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. Vemuri, Member, IEEE, and Marios M. Polycarpou, Member, IEEE
Abstract—Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have
proposed fault diagnosis architectures for robotic manipulators
using the model-based analytical redundancy approach. One of
the key issues in the design of such fault diagnosis schemes is
the effect of modeling uncertainties on their performance. This
paper investigates the problem of fault diagnosis in rigid-link
robotic manipulators with modeling uncertainties. A learning
architecture with sigmoidal neural networks is used to monitor
the robotic system for any off-nominal behavior due to faults. The
robustness and stability properties of the fault diagnosis scheme
are rigorously established. Simulation examples are presented
to illustrate the ability of the neural-network-based robust fault
diagnosis scheme to detect and accommodate faults in a two-link
robotic manipulator.
Index Terms— Adaptive law, analytical redundancy, fault accommodation, fault diagnosis, learning architecture, nonlinear
fault diagnosis, neural networks, robotic systems, robust fault
diagnosis.
I. INTRODUCTION
ROBOTIC systems are integral components of many com- plex engineering systems including manufacturing processes [1] and space-based systems [2]. Stricter operational
and productivity requirements in such systems are resulting in
robotic manipulators working near their design limits for much
of the time. This may often lead to robotic system failures
which are typically characterized by critical changes in the
robotic system parameters or even by nonlinear changes in the
inherent dynamics of the manipulator. Robotic system failures
can potentially result not only in the loss of productivity
but also can lead to unsafe operation of the system. In
general, modern control systems which are designed to handle
small perturbations that may arise under “normal” operating conditions (in the “linear” regime) cannot accommodate
abnormal behavior due to faults. Hence automated health
monitoring of robotic systems and effective accommodation
of any faults play a crucial role in the operation of modern
robotic systems and especially autonomous and intelligent
robotic manipulators.
The design and analysis of fault diagnosis (FD) architectures
for robotic systems using the model-based analytical redundancy approach has received considerable attention [2]–[4].
Manuscript received April 14, 1996; revised September 23, 1996, February
20, 1997, and August 17, 1997.
A. T. Vemuri is with the Department of Engine and Vehicle Research,
Southwest Research Institute, San Antonio, TX 78238-5166 USA.
M. M. Polycarpou is with the Department of Electrical and Computer
Engineering, University of Cincinnati, Cincinnati, OH 45221-0030 USA.
Publisher Item Identifier S 1045-9227(97)08093-4.
In this approach, quantitative nominal models of the robotic
system together with sensory measurements are used to provide estimates of measured and/or unmeasured variables. The
deviations between estimated and measured signals provide
a residual vector which can be utilized to detect and isolate
system failures. In general, a fault is declared if a measure of
the residual vector exceeds a certain threshold value. An alternative to analytical redundancy is the hardware redundancy
approach, where additional physical instrumentation is used to
provide the necessary redundancy [5].
The appeal of model-based FD schemes lies in the fact that
the redundancy required for detecting faults is created using
powerful information processing techniques without the need
of additional physical instrumentation in the system. However,
the model-based FD approach relies on the key assumption that
a mathematical characterization of the manipulator is known a
priori. In practice, this assumption is usually not valid since it
is difficult to obtain the necessary modeling accuracy required
for the construction of reliable analytical redundancy-based
FD architectures. Unavoidable modeling uncertainties, which
arise due to modeling errors, time variations, measurement
noise, and external disturbances, deteriorate the performance
of FD schemes by causing false alarms. This necessitates
the development of FD algorithms which have the ability
to detect manipulator failures in the presence of modeling
uncertainties. Such algorithms are referred to as robust fault
diagnosis schemes.
The construction of robust FD architectures for robotic
manipulators has been investigated to a limited extent. In
[6], Schneider and Frank use threshold adaptation based on
fuzzy logic to improve robustness of state-space model-based
FD architectures. Time-varying state-dependent thresholds are
used in [7] to achieve robustness in parity relations based
FD schemes for remote robots. These studies rely on two
key assumptions: 1) the nominal model of the system is
linear and 2) the failures are modeled as external additive
inputs (functions of time). Although it is convenient from an
analytical viewpoint to study the FD problem in a linear system
framework, the dynamics of robotic systems are inherently
nonlinear. Furthermore, most practical failures are nonlinear
functions of the state and input.
This paper presents a learning methodology for robust fault
diagnosis in rigid-link robotic manipulators, which is based on
a nonlinear nominal model of the manipulator and nonlinear
deviation faults. The modeling uncertainties are assumed to be
bounded while the faults are modeled as nonlinear functions
of the measured variables. The principal idea behind this
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VEMURI AND POLYCARPOU: ROBUST FAULT DIAGNOSIS IN ROBOTIC SYSTEMS 1411
approach is to monitor the plant for any off-nominal system
behavior (which could be either due to faults or uncertainties)
utilizing a sigmoidal neural network. By using the knowledge
of the bound on the uncertainty we develop a systematic
procedure, based on neuro-control techniques, for identifying
the effects of system failures in the presence of modeling
uncertainties. The neural network not only is used to detect
the occurrence of the fault but it also provides a postfault
model of the robotic manipulator. This postfault model can
be effectively used to isolate and identify the fault and, if
possible, for accommodation of the failure.
The fault diagnosis scheme described in this paper is rigorously analyzed for robustness and stability. Specifically, the
robustness result addresses the FD system performance in the
presence of modeling uncertainties prior to the occurrence of
any faults while the stability property characterizes the FD
system performance after the occurrence of the fault.
The organization of this paper is as follows: In Section II,
the robot dynamics and its control law are described, and
the fault diagnosis problem is formulated. In Section III,
the neural-network-based robust fault diagnosis scheme is
described. The analytical properties of the robust FD algorithm are established in Section IV. Simulation examples
illustrating the performance of the FD algorithm on a two-link
robotic manipulator with modeling uncertainties are presented
in Section V. Section VI has some concluding remarks.
II. PROBLEM FORMULATION
Consider a robotic manipulator described by model a much larger class of failures [in the framework of
(4)] is the need to approximate unknown nonlinear functions.
AssignmentTutorOnline
(1)
and software simulation tools have rendered possible the use
where are vectors of joint positions, velocities
and accelerations, respectively, is the input torque
of on-line approximators such as sigmoidal neural networks
for constructing and analyzing nonlinear models [12], [13].
vector, is the inertia matrix (whose inverse In light of the above, the objective of this paper is to
exists [8], [9]), is a matrix containing the
centripetal and Coriolis terms, is the gravity vector,
is a vector containing the unknown static and
dynamic friction terms, and is a vector representing
unknown additive bounded disturbances and noise. The term
is a vector which represents the fault in the
robot manipulator, represents the time profile of
the fault, and is the time of occurrence of the fault.
The control objective of the robotic system (1) is to follow
a desired trajectory. A number of techniques are available in
the literature for deriving position control laws for robotic
manipulators in the presence of modeling uncertainties and in
the absence of faults (i.e., ) [8], [10], [11]. Without any
loss of generality, in this paper we use the computed-torque
method to obtain a trajectory-tracking controller for the robotic
manipulator described by (1). The controller derived using this
method relies on the position and velocity measurements of A1) The failure is abrupt and occurs at some unknown time
i.e., the time-profile of the failure is given by
each link and the nominal model given by (2) III. FAULT DIAGNOSIS ARCHITECTURE
In this section, we describe a robust nonlinear fault diagnosis
if
if
A2) The robotic system states remain bounded after the
occurrence of a fault; i.e., .
A3) The modeling uncertainty is bounded; i.e.,
where is a known constant and is
some compact domain of interest.
The structure of the computed torque controller is described by
(3)
where is the desired trajectory, is the tracking
error, is an diagonal matrix of damping gains,
is an diagonal matrix of position gains. If the robot
dynamics are known exactly, then these matrices can be chosen
so that the control law leads to an exponentially convergent
tracking error [8], [9].
In the remaining portion of the paper, since the above
computed torque control law is a function of and only,
we represent the robotic manipulator model (1) as
(4)
where . Note that the friction and the
disturbance terms in (4) are assumed to represent the modeling
uncertainties in the system.
A fault in the robotic system changes the dynamics of the
manipulator in an unpredictable way. An accurate description
of fault conditions, most often, requires nonlinear modeling of
faults, which is what is described by in (4). The nonlinear
modeling capability is reflected in allowing the deviation
due to faults to be a nonlinear function of the joint positions
and velocities. It is important to note that the fault formulation
described by (4) allows nonadditive types of faults. For
example, if the matrix changes to due to a fault
at time then this can be represented by letting
We refer to FD schemes that
are based on such nonlinearly modeled faults as nonlinear FD
schemes. The price that one has to pay for the potential to
However, recent advances in both hardware implementation
develop a robust nonlinear fault diagnosis architecture with
guaranteed robustness and stability properties for the robotic
system described by (4). We make the following assumptions
throughout the paper.
architecture for detecting system faults in robotic manipulators described by (4). We begin by observing that in the
absence of modeling uncertainties any off-nominal behavior
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1412 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 8, NO. 6, NOVEMBER 1997
observed from input–output measurements can be attributed
to a fault in the robotic system. Thus, the process of fault
detection in the absence of modeling uncertainties can be
achieved by approximating, on-line, the unknown function
[14]–[16]. However, in the presence of modeling
uncertainties, the difference in the dynamics could be either
due to faults or due to modeling uncertainties. Therefore, a
key question is: how does one identify the effects of a fault in
the presence of modeling uncertainties? In the special case that
the modeling uncertainties have certain known characteristics
that distinguish them from faults, then any off-nominal system
behavior provided by the neural network can be classified
(for example, via pattern and signal classification methods) as
being due to either faults or modeling uncertainties. However,
in most practical manipulators, both faults and modeling uncertainties are unknown a priori. Hence the issue of robustness
is very important.
Frank [17] describes a robust fault detection algorithm
which, while providing an on-line estimate of the uncertainty
level, deals exclusively with the detection of faults. In the context of fault diagnosis, in addition to detecting the occurrence
of a fault, it would be useful to obtain an approximation of
the fault function. In this paper, we develop a robust fault
diagnosis algorithm for detecting faults in the presence of
modeling uncertainties that satisfy the bounding condition A3.
An estimate of the fault function is obtained provided that the
ratio between the fault function magnitude and the modeling
uncertainty level is sufficiently large. Note that Assumption
A3 allows the derivation of a robust fault diagnosis algorithm
which is based on bounded unstructured uncertainty.
A. Nonlinear Estimation Model
A key objective of this paper is to design a fault diagnosis
architecture for the robotic manipulator described by (4) using
the approximation properties of sigmoidal neural networks. In
this section, the construction of a neural-network-based nonlinear estimation model is described. Utilizing this estimation
model, a learning algorithm for updating the parameters of the
neural network so that it approximates any off-nominal behavior due to faults, in the presence of modeling uncertainties that
satisfy Assumption A3, is described in the next section.
We consider an estimated model of the form
(5)
where is the estimate of the velocity vector of the
manipulator joints, is a design constant, is a threelayered sigmoidal neural network and represents the
adjustable weights of the network in vector form. If the number
of neurons in the hidden layer is , then (see the
Appendix for details of this representation of a three-layered
sigmoidal neural network).
The estimation model (5) is a nonlinear observer-type
scheme that can be implemented in the form of stable filter as
where is the output of the first-order filter ,
with the filter input given by
The construction of an appropriate estimation model, able
to follow any changes in the input–output behavior of the
physical system, is a crucial component in the development
of the overall fault detection scheme. The output of the above
nonlinear estimation model is used to update the weights of the
neural network. The nonlinear estimation model (5) is not only
easy to implement but, more importantly, has some desirable
stability and performance properties, which are presented in
the next section.
The initial weight vector, of the neural network
is chosen such that
(6)
corresponding to the no-failure situation, while the initial value
of the estimator is selected as . Note that the weight
initialization given by (6) can be achieved by simply setting the
weights of the output layer to zero. Starting from these initial
conditions, the main objective is to adjust (using input–output
information) the weight vector at each time so that
approximates the unknown function
Once this is achieved then the output of the neural network
can be used to detect, diagnose, and accommodate system
failures.
B. Learning Algorithm
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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. Vemuri, Member, IEEE, and Marios M. Polycarpou, Member, IEEE
Abstract—Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have
proposed fault diagnosis architectures for robotic manipulators
using the model-based analytical redundancy approach. One of
the key issues in the design of such fault diagnosis schemes is
the effect of modeling uncertainties on their performance. This
paper investigates the problem of fault diagnosis in rigid-link
robotic manipulators with modeling uncertainties. A learning
architecture with sigmoidal neural networks is used to monitor
the robotic system for any off-nominal behavior due to faults. The
robustness
