=Paper=
{{Paper
|id=Vol-1507/dx15paper23
|storemode=property
|title=Fault Tolerant Control for a 4-Wheel Skid Steering Mobile Robot
|pdfUrl=https://ceur-ws.org/Vol-1507/dx15paper23.pdf
|volume=Vol-1507
|dblpUrl=https://dblp.org/rec/conf/safeprocess/FourlasKK15
}}
==Fault Tolerant Control for a 4-Wheel Skid Steering Mobile Robot==
https://ceur-ws.org/Vol-1507/dx15paper23.pdf
Proceedings of the 26th International Workshop on Principles of Diagnosis
Fault Tolerant Control for a 4-Wheel Skid Steering Mobile Robot
George K. Fourlas1, George C. Karras2 and Kostas J. Kyriakopoulos 2
1
Department of Computer Engineering, Technological Educational Institute (T. E. I.) of Central
Greece, Lamia, Greece
email: gfourlas@teiste.gr
2
Control Systems Laboratory, School of Mechanical Eng. National Technical University of Athens
(NTUA) Athens, Greece
email: karrasg@mail.ntua.gr, kkyria@mail.ntua.gr
Abstract
This paper studies a fault tolerant control strategy
for a four wheel skid steering mobile robot
(SSMR). Through this work the fault diagnosis
procedure is accomplished using structural analy-
sis technique while fault accommodation is based
on a Recursive Least Squares (RLS) approxima-
tion. The goal is to detect faults as early as possi-
ble and recalculate command inputs in order to
achieve fault tolerance, which means that despites
the faults occurrences the system is able to recov-
er its original task with the same or degraded per- Figure 1. 4-Wheel Skid Steering Mobile Robot.
formance. Fault tolerance can be considered that
it is constituted by two basic tasks, fault diagnosis Fault diagnosis and accommodation for wheeled mobile
and control redesign. In our research using the di- robots is a complex problem due to the large number of
agnosis approach presented in our previous work faults that can be present such as faults of sensors and ac-
we addressed mainly to the second task proposing tuators [10] - [20].
a framework for fault tolerant control, which al- Model based fault detection and isolation is a method to
lows retaining acceptable performance under sys- perform fault diagnosis using a certain model of the sys-
tems faults. In order to prove the efficacy of the tem. The goal is to detect faults as early as possible in or-
proposed method, an experimental procedure was der to provide a timely warning [8]. The aim of timely
carried out using a Pioneer 3-AT mobile robot. handling the fault occurrence is to accommodate their con-
sequences so that the system remains functional. This can
1 Introduction be achieved with fault tolerance.
In cases where fault could not be tolerated, it is necessary
The higher demands to achieve more reliable performance
to use redundant hardware. In practice there exist two dif-
in modern robotic systems have necessitated the develop-
ferent approaches for fault tolerance control, static redun-
ment of appropriate fault diagnosis methods. The appear-
dancy and dynamic redundancy [8].
ance of faults is inevitable in all systems, such as wheeled
In [10] and [16], the research is focused only on the prob-
robots, either because their elements are worn out or be-
lem of fault detection and identification in a mobile robot
cause the environment in which they operate, presents un-
and different approaches related to state estimation were
anticipated situations [4].
introduced. In [9] and [15], the research interest is focused
In a large number of applications, as for example search
only on the problem of fault detection which is a sepa-
and rescue, planetary exploration, nuclear waste cleanup or
rate problem in the fault diagnosis domain. The research
mine decommissioning, the wheeled robots operate in en-
efforts in [7] and [12] – [14] are primarily intended to de-
vironments where human intervention can be very costly,
tect faults in the sensors of a wheeled robot. Concerning
slow or even impossible. They can move freely in such
the research area of detection and accommodation on
dynamic environments. It is therefore essential for the ro-
wheeled robots there is also a small number of efforts [18]
bots to monitor their behavior so that faults may be ad-
with different approaches and methodologies.
dressed before they result in catastrophic failures.
As a fault, it can be considered any unpermitted deviation
A wheeled mobile robot is usually an embedded control
from the normal behavior of a system. Fault diagnosis is
platform, which consists of an on-board computer, power,
the procedure of determination of the component which is
motor control system, communications, sonars, cameras,
faulty. Consequently, the aim of fault diagnosis is to pro-
laser radar system and sensors such as gyroscope, encod-
duce the suitable fault statement regarding the malfunction
ers, accelerometers etc, Fig. 1.
of a wheeled robot.
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Proceedings of the 26th International Workshop on Principles of Diagnosis
Fault diagnosis includes fault detection, which is the indi- The kinematic model describes the motion constrains of
cation that something is going wrong in the system and the system, as well as the relationship of the sensors meas-
fault isolation, which is the determination of the magnitude urements with the system states and it is crucial for the
of the fault, by evaluating symptoms. Follows fault detec- fault diagnosis procedure.
tion. Fault detection and isolation tasks together are re-
ferred to as fault diagnosis (FDI - Fault Detection and Iso- 2.1 Kinematic Model
lation). The geometry of the robot is presented in Fig.2. To con-
Among the various methods in the design of a residual sider the model of the four wheel skid steering mobile ro-
generator, only few deal with nonlinear systems. Structural bot (SSMR) it is assumed that the robot is placed on a
analysis is a technique that provides feasible solutions to
plane surface where ( Χ Ι ,Υ Ι ) is the inertial reference
the residual generation of nonlinear systems
Structural analysis methods are used in research publica- frame and ( Χ ,Υ ) is a local coordinate frame fixed on the
tions [2] and [6]. Paper [3] presents a structural analysis robot at its center of mass (COM). The position of the
for complex systems such as a ship propulsion benchmark.
In [13] and [14] the authors discusses how structural anal- COM is ( x, y ) with respect to the inertial frame and ϑ is
ysis technique is applied to an unmanned ground vehicle the orientation of the local coordinate frame with respect to
for residual generation. the inertial frame.
In this research, a model based fault diagnosis for a four
wheel skid steering mobile robot (SSMR) is presented. YΙ
The basic idea is to use structural analysis based technique v1
X
in order to generate residuals. For this purpose we use the Y v1x
kinematic model of the mobile robot that serves to the de- b v1y ϑ
yICR
sign of the structural model of the system. This technique a v
ΙCR
provides the parity equations which can be used as residual v4
vx v4 x
generators. The advantage of the proposed method is that
y 2 RL v2 x vy v4 y
offers feasible solution to the residual generation of non- v2
COM
linear systems. Additionally, we a propose a fault accom- xICR
v2 y 2 RR
modation technique based on RLS approximation in order v3x
to provide recalculated control inputs in the case that the v3
left or right set of the robot tires becomes flat. 2c
The mobile robot is supposed to be equipped with two v3 y
high resolution optical quadrature shaft encoders mounted XΙ
on reversible-DC motors which provide rotational speeds
x
of the left and right wheels ωL and ωR respectively and
Figure 2. Mobile Robot Geometry.
an inertial measurement unit (IMU) which provides the
forward linear acceleration and the angular velocity well as As depicted in Fig. 2, a is the distance between the center
the angle θ between the mobile robot axle and the x axis of mass and the front wheels axle along X, b is the distance
of the mobile robot. The absolute pose (horizontal position between the center of mass and the rear wheels axle along
and orientation) of the robot is available via a camera sys- X, c is half distance between wheels along Y and RL , RR
tem mounted on the workspace of the robot. A distinctive
are the radii of left and right wheels respectively. The co-
marker is place at the top side of the robot.
ordinates of the instantaneous center of rotation (ICR) are
The paper is organized as follows. We start by presenting
the mathematical model of a Pioneer 3-AT mobile robot in ( xICR ,yICR ) .
section 2. Section 3 describes the fault diagnosis proce- Assuming that the robot moves on a horizontal plane the
dure. Section 4 describes the methodology of fault ac- linear velocity with respect to the local frame is given by
commodation. In section 5 we present the application re-
sults of the proposed method to the robotic platform. Con- υx
clusions and directions for future work are presented in υ = υy (1)
Section 6.
0
2 Mathematical Model of Pioneer 3-AT Mo- and its angular velocity is given by
bile Robot
0
ω = 0
In this work, the mobile robot Pioneer 3-AT was used as a
robotic platform. This robot is a four wheel skid – steering (2)
vehicle actuated by two motors, one for the left sided ω
wheels and the other for the right sided wheels. The wheels
on the same side are mechanically coupled and thus have The state vector with respect to the inertial frame is
the same velocity. Also, they are equipped with encoders
and the angular readings are available through routine x
calls. q = y (3)
ϑ
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Proceedings of the 26th International Workshop on Principles of Diagnosis
The time derivatives of (3) denotes the robot’s velocity We suppose that the mobile robot localization is calculated
vector and is given by via the following measurement devices:
• two high resolution optical quadrature shaft encod-
x cos ϑ − sin ϑ 0 υ x er mounted on reversible-DC motors which provide
y = sin ϑ cos ϑ 0 υ
y (4) rotational speeds of the left and right wheels ωL
ϑ 0 0 1 ω and ωR respectively,
Assuming that longitudinal slip between the wheels and • an Inertial Measurement Unit (IMU) which pro-
the surface can be neglected we have the following equa- vides the forward linear acceleration and the angu-
tion, lar velocity as well as the angle ϑ between the
mobile robot axle and the x axis of the mobile ro-
υix = Riωi (5) bot.
• A camera system, which calculates the pose of the
where υix is the longitudinal component of the total veloci- robot, by tracking a marker placed at the top side of
ty vector υi of the i-th wheel expressed with respect to the it.
In this work we are only interested in abrupt faults which
local frame and Ri is the rolling radius of that wheel. occur in the actuators of the mobile robot and as conse-
If we take into account all wheels (Fig. 2), the following quence, we make the following assumptions.
relationships between the wheels can be obtained [11], • Assumption 1: When the mobile robot starts func-
tioning all its components are in normal mode.
υ=
L υ=1x υ2 x • Assumption 2: The magnitude of the noise is as-
υ= υ= υ4 x sumed to be significantly smaller than the magni-
(6)
R 3x
υ= υ= υ tude of the faults.
F 1y 4y
• Assumption 3: Regarding the wheel radius the fol-
υ=B υ=2y υ 3y lowing inequalities are satisfied:
where υ L refers to the longitudinal coordinates of the left RR + δ RR > 0 & RL + δ RL > 0
wheels velocities, υ R refers to the longitudinal coordinates According to this assumption, faults that result in the com-
of the right wheels velocities, υ F refers to the lateral coor- plete loss of the wheel are not considered.
dinates of the front wheels velocities and υ B refers to the
lateral coordinates of the rear wheels velocities. 3 Fault Detection and Isolation
Unlike other mobile robots, lateral velocities of the four Between several techniques for generating residuals, lim-
wheel skid steering mobile robot are generally nonzero ited number of them concerns nonlinear systems. Such one
since from its mechanical structure the lateral skidding is is structural analysis. Using this method we can extract
necessary if the robot changes its orientation. Therefore, in information about system components that we are not able
order to complete the kinematic model, the following non- to measure. Also we can take the parity equations that al-
holonomic constrain in Pfaffian form is introduced low generating residuals.
The structure of the mobile robot is described using the
x following sets of constrains C and variables V
[ − sin ϑ cos ϑ − xICR ] y =A ( q ) q =0 (7) C = {c1 , c2 ,..., c9 } (12)
ϑ
V= X ∪ K (13)
Then we have
X is a subset of the unknown ones and K is a subset of
q = S ( q )η (8) known that are measurements and inputs.
The above subsets are
where
cos ϑ xICR sin ϑ
{
X = x , y , ϑ,υ x ,υ y } (14)
S ( q ) sin ϑ
= − xICR cos ϑ (9) K = { x, y, ϑ , y, ω , ωL , ωR }
x, (15)
0 1
The constrain set of the mobile robot is
υ c1 : x cos ϑυ x − sin ϑυ y
= (16)
η = x (10)
ω
c= sin ϑυ x + cos ϑυ y
2 : y (17)
S ( q ) is a full rank matrix, whose columns are in the null
space of A ( q ) , c3 : ϑ = ω (18)
S T ( q ) AT ( q ) = 0 (11) dx
c4 :
x= (19)
It is noted that since dim ( η ) =2 < dim ( q ) =
3 , equation dt
(8) describes the kinematic of a sub-actuated robot with the
nonholonomic constraint given by (7).
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Proceedings of the 26th International Workshop on Principles of Diagnosis
dy t
c5 :
y= (20) r2= ϑ − ∫ ω dt (32)
dt 0
t
c6 : ϑ = ∫ ω dt (21) dx
0
=r3 ∫ xdt − dt (33)
r dy
υx
c7 := (ωR + ωL ) (22) =r4 ∫ ydt − dt (34)
2
dx
c8 : x = (23) 4 Fault Accommodation
dt
Fault accommodation is the phase that follows the fault
dy diagnosis. One of the most important issues to consider for
c9 : y = (24)
dt the design of fault tolerant control is relative to the per-
formance and functionality of the system under considera-
Through the above technique we create the following inci- tion. More specific it should take into consideration, the
dence matrix that describes the robot structure, Table 1. degree of performance degradation that is acceptable.
Table 1. Incidence Matrix There are two aspects of system performance, dynamic and
steady state. In our approach we take into account the sec-
KNOWN UNKNOWN ond one. We also use the aforementioned fault diagnosis
υy
method to monitor the system. The goal is to have the nec-
x y θ x y ω ωL ωR x y ϑ υx
essary information about the fault occurrence for timely
c1 1 1 1 1 counteraction. Figure 3 shows the overall structure of the
c2 1 proposed fault tolerant mechanism. It consists of two parts:
1 1 1
i) the fault detection module which accepts as inputs the
c3 1 1 measurement of the linear and angular velocity of the
c4 1 1 SSMR and decides about the type of fault according to the
method described in Section 3, and ii) the fault accommo-
c5 1 1 dation module which accepts as inputs the type of fault as
c6 1 1 well as the measurement of the linear and angular velocity
c7 1 1 1 and recalculates accordingly the command inputs in order
to compensate for the fault.
c8 1 1
c9 1 1
Applying matching algorithm [1] to the incidence matrix,
we take out the following matched M and unmatched U
constrains
M = {c1 , c2 , c3 , c4 , c7 } (25)
U = {c5 , c6 , c8 , c9 } (26)
In order to have residual generators we use the following
parity equations
c5 ( y ,
y) = 0 (27) Figure 3. Fault Tolerance System Architecture.
(
c6 ϑ , ϑ = 0 ) (28)
When a fault occurs the appropriate action is undertaken
c8 ( x, x ) = 0 (29) (e.g. maintenance, repair, reconfiguration, stop operation)
in such a way to prevent system failures. In that level the
c9 ( y, y ) = 0 (30) performance degradation that is acceptable is relative to
the minimum requirements that ensure the system func-
By starting from the unknown variables through backtrack- tionality. There is always the case that the malfunction
ing to known variables, the residuals are: may cause hazard for the process or the environment, and a
decision for stopping the operation is unavoidable.
d r In this work, we propose a fault accommodation technique
r1 =
y− sin ϑ (ωR + ωL ) + which is employed when either the left or the right set of
dt 2
tires becomes flat during the operation of a SSMR. It is
r (31)
cos ϑ (ωR + ωL ) − ∫
xdt obvious that when a flat tire fault occurs, the total nominal
+ cos ϑ
2
radius RNOM (rim and tire) of the fault wheel changes to
sin ϑ
RF , where RF < RNOM . The proposed fault accommoda-
180
Proceedings of the 26th International Workshop on Principles of Diagnosis
tion strategy relays on the online estimation of the new 3. Update the estimate Rˆ Fk and the covariance Pk of the
radius RF , in order to correct the commanded rotational
estimation error sequentially according to:
speeds of the faulty wheel and compensate for the fault
K k Pk −1 H kT ( H k Pk −1 H kT + Rk )
which otherwise will inevitable lead the vehicle to diverge −1
=
from its nominal course.
As explained in [11], the kinematic model of the SSMR
can be consider equivalent with the unicycle differential
Rˆ Fk = (
Rˆ Fk −1 + K k ωk − H k Rˆ Fk −1 ) (39)
drive one, mainly due to the existence of a single motor P=
k ( I − K k H k ) Pk −1
drive and a transmission belt for each set of wheels (left
and right), which impose the same rotational speed for where ωk is the actual measurement of the body an-
each set of wheels. According to this assumption we can gular velocity as delivered by the IMU sensor.
safely assume that: 4. Using the estimated wheel radius Rˆ Fk we correct the
u x 1 c c u L commanded wheel angular velocity as follows:
ω = 2c −1 1 u (35)
R −2ωk c + ωR RR
ωL _ cor = (40)
=
where υ L ω= L RL , υ R ωR RR are the equivalent linear Rˆ Fk
velocities of the left and right wheels respectively in rela-
2ωk c + ωL RL
tion to the rotational speeds and radii. If we consider that ωR _ cor = (41)
the fault will occur only at the one set of the wheels (left or Rˆ Fk
right), we may consider only the angular velocity equation
for the accommodation. Thus, only the angular velocity in case there is a left or a right wheel fault respectively.
measurement is needed. The fault accommodation is based
on the online estimation of the new radius RF employing a 5 Application Results
Recursive Least Squares algorithm. More specific, we may The proposed method has been implemented and tested
consider the following linear equation for the measurement experimentally on Pioneer 3-AT mobile robot. All experi-
of the mobile’s robot body angular velocity, in case a left ments have been performed indoors. We consider a faulty
side fault occurs: situation where the right wheel set is flat (forward and
backward wheels). We apply a command of
0.5
ωˆ k − ωR RR = H k Rˆ Fk + vk ω= L ω=R 5 rad / s for both set of wheels. In the nominal
c situation (no faults) the robot should move (almost)
0.5 straight forwards without any deviation. The robot starts
H k = H Lk = − ωL (36)
c from the origin of the inertial frame and moves for 2.5m.
vk − ( 0, Rk ) The time interval dt between successive IMU measure-
ments is 2.5m sec . The nominal radius of the wheels
(proper inflation) is R=
L R=
R 0.115 m .
while in the case of a right side fault:
In the first experiment (Fig. 4), the fault accommodation
0.5 algorithm is not enabled and as we can observe from the
ωˆ k + ωL RL = H k Rˆ Fk + vk trajectory of the vehicle, the SSMR significantly diverges
c
from its nominal course to the right.
0.5
=
H k H= Rk ωR (37)
c
vk ( 0, Rk )
SSMR Position along Y-axis (m)
0.4
Having defined the measurement model of the robot angu-
lar velocity in the body frame, we proceed to the on line
estimation of the fault wheel radius employing the follow- 0.2
ing Recursive Least Squares approximation algorithm:
1. Initialize the estimator: 0
= ( RF ) RL R
Rˆ F0 E=
(( ))
2 (38) -0.2
=P0 E RF − Rˆ F0 0 0.5 1
SSMR Position along X-axis (m)
1.5 2
where RL| R is the nominal radius of the left or right Figure 4. Robot’s position while the right wheel set is flat.
wheel set.
The fault detection algorithm is enabled, and as we can see
2. Obtain a new measurement ωk , assuming that it is from Fig. 5 the fault was successfully detected by the pro-
posed structural analysis algorithm.
given by the equation (36), or (37).
181
Proceedings of the 26th International Workshop on Principles of Diagnosis
As we can observe from Fig. 8 the trajectory of the SSMR
was successfully detained in an almost straight line form.
Figure 5. Fault signal as the right wheel set is flat.
In the second experiment we impose the same control in-
Figure 8. SSMR Corrected Planar Trajectory.
puts to the SSMR , but this time not
only the fault detection but also the proposed fault accom- 6 Conclusion
modation algorithm is enabled. As we can see in Fig. 6 the
on line estimation algorithm quickly converge to the new The notion of fault tolerant control for a 4-wheel skid
radius of the faulty wheel set and consequently the fault steering mobile robot is an important problem to deal with,
accommodation algorithm provides modified inputs to the since faults appearance is inevitable in such systems. The
right wheel set (Fig. 7). most significant challenge arises from the complexity of
the system. In this paper we have introduced the underly-
ing concepts for our approach to fault tolerant control for
mobile robots focusing our attention mainly to control re-
configuration. As concerning the issue of fault diagnosis
the structural analysis based technique is used in order to
generate residuals. We use the kinematic model of the mo-
bile robot that serves to the development of the structural
model of the system. The above technique provides the
parity equations which can be used as residual generators
since model based fault diagnosis approach is based on
residuals. The advantage of the above method is that it can
offer a feasible solution to the residual generation of non-
linear systems. The fault accommodation procedure targets
in the case where one of the two wheel tire sets becomes
flat. The proposed accommodation method is based on a
RLS approximation of the new faulty wheel radius and via
this information a new control input is calculated in order
Figure 6. On line estimation of faulty radius. to compensate for the fault.
The efficacy of the proposed method is demonstrated
through an extensive experimental procedure using a mo-
bile robot Pioneer 3-AT.
Acknowledgments
This research is implemented through the Operational Pro-
gram "Education and Lifelong Learning" and is co-
financed by the European Union (European Social Fund)
and Greek national funds. The work is part of the research
project entitled «DIAGNOR - Fault Diagnosis and Ac-
commodation for Wheeled Mobile Robot» of the Act "Ar-
chimedes III - Strengthening Research Groups in TEI La-
mia".
Figure 7. Recalculated input from the fault accommodation
algorithm.
182
Proceedings of the 26th International Workshop on Principles of Diagnosis
References [14] A. Monteriù, P. Asthan, K. Valavanis and S. Longhi,
“Model-Based Sensor Fault Detection and Isolation
[1] M. Blanke, M. Kinnaert, J. Luzne, M. Staroswiecki, System for Unmanned Ground Vehicles: Experi-
«Diagnosis and Fault Tolerant Control», ser. Heidel- mental Validation (part II), 2007 IEEE International
berg, Springer-Verlag, 2003. Conference on Robotics and Automation Roma, Italy,
[2] M. Blanke, H. Niemann, and T. Lorentzen, “Structural 10-14 April 2007.
analysis – a case study of the Rømer satellite,” in [15] P. Sundvall and P. Jensfelt, “Fault detection for mo-
Proc. of IFAC Safeprocess 2003, Washington, DC, bile robots using redundant positioning systems” Pro-
USA, 2003. ceedings of the 2006 IEEE International Conference
[3] M. Blanke, V. Cocquempot, R. I. Zamanabadi, and M. on Robotics and Automation, Orlando, Florida - May
Staroswiecki, “Residual generation for the ship 2006.
benchmark using structural approach,” in Proc. of Int. [16] C. Valdivieso, and A. Cipriano, “Fault Detection and
Conference on CONTROL’98, Swansea, UK, Sep Isolation System Design for Omnidirectional Soccer-
1998. Playing Robots”, Proceedings of the 2006 IEEE Con-
[4] Steven X. Ding, “Model-based Fault Diagnosis Tech- ference on Computer Aided Control Systems Design
niques: Design Schemes, Algorithms, and Tools, Munich, Germany, October 4-6, 2006.
Springer-Verlag Berlin, 2008. [17] R. Izadi-Zamanabadi, “Structural Analysis Approach
[5] G.K. Fourlas, K.J. Kyriakopoulos, N.J. Krikelis, to Fault Diagnosis with Application to Fixed-wing
“Fault Diagnosis of Hybrid Systems”, Proceedings of Aircraft Motion” in Proc. of American control Con-
the 2005 IEEE International Symposium on Intelligent ference, USA, 2002.
Control, 13th IEEE Mediterranean Conference on Con- [18] D. Zhuo-hua, CAI Zi-xing, YU Jin-xia “Fault Diagno-
trol and Automation, Limassol, Cyprus, 2005. sis and Fault Tolerant Control for Wheeled Mobile
[6] G.K. Fourlas, “Theoretical Approach of Model Based Robots under Unknown Environments: A Survey”,
Fault Diagnosis for a 4 - Wheel Skid Steering Mobile Proceedings of the 2005 IEEE International Confer-
Robot, 21st IEEE Mediterranean Conference on Con- ence on Robotics and Automation, Barcelona, Spain,
trol and Automation (MED '13), Platanias-Chania, April 2005.
Crete, GREECE, June 25-28, 2013. [19] S.Zaman, G. Steinbauer, J.Maurer, P.Lepej, and
[7] G. Ippoliti, S. Longhi, A. Monteriµu, “Model-based S.Uran, “An integrated model-based diagnosis and re-
sensor fault detection system for a smart wheelchair”, pair architecture for ROS-based robot systems”, IEEE
IFAC 2005. International Conference on Robotics and Automa-
[8] R. Isermann, “Fault Diagnosis Systems – An Introduc- tion (ICRA), Karlsruhe, Germany, 2013.
tion from Fault Detection to Fault Tolerant”, Springer- [20] D. Portugal, and Rui P. Rocha, “Scalable, Fault-
Verlag Berlin Heidelberg, 2006. Tolerant and Distributed Multi-Robot Patrol in Real
[9] B. Halder, and N. Sarkar, “Robust Fault Detection of World Environments” 2013 IEEE/RSJ International
Robotic Systems: New Results and Experiments”, Conference on Intelligent Robots and Systems
Proceedings of the 2006 IEEE International Confer- (IROS), November 3-7, Tokyo, Japan, 2013.
ence on Robotics and Automation, Orlando, Florida -
May 2006.
[10] Z. Kira, “Modeling Cross-Sensory and Sensorimotor
Correlations to Detect and Localize Faults in Mobile
Robots”, Proceedings of the 2007 IEEE/RSJ Interna-
tional Conference on Intelligent Robots and Systems
San Diego, CA, USA, Oct 29 - Nov 2, 2007.
[11] K. Kozlowski and D. Pazderski, “Modeling and Con-
trol of a 4-Wheel Skid-Steering Mobile Robot”, Int. J.
Appl. Math, Comput. Sci., 2004, vol. 14, no. 4, 477-
496.
[12] Y. Morales, E. Takeuchi and T. Tsubouchi, “Vehicle
Localization in Outdoor Woodland Environments with
sensor fault detection”, 2008 IEEE International Con-
ference on Robotics and Automation, Pasadena, CA,
USA, May 19-23, 2008.
[13] A. Monteriù, P. Asthan, K. Valavanis and S. Longhi,
“Model-Based Sensor Fault Detection and Isolation
System for Unmanned Ground Vehicles: Theoretical
Aspects (part I)”, 2007 IEEE International Conference
on Robotics and Automation Roma, Italy, 10-14 April
2007.
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184