next section.
\nWe consider an estimated model of the form
\n(5)
\nwhere is the estimate of the velocity vector of the
\nmanipulator joints, is a design constant, is a threelayered sigmoidal neural network and represents the
\nadjustable weights of the network in vector form. If the number
\nof neurons in the hidden layer is , then (see the
\nAppendix for details of this representation of a three-layered
\nsigmoidal neural network).
\nThe estimation model (5) is a nonlinear observer-type
\nscheme that can be implemented in the form of stable filter as
\nwhere is the output of the first-order filter ,
\nwith the filter input given by
\nThe construction of an appropriate estimation model, able
\nto follow any changes in the input\u2013output behavior of the
\nphysical system, is a crucial component in the development
\nof the overall fault detection scheme. The output of the above
\nnonlinear estimation model is used to update the weights of the
\nneural network. The nonlinear estimation model (5) is not only
\neasy to implement but, more importantly, has some desirable
\nstability and performance properties, which are presented in
\nthe next section.
\nThe initial weight vector, of the neural network
\nis chosen such that
\n(6)
\ncorresponding to the no-failure situation, while the initial value
\nof the estimator is selected as . Note that the weight
\ninitialization given by (6) can be achieved by simply setting the
\nweights of the output layer to zero. Starting from these initial
\nconditions, the main objective is to adjust (using input\u2013output
\ninformation) the weight vector at each time so that
\napproximates the unknown function
\nOnce this is achieved then the output of the neural network
\ncan be used to detect, diagnose, and accommodate system
\nfailures.
\nB. Learning Algorithm<\/p>\n
0000000000<\/p>\n
Diagnosis in Robotic Systems 1410 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 8, NO. 6, NOVEMBER 1997<\/p>\n
Neural-Network-Based Robust Fault<\/p>\n
Diagnosis in Robotic Systems<\/p>\n
Arun T. Vemuri, Member, IEEE, and Marios M. Polycarpou, Member, IEEE<\/p>\n
Abstract\u2014Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have<\/p>\n
proposed fault diagnosis architectures for robotic manipulators<\/p>\n
using the model-based analytical redundancy approach. One of<\/p>\n
the key issues in the design of such fault diagnosis schemes is<\/p>\n
the effect of modeling uncertainties on their performance. This<\/p>\n
paper investigates the problem of fault diagnosis in rigid-link<\/p>\n
robotic manipulators with modeling uncertainties. A learning<\/p>\n
architecture with sigmoidal neural networks is used to monitor<\/p>\n
the robotic system for any off-nominal behavior due to faults. The<\/p>\n
robustness<\/p>\n","protected":false},"excerpt":{"rendered":"
Diagnosis in Robotic Systems 1410 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 8, NO. 6, NOVEMBER 1997 Neural-Network-Based Robust Fault Diagnosis in Robotic Systems Arun T.\u2026<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9033,7586,1386,7589,9034,9031,7587,7588,7584,7585,9032],"tags":[8809,7838,8811,8808,8813,8807,8806,8814,8810,8812],"class_list":["post-106961","post","type-post","status-publish","format-standard","hentry","category-assignment-help-uae","category-best-dissertation-writing-service-in-australia","category-best-research-paper-writing-services-in-usa","category-capstone-project-writing-service","category-cheap-essay-writing-services-china","category-essay-writing-service-usa","category-legitimate-phd-dissertation-writing-services-usa","category-term-paper-writing-service","category-thesis-writing-service-in-canada","category-uae-best-dissertation-writing-help-service","category-write-my-essay-australia","tag-best-master-thesis-writing-service","tag-best-thesis-writing-services","tag-cheap-thesis-writing-services","tag-master-thesis-help","tag-master-thesis-writing-service","tag-thesis-help-online-free","tag-thesis-writing-help-online","tag-thesis-writing-services-cost","tag-thesis-writing-services-near-me","tag-thesis-writing-services-reviews"],"_links":{"self":[{"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/posts\/106961","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/comments?post=106961"}],"version-history":[{"count":0,"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/posts\/106961\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/media?parent=106961"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/categories?post=106961"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.studyproessays.com\/help\/wp-json\/wp\/v2\/tags?post=106961"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}