Diagnosis in Robotic Systems
1410 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. eight, NO. 6, NOVEMBER 1997
Neural-Community-Primarily based Sturdy Fault
Diagnosis in Robotic Systems
Arun T. Vemuri, Member, IEEE, and Marios M. Polycarpou, Member, IEEE
Summary—Fault prognosis performs an vital function in the operation of contemporary robotic methods. Numerous researchers have
proposed fault prognosis architectures for robotic manipulators
utilizing the model-based analytical redundancy method. Considered one of
the important thing points in the design of such fault prognosis schemes is
the impact of modeling uncertainties on their efficiency. This
paper investigates the issue of fault prognosis in rigid-link
robotic manipulators with modeling uncertainties. A studying
structure with sigmoidal neural networks is used to observe
the robotic system for any off-nominal conduct on account of faults. The
robustness and stability properties of the fault prognosis scheme
are rigorously established. Simulation examples are offered
for instance the flexibility of the neural-network-based sturdy fault
prognosis scheme to detect and accommodate faults in a two-link
robotic manipulator.
Index Phrases— Adaptive legislation, analytical redundancy, fault lodging, fault prognosis, studying structure, nonlinear
fault prognosis, neural networks, robotic methods, sturdy fault
prognosis.
I. INTRODUCTION
ROBOTIC methods are integral elements of many com- plex engineering methods together with manufacturing processes [1] and space-based methods [2]. Stricter operational
and productiveness necessities in such methods are ensuing in
robotic manipulators working close to their design limits for a lot
of the time. This may occasionally typically result in robotic system failures
that are sometimes characterised by crucial modifications in the
robotic system parameters and even by nonlinear modifications in the
inherent dynamics of the manipulator. Robotic system failures
can probably consequence not solely in the lack of productiveness
but in addition can result in unsafe operation of the system. In
normal, fashionable management methods that are designed to deal with
small perturbations that will come up beneath “regular” working circumstances (in the “linear” regime) can not accommodate
irregular conduct on account of faults. Therefore automated well being
monitoring of robotic methods and efficient lodging
of any faults play an important function in the operation of contemporary
robotic methods and particularly autonomous and clever
robotic manipulators.
The design and Assessment of fault prognosis (FD) architectures
for robotic methods utilizing the model-based analytical redundancy method has acquired appreciable consideration [2]–[4].
Manuscript acquired April 14, 1996; revised September 23, 1996, February
20, 1997, and August 17, 1997.
A. T. Vemuri is with the Division of Engine and Automobile Analysis,
Southwest Analysis Institute, San Antonio, TX 78238-5166 USA.
M. M. Polycarpou is with the Division of Electrical and Laptop
Engineering, College of Cincinnati, Cincinnati, OH 45221-0030 USA.
Writer Merchandise Identifier S 1045-9227(97)08093-Four.
On this method, quantitative nominal fashions of the robotic
system along with sensory measurements are used to supply estimates of measured and/or unmeasured variables. The
deviations between estimated and measured indicators present
a residual vector which may be utilized to detect and isolate
system failures. On the whole, a fault is said if a measure of
the residual vector exceeds a sure threshold worth. A substitute for analytical redundancy is the redundancy
method, the place extra bodily instrumentation is used to
present the mandatory redundancy [5].
The attraction of model-based FD schemes lies in the truth that
the redundancy required for detecting faults is created utilizing
highly effective data processing strategies with out the necessity
of extra bodily instrumentation in the system. Nevertheless,
the model-based FD method depends on the important thing assumption that
a mathematical characterization of the manipulator is understood a
priori. In observe, this assumption is often not legitimate because it
is troublesome to acquire the mandatory modeling accuracy required
for the development of dependable analytical redundancy-based
FD architectures. Unavoidable modeling uncertainties, which
come up on account of modeling errors, time variations, measurement
noise, and exterior disturbances, deteriorate the efficiency
of FD schemes by inflicting false alarms. This necessitates
the event of FD algorithms which have the flexibility
to detect manipulator failures in the presence of modeling
uncertainties. Such algorithms are known as sturdy fault
prognosis schemes.
The development of sturdy FD architectures for robotic
manipulators has been investigated to a restricted extent. In
[6], Schneider and Frank use threshold adaptation based mostly on
fuzzy logic to enhance robustness of state-space model-based
FD architectures. Time-varying state-dependent thresholds are
used in [7] to realize robustness in parity relations based mostly
FD schemes for distant robots. These research depend on two
key assumptions: 1) the nominal mannequin of the system is
linear and a couple of) the failures are modeled as exterior additive
inputs (features of time). Though it’s handy from an
analytical viewpoint to review the FD downside in a linear system
framework, the dynamics of robotic methods are inherently
nonlinear. Moreover, most sensible failures are nonlinear
features of the state and enter.
This paper presents a studying methodology for sturdy fault
prognosis in rigid-link robotic manipulators, which relies on
a nonlinear nominal mannequin of the manipulator and nonlinear
deviation faults. The modeling uncertainties are assumed to be
bounded whereas the faults are modeled as nonlinear features
of the measured variables. The principal thought behind this
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VEMURI AND POLYCARPOU: ROBUST FAULT DIAGNOSIS IN ROBOTIC SYSTEMS 1411
method is to observe the plant for any off-nominal system
conduct (which could possibly be both on account of faults or uncertainties)
using a sigmoidal neural community. By utilizing the information
of the sure on the uncertainty we develop a scientific
process, based mostly on neuro-control strategies, for figuring out
the results of system failures in the presence of modeling
uncertainties. The neural community not solely is used to detect
the incidence of the fault but it surely additionally offers a postfault
mannequin of the robotic manipulator. This postfault mannequin can
be successfully used to isolate and determine the fault and, if
doable, for lodging of the failure.
The fault prognosis scheme described in this paper is rigorously analyzed for robustness and stability. Particularly, the
robustness consequence addresses the FD system efficiency in the
presence of modeling uncertainties previous to the incidence of
any faults whereas the soundness property characterizes the FD
system efficiency after the incidence of the fault.
The group of this paper is as follows: In Part II,
the robotic dynamics and its management legislation are described, and
the fault prognosis downside is formulated. In Part III,
the neural-network-based sturdy fault prognosis scheme is
described. The analytical properties of the sturdy FD algorithm are established in Part IV. Simulation examples
illustrating the efficiency of the FD algorithm on a two-link
robotic manipulator with modeling uncertainties are offered
in Part V. Part VI has some concluding remarks.
II. PROBLEM FORMULATION
Think about a robotic manipulator described by mannequin a a lot bigger class of failures [in the framework of
(4)] is the necessity to approximate unknown nonlinear features.
AssignmentTutorOnline
(1)
and software program simulation instruments have rendered doable the use
the place are vectors of joint positions, velocities
and accelerations, respectively, is the enter torque
of on-line approximators akin to sigmoidal neural networks
for setting up and analyzing nonlinear fashions [12], [13].
vector, is the inertia matrix (whose inverse In gentle of the above, the target of this paper is to
exists [8], [9]), is a matrix containing the
centripetal and Coriolis phrases, is the gravity vector,
is a vector containing the unknown static and
dynamic friction phrases, and is a vector representing
unknown additive bounded disturbances and noise. The time period
is a vector which represents the fault in the
robotic manipulator, represents the time profile of
the fault, and is the time of incidence of the fault.
The management goal of the robotic system (1) is to comply with
a desired trajectory. Numerous strategies can be found in
the literature for deriving place management legal guidelines for robotic
manipulators in the presence of modeling uncertainties and in
the absence of faults (i.e., ) [8], [10], [11]. With none
lack of generality, in this paper we use the computed-torque
technique to acquire a trajectory-tracking controller for the robotic
manipulator described by (1). The controller derived utilizing this
technique depends on the place and velocity measurements of A1) The failure is abrupt and happens at some unknown time
i.e., the time-profile of the failure is given by
every hyperlink and the nominal mannequin given by (2) III. FAULT DIAGNOSIS ARCHITECTURE
On this part, we describe a strong nonlinear fault prognosis
if
if
A2) The robotic system states stay bounded after the
incidence of a fault; i.e., .
A3) The modeling uncertainty is bounded; i.e.,
the place is a identified fixed and is
some compact area of curiosity.
The construction of the computed torque controller is described by
(three)
the place is the specified trajectory, is the monitoring
error, is an diagonal matrix of damping good points,
is an diagonal matrix of place good points. If the robotic
dynamics are identified precisely, then these matrices may be chosen
in order that the management legislation results in an exponentially convergent
monitoring error [8], [9].
Within the remaining portion of the paper, for the reason that above
computed torque management legislation is a operate of and solely,
we signify the robotic manipulator mannequin (1) as
(Four)
the place . Notice that the friction and the
disturbance phrases in (Four) are assumed to signify the modeling
uncertainties in the system.
A fault in the robotic system modifications the dynamics of the
manipulator in an unpredictable means. An correct description
of fault circumstances, most frequently, requires nonlinear modeling of
faults, which is what’s described by in (Four). The nonlinear
modeling functionality is mirrored in permitting the deviation
on account of faults to be a nonlinear operate of the joint positions
and velocities. It is very important be aware that the fault formulation
described by (Four) permits nonadditive kinds of faults. For
instance, if the matrix modifications to on account of a fault
at time then this may be represented by letting
We check with FD schemes that
are based mostly on such nonlinearly modeled faults as nonlinear FD
schemes. The value that one has to pay for the potential to
Nevertheless, current advances in each implementation
develop a strong nonlinear fault prognosis structure with
assured robustness and stability properties for the robotic
system described by (Four). We make the next assumptions
all through the paper.
structure for detecting glitches in robotic manipulators described by (Four). We start by observing that in the
absence of modeling uncertainties any off-nominal conduct
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1412 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. eight, NO. 6, NOVEMBER 1997
noticed from enter–output measurements may be attributed
to a fault in the robotic system. Thus, the method of fault
detection in the absence of modeling uncertainties may be
achieved by approximating, on-line, the unknown operate
[14]–[16]. Nevertheless, in the presence of modeling
uncertainties, the distinction in the dynamics could possibly be both
on account of faults or on account of modeling uncertainties. Subsequently, a
key Question Assignment is: how does one determine the results of a fault in
the presence of modeling uncertainties? Within the particular case that
the modeling uncertainties have sure identified traits
that distinguish them from faults, then any off-nominal system
conduct supplied by the neural community may be categorized
(for instance, through sample and sign classification strategies) as
being on account of both faults or modeling uncertainties. Nevertheless,
in most sensible manipulators, each faults and modeling uncertainties are unknown a priori. Therefore the problem of robustness
is essential.
Frank [17] describes a strong fault detection algorithm
which, whereas offering an on-line estimate of the uncertainty
stage, offers completely with the detection of faults. Within the context of fault prognosis, in addition to detecting the incidence
of a fault, it will be helpful to acquire an approximation of
the fault operate. On this paper, we develop a strong fault
prognosis algorithm for detecting faults in the presence of
modeling uncertainties that fulfill the bounding situation A3.
An estimate of the fault operate is obtained supplied that the
ratio between the fault operate magnitude and the modeling
uncertainty stage is sufficiently giant. Notice that Assumption
A3 permits the derivation of a strong fault prognosis algorithm
which relies on bounded unstructured uncertainty.
A. Nonlinear Estimation Mannequin
A key goal of this paper is to design a fault prognosis
structure for the robotic manipulator described by (Four) utilizing
the approximation properties of sigmoidal neural networks. In
this part, the development of a neural-network-based nonlinear estimation mannequin is described. Using this estimation
mannequin, a studying algorithm for updating the parameters of the
neural community in order that it approximates any off-nominal conduct on account of faults, in the presence of modeling uncertainties that
fulfill Assumption A3, is described in the subsequent part.
We take into account an estimated mannequin of the shape
(5)
the place is the estimate of the speed vector of the
manipulator joints, is a design fixed, is a threelayered sigmoidal neural community and represents the
adjustable weights of the community in vector type. If the quantity
of neurons in the hidden layer is , then (see the
Appendix for particulars of this illustration of a three-layered
sigmoidal neural community).
The estimation mannequin (5) is a nonlinear observer-type
scheme that may be carried out in the type of steady filter as
the place is the output of the first-order filter ,
with the filter enter given by
The development of an acceptable estimation mannequin, in a position
to comply with any modifications in the enter–output conduct of the
bodily system, is a vital element in the event
of the general fault detection scheme. The output of the above
nonlinear estimation mannequin is used to replace the weights of the
neural community. The nonlinear estimation mannequin (5) shouldn’t be solely
simple to implement however, extra importantly, has some fascinating
stability and efficiency properties, that are offered in
the subsequent part.
The preliminary weight vector, of the neural community
is chosen such that
(6)
similar to the no-failure state of affairs, whereas the preliminary worth
of the estimator is chosen as . Notice that the burden
initialization given by (6) may be achieved by merely setting the
weights of the output layer to zero. Ranging from these preliminary
circumstances, the principle goal is to regulate (utilizing enter–output
data) the burden vector at every time in order that
approximates the unknown operate
As soon as that is achieved then the output of the neural community
can be utilized to detect, diagnose, and accommodate system
failures.
B. Studying Algorithm
0000000000
Diagnosis in Robotic Systems 1410 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. eight, NO. 6, NOVEMBER 1997
Neural-Community-Primarily based Sturdy Fault
Diagnosis in Robotic Systems
Arun T. Vemuri, Member, IEEE, and Marios M. Polycarpou, Member, IEEE
Summary—Fault prognosis performs an vital function in the operation of contemporary robotic methods. Numerous researchers have
proposed fault prognosis architectures for robotic manipulators
utilizing the model-based analytical redundancy method. Considered one of
the important thing points in the design of such fault prognosis schemes is
the impact of modeling uncertainties on their efficiency. This
paper investigates the issue of fault prognosis in rigid-link
robotic manipulators with modeling uncertainties. A studying
structure with sigmoidal neural networks is used to observe
the robotic system for any off-nominal conduct on account of faults. The
robustness
