Diagnosis in Robotic Systems
\n1410 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. eight, NO. 6, NOVEMBER 1997
\nNeural-Community-Primarily based Sturdy Fault
\nDiagnosis in Robotic Systems
\nArun T. Vemuri, Member, IEEE, and Marios M. Polycarpou, Member, IEEE
\nSummary\u2014Fault prognosis performs an vital function in the operation of contemporary robotic methods. Numerous researchers have
\nproposed fault prognosis architectures for robotic manipulators
\nutilizing the model-based analytical redundancy method. Considered one of
\nthe important thing points in the design of such fault prognosis schemes is
\nthe impact of modeling uncertainties on their efficiency. This
\npaper investigates the issue of fault prognosis in rigid-link
\nrobotic manipulators with modeling uncertainties. A studying
\nstructure with sigmoidal neural networks is used to observe
\nthe robotic system for any off-nominal conduct on account of faults. The
\nrobustness and stability properties of the fault prognosis scheme
\nare rigorously established. Simulation examples are offered
\nfor instance the flexibility of the neural-network-based sturdy fault
\nprognosis scheme to detect and accommodate faults in a two-link
\nrobotic manipulator.
\nIndex Phrases\u2014 Adaptive legislation, analytical redundancy, fault lodging, fault prognosis, studying structure, nonlinear
\nfault prognosis, neural networks, robotic methods, sturdy fault
\nprognosis.
\nI. INTRODUCTION
\nROBOTIC methods are integral elements of many com- plex engineering methods together with manufacturing processes [1] and space-based methods [2]. Stricter operational
\nand productiveness necessities in such methods are ensuing in
\nrobotic manipulators working close to their design limits for a lot
\nof the time. This may occasionally typically result in robotic system failures
\nthat are sometimes characterised by crucial modifications in the
\nrobotic system parameters and even by nonlinear modifications in the
\ninherent dynamics of the manipulator. Robotic system failures
\ncan probably consequence not solely in the lack of productiveness
\nbut in addition can result in unsafe operation of the system. In
\nnormal, fashionable management methods that are designed to deal with
\nsmall perturbations that will come up beneath \u201cregular\u201d working circumstances (in the \u201clinear\u201d regime) can not accommodate
\nirregular conduct on account of faults. Therefore automated well being
\nmonitoring of robotic methods and efficient lodging
\nof any faults play an important function in the operation of contemporary
\nrobotic methods and particularly autonomous and clever
\nrobotic manipulators.
\nThe design and Assessment of fault prognosis (FD) architectures
\nfor robotic methods utilizing the model-based analytical redundancy method has acquired appreciable consideration [2]\u2013[4].
\nManuscript acquired April 14, 1996; revised September 23, 1996, February
\n20, 1997, and August 17, 1997.
\nA. T. Vemuri is with the Division of Engine and Automobile Analysis,
\nSouthwest Analysis Institute, San Antonio, TX 78238-5166 USA.
\nM. M. Polycarpou is with the Division of Electrical and Laptop
\nEngineering, College of Cincinnati, Cincinnati, OH 45221-0030 USA.
\nWriter Merchandise Identifier S 1045-9227(97)08093-Four.
\nOn this method, quantitative nominal fashions of the robotic
\nsystem along with sensory measurements are used to supply estimates of measured and\/or unmeasured variables. The
\ndeviations between estimated and measured indicators present
\na residual vector which may be utilized to detect and isolate
\nsystem failures. On the whole, a fault is said if a measure of
\nthe residual vector exceeds a sure threshold worth. A substitute for analytical redundancy is the redundancy
\nmethod, the place extra bodily instrumentation is used to
\npresent the mandatory redundancy [5].
\nThe attraction of model-based FD schemes lies in the truth that
\nthe redundancy required for detecting faults is created utilizing
\nhighly effective data processing strategies with out the necessity
\nof extra bodily instrumentation in the system. Nevertheless,
\nthe model-based FD method depends on the important thing assumption that
\na mathematical characterization of the manipulator is understood a
\npriori. In observe, this assumption is often not legitimate because it
\nis troublesome to acquire the mandatory modeling accuracy required
\nfor the development of dependable analytical redundancy-based
\nFD architectures. Unavoidable modeling uncertainties, which
\ncome up on account of modeling errors, time variations, measurement
\nnoise, and exterior disturbances, deteriorate the efficiency
\nof FD schemes by inflicting false alarms. This necessitates
\nthe event of FD algorithms which have the flexibility
\nto detect manipulator failures in the presence of modeling
\nuncertainties. Such algorithms are known as sturdy fault
\nprognosis schemes.
\nThe development of sturdy FD architectures for robotic
\nmanipulators has been investigated to a restricted extent. In
\n[6], Schneider and Frank use threshold adaptation based mostly on
\nfuzzy logic to enhance robustness of state-space model-based
\nFD architectures. Time-varying state-dependent thresholds are
\nused in [7] to realize robustness in parity relations based mostly
\nFD schemes for distant robots. These research depend on two
\nkey assumptions: 1) the nominal mannequin of the system is
\nlinear and a couple of) the failures are modeled as exterior additive
\ninputs (features of time). Though it’s handy from an
\nanalytical viewpoint to review the FD downside in a linear system
\nframework, the dynamics of robotic methods are inherently
\nnonlinear. Moreover, most sensible failures are nonlinear
\nfeatures of the state and enter.
\nThis paper presents a studying methodology for sturdy fault
\nprognosis in rigid-link robotic manipulators, which relies on
\na nonlinear nominal mannequin of the manipulator and nonlinear
\ndeviation faults. The modeling uncertainties are assumed to be
\nbounded whereas the faults are modeled as nonlinear features
\nof the measured variables. The principal thought behind this
\n1045\u20139227\/97$10.00 \uf8e9 1997 IEEE
\nApproved licensed use restricted 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
\nmethod is to observe the plant for any off-nominal system
\nconduct (which could possibly be both on account of faults or uncertainties)
\nusing a sigmoidal neural community. By utilizing the information
\nof the sure on the uncertainty we develop a scientific
\nprocess, based mostly on neuro-control strategies, for figuring out
\nthe results of system failures in the presence of modeling
\nuncertainties. The neural community not solely is used to detect
\nthe incidence of the fault but it surely additionally offers a postfault
\nmannequin of the robotic manipulator. This postfault mannequin can
\nbe successfully used to isolate and determine the fault and, if
\ndoable, for lodging of the failure.
\nThe fault prognosis scheme described in this paper is rigorously analyzed for robustness and stability. Particularly, the
\nrobustness consequence addresses the FD system efficiency in the
\npresence of modeling uncertainties previous to the incidence of
\nany faults whereas the soundness property characterizes the FD
\nsystem efficiency after the incidence of the fault.
\nThe group of this paper is as follows: In Part II,
\nthe robotic dynamics and its management legislation are described, and
\nthe fault prognosis downside is formulated. In Part III,
\nthe neural-network-based sturdy fault prognosis scheme is
\ndescribed. The analytical properties of the sturdy FD algorithm are established in Part IV. Simulation examples
\nillustrating the efficiency of the FD algorithm on a two-link
\nrobotic manipulator with modeling uncertainties are offered
\nin Part V. Part VI has some concluding remarks.
\nII. PROBLEM FORMULATION<\/p>\n
Think about a robotic manipulator described by\tmannequin a a lot bigger class of failures [in the framework of
\n(4)] is the necessity to approximate unknown nonlinear features.
\nAssignmentTutorOnline<\/p>\n
(1)
\nand software program simulation instruments have rendered doable the use
\nthe place are vectors of joint positions, velocities
\nand accelerations, respectively, is the enter torque
\nof on-line approximators akin to sigmoidal neural networks
\nfor setting up and analyzing nonlinear fashions [12], [13].
\nvector, is the inertia matrix (whose inverse\tIn gentle of the above, the target of this paper is to
\nexists [8], [9]), is a matrix containing the
\ncentripetal and Coriolis phrases, is the gravity vector,
\nis a vector containing the unknown static and
\ndynamic friction phrases, and is a vector representing<\/p>\n
unknown additive bounded disturbances and noise. The time period
\nis a vector which represents the fault in the
\nrobotic manipulator, represents the time profile of
\nthe fault, and is the time of incidence of the fault.
\nThe management goal of the robotic system (1) is to comply with
\na desired trajectory. Numerous strategies can be found in
\nthe literature for deriving place management legal guidelines for robotic
\nmanipulators in the presence of modeling uncertainties and in
\nthe absence of faults (i.e., ) [8], [10], [11]. With none
\nlack of generality, in this paper we use the computed-torque
\ntechnique to acquire a trajectory-tracking controller for the robotic
\nmanipulator described by (1). The controller derived utilizing this
\ntechnique depends on the place and velocity measurements of\tA1) The failure is abrupt and happens at some unknown time
\ni.e., the time-profile of the failure is given by
\nevery hyperlink and the nominal mannequin given by\t(2)\tIII. FAULT DIAGNOSIS ARCHITECTURE
\nOn this part, we describe a strong nonlinear fault prognosis
\nif
\nif
\nA2) The robotic system states stay bounded after the
\nincidence of a fault; i.e., .
\nA3) The modeling uncertainty is bounded; i.e.,
\nthe place is a identified fixed and is
\nsome compact area of curiosity.
\nThe construction of the computed torque controller is described by
\n(three)
\nthe place is the specified trajectory, is the monitoring
\nerror, is an diagonal matrix of damping good points,
\nis an diagonal matrix of place good points. If the robotic
\ndynamics are identified precisely, then these matrices may be chosen
\nin order that the management legislation results in an exponentially convergent
\nmonitoring error [8], [9].
\nWithin the remaining portion of the paper, for the reason that above
\ncomputed torque management legislation is a operate of and solely,
\nwe signify the robotic manipulator mannequin (1) as
\n(Four)
\nthe place . Notice that the friction and the
\ndisturbance phrases in (Four) are assumed to signify the modeling
\nuncertainties in the system.
\nA fault in the robotic system modifications the dynamics of the
\nmanipulator in an unpredictable means. An correct description
\nof fault circumstances, most frequently, requires nonlinear modeling of
\nfaults, which is what’s described by in (Four). The nonlinear
\nmodeling functionality is mirrored in permitting the deviation
\non account of faults to be a nonlinear operate of the joint positions
\nand velocities. It is very important be aware that the fault formulation
\ndescribed by (Four) permits nonadditive kinds of faults. For
\ninstance, if the matrix modifications to on account of a fault
\nat time then this may be represented by letting
\nWe check with FD schemes that
\nare based mostly on such nonlinearly modeled faults as nonlinear FD
\nschemes. The value that one has to pay for the potential to
\nNevertheless, current advances in each implementation
\ndevelop a strong nonlinear fault prognosis structure with
\nassured robustness and stability properties for the robotic
\nsystem described by (Four). We make the next assumptions
\nall through the paper.
\nstructure for detecting glitches in robotic manipulators described by (Four). We start by observing that in the
\nabsence of modeling uncertainties any off-nominal conduct
\nApproved licensed use restricted to: WRIGHT STATE UNIVERSITY. Downloaded on December 28, 2008 at 09:49 from IEEE Xplore. Restrictions apply.
\n1412 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. eight, NO. 6, NOVEMBER 1997
\nnoticed from enter\u2013output measurements may be attributed
\nto a fault in the robotic system. Thus, the method of fault
\ndetection in the absence of modeling uncertainties may be
\nachieved by approximating, on-line, the unknown operate
\n[14]\u2013[16]. Nevertheless, in the presence of modeling
\nuncertainties, the distinction in the dynamics could possibly be both
\non account of faults or on account of modeling uncertainties. Subsequently, a
\nkey Question Assignment is: how does one determine the results of a fault in
\nthe presence of modeling uncertainties? Within the particular case that
\nthe modeling uncertainties have sure identified traits
\nthat distinguish them from faults, then any off-nominal system
\nconduct supplied by the neural community may be categorized
\n(for instance, through sample and sign classification strategies) as
\nbeing on account of both faults or modeling uncertainties. Nevertheless,
\nin most sensible manipulators, each faults and modeling uncertainties are unknown a priori. Therefore the problem of robustness
\nis essential.
\nFrank [17] describes a strong fault detection algorithm
\nwhich, whereas offering an on-line estimate of the uncertainty
\nstage, offers completely with the detection of faults. Within the context of fault prognosis, in addition to detecting the incidence
\nof a fault, it will be helpful to acquire an approximation of
\nthe fault operate. On this paper, we develop a strong fault
\nprognosis algorithm for detecting faults in the presence of
\nmodeling uncertainties that fulfill the bounding situation A3.
\nAn estimate of the fault operate is obtained supplied that the
\nratio between the fault operate magnitude and the modeling
\nuncertainty stage is sufficiently giant. Notice that Assumption
\nA3 permits the derivation of a strong fault prognosis algorithm
\nwhich relies on bounded unstructured uncertainty.
\nA. Nonlinear Estimation Mannequin
\nA key goal of this paper is to design a fault prognosis
\nstructure for the robotic manipulator described by (Four) utilizing
\nthe approximation properties of sigmoidal neural networks. In
\nthis part, the development of a neural-network-based nonlinear estimation mannequin is described. Using this estimation
\nmannequin, a studying algorithm for updating the parameters of the
\nneural community in order that it approximates any off-nominal conduct on account of faults, in the presence of modeling uncertainties that
\nfulfill Assumption A3, is described in the subsequent part.
\nWe take into account an estimated mannequin of the shape
\n(5)
\nthe place is the estimate of the speed vector of the
\nmanipulator joints, is a design fixed, is a threelayered sigmoidal neural community and represents the
\nadjustable weights of the community in vector type. If the quantity
\nof neurons in the hidden layer is , then (see the
\nAppendix for particulars of this illustration of a three-layered
\nsigmoidal neural community).
\nThe estimation mannequin (5) is a nonlinear observer-type
\nscheme that may be carried out in the type of steady filter as
\nthe place is the output of the first-order filter ,
\nwith the filter enter given by
\nThe development of an acceptable estimation mannequin, in a position
\nto comply with any modifications in the enter\u2013output conduct of the
\nbodily system, is a vital element in the event
\nof the general fault detection scheme. The output of the above
\nnonlinear estimation mannequin is used to replace the weights of the
\nneural community. The nonlinear estimation mannequin (5) shouldn’t be solely
\nsimple to implement however, extra importantly, has some fascinating
\nstability and efficiency properties, that are offered in
\nthe subsequent part.
\nThe preliminary weight vector, of the neural community
\nis chosen such that
\n(6)
\nsimilar to the no-failure state of affairs, whereas the preliminary worth
\nof the estimator is chosen as . Notice that the burden
\ninitialization given by (6) may be achieved by merely setting the
\nweights of the output layer to zero. Ranging from these preliminary
\ncircumstances, the principle goal is to regulate (utilizing enter\u2013output
\ndata) the burden vector at every time in order that
\napproximates the unknown operate
\nAs soon as that is achieved then the output of the neural community
\ncan be utilized to detect, diagnose, and accommodate system
\nfailures.
\nB. Studying Algorithm<\/p>\n
0000000000<\/p>\n
Diagnosis in Robotic Systems 1410 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. eight, NO. 6, NOVEMBER 1997<\/p>\n
Neural-Community-Primarily based Sturdy Fault<\/p>\n
Diagnosis in Robotic Systems<\/p>\n
Arun T. Vemuri, Member, IEEE, and Marios M. Polycarpou, Member, IEEE<\/p>\n
Summary\u2014Fault prognosis performs an vital function in the operation of contemporary robotic methods. Numerous researchers have<\/p>\n
proposed fault prognosis architectures for robotic manipulators<\/p>\n
utilizing the model-based analytical redundancy method. Considered one of<\/p>\n
the important thing points in the design of such fault prognosis schemes is<\/p>\n
the impact of modeling uncertainties on their efficiency. This<\/p>\n
paper investigates the issue of fault prognosis in rigid-link<\/p>\n
robotic manipulators with modeling uncertainties. A studying<\/p>\n
structure with sigmoidal neural networks is used to observe<\/p>\n
the robotic system for any off-nominal conduct on account of faults. The<\/p>\n
robustness<\/p>\n","protected":false},"excerpt":{"rendered":"
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