sensor fault tolerance method by using a bayesian network for robot behavior

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Sensor Fault Tolerance Methodby Using a Bayesian Network forRobot BehaviorAlireza Rezaee a , Abolghasem A. Raie b , Abolfazl Nadi c

& Saeed Shiry Ghidary da Amirkabir University of Technology, Tehran, Iranb Amirkabir University of Technology, Tehran, Iran;,Email: [email protected] Amirkabir University of Technology, Tehran, Irand Amirkabir University of Technology, Tehran, IranPublished online: 02 Apr 2012.

To cite this article: Alireza Rezaee , Abolghasem A. Raie , Abolfazl Nadi & Saeed ShiryGhidary (2011) Sensor Fault Tolerance Method by Using a Bayesian Network for RobotBehavior, Advanced Robotics, 25:16, 2039-2064, DOI: 10.1163/016918611X590238

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Advanced Robotics 25 (2011) 2039–2064brill.nl/ar

Full paper

Sensor Fault Tolerance Method by Usinga Bayesian Network for Robot Behavior

Alireza Rezaee, Abolghasem A. Raie ∗, Abolfazl Nadi and Saeed Shiry Ghidary

Amirkabir University of Technology, Tehran, Iran

Received 24 August 2010; accepted 15 January 2010

AbstractThis paper presents FTBN, a new framework that performs learning autonomous mobile robot behavior andfault tolerance simultaneously. For learning behavior in the presence of a robot sensor fault this frameworkuses a Bayesian network. In the proposed framework, sensor data are used to detect a faulty sensor. Faultisolation is accomplished by changing the Bayesian network structure using interpreted evidence from robotsensors. Experiments including both simulation and a real robot are performed for door-crossing behaviorusing prior knowledge and sensor data at several maps. This paper explains the learning behavior, optimaltracking, exprimental setup and structure of the proposed framework. The robot uses laser and sonar sensorsfor door-crossing behavior, such that each sensor can be corrupted during the behavior. Experimental resultsshow FTBN leads to robust behavior in the presence of a sensor fault as well as performing better comparedto the conventional Bayesian method.© Koninklijke Brill NV, Leiden, 2011

KeywordsBayesian network, sensor, fault detection, mobile robot, behavior

1. Introduction

Man is interested in autonomous mobile robots performing tasks in various envi-ronments. An intelligent mobile robot has to perform reasoning under uncertainty.Probability theory is one approach for dealing with uncertainty in many fields ofscience, such as physics, engineering, economics and robotics. It is surprising that,for many years, artificial intelligence did not use probabilistic models. Perhaps themost important reason for this was the lack of compact ways to show probabilitydistributions. A Bayesian network is a popular tool for reasoning about uncertainty.This network is a graphical model indicating probabilistic relationships betweenvariables of the system. In this paper, we motivate our work using the domain of

* To whom correspondence should be addressed. E-mail: [email protected]

© Koninklijke Brill NV, Leiden, 2011 DOI:10.1163/016918611X590238

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2040 A. Rezaee et al. / Advanced Robotics 25 (2011) 2039–2064

sensor fault diagnosis for mobile robot behavior. In this application, we have to an-swer such questions as “What is the probability of the sensor being faulty given itsvalue (reading) and the value of other sensors”.

The motivation for this research comes from the need for an instrument faultdetection and isolation (IFDI) method that is applicable to robotics.

We apply a Bayesian network to the task of fault diagnosis in a complex be-havior for a mobile robot, such as door crossing. Bayesian networks have impor-tant features, such as representing direct causal dependency and ability to imitatehuman-like thinking.

There are a number of other models for data analysis, such as fuzzy logic, rulebases, decision trees and artificial neural networks. Also, there are several tech-niques for data analysis, such as classification, density estimation, regression andclustering. However, Bayesian networks are selected for fault detection on mobilerobot behavior for the following reasons:

• They represent a complete unique probability distribution over the network vari-ables.

• As a compact model they can change an exponentially sized probability distri-bution to a polynomial number of probabilities.

• They are modular; thus, the effect of parameters can be checked by using local-ized tests applied only to the variables and their direct causes [1].

• They deal with incomplete information without difficulty for discovering thedependencies between all variables. However, when one of the inputs is notdetermined, most of the other models will end up with a miscalculation due tothe correlation between input variables.

• Causal relations can be explored by using Bayesian networks. The explorationof these relations is considered beneficial for people (e.g., in exploratory dataanalysis or when an agent is exploring the environment) [2].

• Prior knowledge is very important especially when performing a real-worldanalysis. Bayesian networks facilitate the combination of prior knowledge anddata, especially when data is inadequate or expensive. In Bayesian networks,causal semantics encoding of causal prior knowledge is straightforward. Ad-ditionally, Bayesian networks encode the strength of causal relationships withprobabilities between variables. Thus, prior knowledge and data can be com-bined together.

• They also give an efficient approach to avoid the over-fitting of data [3].

• They facilitate many of the theoretical and computational difficulties of the rule-based systems by combining graphical structures for representing probabilisticknowledge [4, 5].

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A. Rezaee et al. / Advanced Robotics 25 (2011) 2039–2064 2041

• The main driving force to choose Bayesian networks is Bayesian’s ability thatcan change its structure easier than other networks like neural networks wherethey cannot change their structure (this changing can be used for node removalafter detecting the faulty sensor).

• Bayesian network models are very robust. This means that small changes inmodels do not affect system performance significantly where if the modelchanges smoothly, updating a model can be very easy.

Another reason for selecting Bayesian networks is showing dependencies so thathumans understand the model easily. Furthermore, a Bayesian network can workwith several types of variables easily without the necessity of using transforma-tion to other types, whereas other models like neural networks need some kind oftransformation to use these data.

For the reasons of being easy to understand and the modularity of the networkstructure, not only can we easily remove some parts of the modeling structure, butalso add new modules to the structure.

The remainder of this paper is structured as follows. Section 2 reviews some pre-vious efforts in sensor fault detection. In Section 3, Bayesian networks are reviewed.Section 4 describes our proposed method that shows how the Bayesian network hasbeen applied to door-crossing behavior with defective sensors. Section 5 describesthe experimental results of the simulation environment and Sourena real robot. Fi-nally, conclusions and future work are given in Section 6.

2. Related Approaches

The Kalman filter is a common method used for fault detection and identification.Owing to the systematic design of the Kalman filter, it has gained widespread at-tention [6]. The extended Kalman filter (EKF) is another method working withnonlinear systems, and is also used for fault detection and identification. In Refs [7,8] EKFs are used as parameter and state estimators for fault detection. This ap-proach does not need any prior knowledge about the faults. It has two stages: thefirst approximates the nonlinear system by a linear system, and the second consistsof fault detection and identification.

The problem of fault diagnosis can be considered as a problem of selectingamong models. Narasimhan and Mah [9] proposed a method based on the likeli-hood ratio that allows differentiation between models. This method needs extensivemodeling for each possible fault scenario.

Hardware redundancy is one of the diagnostic techniques that depend on theduplication of components. Triple hardware redundancy is the most common form,in which every system with redundancy has three separate components that arecapable of performing the same function [10]. A fault can be detected by comparingthe outputs of all three systems using comparison logic. The main problem of sucha system is the added weight, cost and complexity. Hardware redundancy is mainly

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Figure 1. Model-based fault detection.

used for highly critical systems, especially in the aerospace industry. For instance,the Boeing 777 airplane is designed with triple redundancy [11].

Analytical redundancy [12] is another method based on residual generation. Theresidual can be computed through comparison of the measurements of sensors andexpected values provided analytically by models. Parity relations, principal compo-nent analysis and artificial neural networks are the most important techniques usinganalytical redundancy.

The model-based method is another method used in diagnosis for systems suchas electro-mechanical systems. These methods use analytical redundancy to reducethe cost for adding extra sensors. This idea was introduced in the 1970s [13, 14] andhas been shown to be successful in a wide variety of applications [15]. As shownin Fig. 1, model-based fault detection and identification (FDI) techniques includetwo stages [16]. In the first stage, the residual is generated. This residual is thenanalyzed in the decision maker to determine whether a fault has occurred and, ifso, to identify the fault. When this information is used for reducing the effects ofthe faults, the system is called FDIR, where the ‘R’ stands for recovery. Recoverymethods focus on ways to reconfigure a sensor to perform better.

Usually, the residuals are compared with a threshold to determine whether a faulthas occurred or not. However, due to the complexity of the systems, the generationof accurate residuals requires extensive modeling and high computational effort.Most methods often lack a structure for setting thresholds. Residual generation isaffected by all of the components of a system, such as actuators and sensors. In addi-tion, faults come in a variety of types, such as biases, drifts, scaling errors or noises.

The analytical redundancy methods are harder to implement in comparison withphysical redundancy methods. The effectiveness of the IFDI system in the analyt-

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ical redundancy methods depends on the reliability of the model or sensor data.These methods do not need any additional hardware. This feature is very importantfor applications with limitations for additional sensors, such as in the aerospace in-dustry. Another advantage of the analytical method is the possibility of integratingthese methods as part of an optimization or control system.

All the approaches mentioned, like the Kalman filter and analytical methods,need system models (models of sensors and models of the robot to predict the sensorvalue to calculate the residuals), but in our application we do not have such modelsfor the robot and its sensors.

the Bayesian network has been categorized as an analytical redundancy method.It is a generalization of hidden Markov models (HMMs) [17, 18] and is used tomodel sequential data. Recently, Bayesian networks have been used for diagnosticproblems [19].

The literature is not rich when it comes to the application of Bayesian networksfor fault detection and diagnosis, especially in robotics. Nicholson and Brady [20]and Ibarguengoytia et al. [21] used Bayesian belief networks for IFDI. They focusedon the detection of faulty sensors. Nicholson and Brady used a Bayesian network todetect faulty sensors by observing inconsistencies between sensor readings. Arad-hye [22] also used Bayesian networks for both detection and identification of sensorfaults. Aradhye used dynamic Bayesian networks and Bayesian networks for IFDIfor dynamic systems and systems under steady-state conditions. He proposed ascheme for FDI in a dynamic system using a continuous node-Bayesian network.The use of continuous nodes in a Bayesian network needs the process model tobe linear. Several major issues were not addressed in that work, such as setting ofthe threshold for discredited nodes and effect of design parameters of the Bayesiannetwork model on IFDI performance. Mehranbod et al. [23] proposed a Bayesiannetwork model with discredited nodes and showed that this model did not requirethe unrealistic one-to-one cause–effect mappings. In their work, the Bayesian net-work is used to progress a multi-sensor model for all sensors in the process underconsideration.

The diagnostic framework presented in this paper consists of components thathave been adapted from previous research in a variety of fields. It is mainly basedon Bayesian network theory and statistical decision analysis.

We use the prior knowledge about the probabilistic dependencies in the structureof the Bayesian network, but in the methods like reinforcement learning and neuralnetworks, we cannot use the prior knowledge at the modeling. Furthermore, simplystated, HMMs are a particular kind of Bayesian network. We need a framework ableto work with data at one step (like a Bayesian network) and also work with data ofother time steps (time series). This is why we selected a dynamic Bayesian for ourcase and we used a simple dynamic Bayesian (Bayesian network) too. Another rea-son is that HMMs cannot be applied for modeling of movement of several objectsin sequence information of sensors robot, but Bayesian networks can. Furthermore,reinforcement learning often needs a great deal of memory, which is usually ex-

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pensive to store for each state, since the problems can be pretty complex. Learningthrough reinforcement learning is long and reinforcement learning does not useprior knowledge. In this paper, experimental results are based on doing or not do-ing the desired behavior, and the test method is just like an reinforcement learning,but decision for action is based on a Bayesian network. It is very different fromreinforcement learning, whose aim is to produce maximum reward in each action.

This paper shows how a Bayesian network can be effective when it is partof a framework that includes behavior-based diagnostics. Furthermore, this paperpresents a new structure for determining dynamic fault probabilities based on rawsensor data and the behavior of the robot. This is accomplished by using a Bayesiannetwork to interpret evidence.

3. Bayesian Networks

Bayesian networks are graphical models that provide a framework for dealing withthe uncertainty and complexity in many probabilistic problems. Graphical modelsare an attractive interface for modeling complex relations between sets of randomvariables. Probability theory provides inference mechanisms for obtaining the prob-abilities of subsets of random variables and propagating them through the evidenceof the model data.

Bayesian networks (Fig. 2) are directed acyclic graphs, where each node wouldhave discrete or continuous values corresponding to random variables. Arcs corre-spond to the conditional probabilities. The evidence can be entered for each node toupdate the probabilities through the entire network using an inference mechanism.

A Bayesian network shows the exponentially sized joint probability distribution(JPD) in a compact manner. Each probability in the JPD can be computed from theinformation in the Bayesian network by the chain rule:

P(x1, . . . , xn) =n∏

i=1

P(xi |Parents(xi)). (1)

Figure 2. A Bayesian network.

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Every Bayesian network needs two elements: the graph topology (structure)and conditional probability distribution (CPD) for each node. The structure of theBayesian network can be designed in different ways. In this work, the structure ofthe network is designed by an expert human, while the CPDs can be determined byusing the robot’s training data. The nodes are sensor values or states. Each node inthe structure is connected by directed arcs and has a CPD. Evidences are sensorsdata that are propagated through the network and affect the overall joint distribution.

4. Proposed Method

In this section, a Bayesian network for implementing the door-crossing behavior ofa mobile robot is first introduced (Fig. 3). This framework is adapted from Ref. [24];however, as it is unable to detect and tolerate sensor faults, a new Bayesian networkframework able to detect sensor faults and continue corrected behavior in the pres-ence of sensor malfunction is introduced.

4.1. Door-Crossing Behavior

Navigation is a compound task that is difficult to abstract and learn. We selected thedoor-crossing behavior as a part of a navigation system for our implementation.

Door crossing is used everywhere and plays an important role in navigation.Bayesian reasoning and other learning techniques such as neural networks and ge-netic algorithms are widely used, especially for robot localization. We found only afew papers in the literature about the application of Bayesian networks in the area

Figure 3. Bayesian network structure for door-crossing behavior.

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of mobile robotics. We found no reason for this absence except for the difficultiesof reasoning in real-time due to the computational burden of the probabilistic infer-ence process. Therefore, the main motivation of the experiments presented in thispaper is to emphasize that the learning capabilities of Bayesian networks with faultdetection can be used for real-time robot learning.

In this paper, it is assumed that the robot is located in a room with one open doorand a static object inside it. The robot is equipped with 13 Sonar sensors locatedsymmetrically in front of it and the desired door can be sensed with these sensors.The goal is to train the robot to learn door-crossing behavior without collision withwalls of the room. The robot receives an error when it cannot cross a door in aspecified time intervals. Two types of error are recognized: lost or collision. A robotis lost when it cannot pass the door in a specified time. Collision takes place everytime the robot hits the walls.

We adapt the Bayesian network model proposed by Lazkano et al. [24] for ourdoor-crossing behavior. As shown in Fig. 3, this model assumes that the networkstructure is determined by an expert [24].

In Ref. [24], the proposed structure is compared with the other structures. Forthis reason, we do not show these comparison results in our paper and we use thisstructure for door-crossing behavior.

In this structure, the sensor values depend on the neighboring sensor. In Fig. 3,evidence from 13 ultrasonic sensors, labeled S1–S13, is used to determine an ac-tion (C) of the robot. Any action has three states: turn left, turn right and go straight.

Figure 3 shows that each node is linked to its immediate neighbor. The threeactions of the robot are computed based on:

p(C = v|S1 = s1, . . . , S13 = s13)

= p(S7 = s7|C = v) × p(S13 = s13|C = v)

× p(S1 = s1|S2 = s2, S8 = s8,C = v)

×6∏

i=2

p(Si = si |Si+1 = si+1,C = v)

12∏

i=8

p(Si = si |Si+1 = si+1,C = v),

where si (i = 1, . . . ,13) stands for the value of sonar sensors (Si; i = 1, . . . ,13) ateach step. Each sensor may have an integer value between 0 and 19 (the values arediscretized). C is a variable for action of robot and ν represents its values (−1 forturning left, 0 for going straight and 1 for turning right). Equation (2) is used tocalculate the posterior probability of these three actions. Then, by using maximumlikelihood, the action of robot is selected at each step.

The speeds of the left and right wheels of the robot are computed using:

Vleft = 1 + 0.5 × action(t) + (action(t − 1) + action(t)) × 0.1(2)

Vright = 1 − 0.5 × action(t) − (action(t − 1) + action(t)) × 0.1,

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Figure 4. Dynamic Bayesian network for door-crossing behavior.

where the action has three values to show the sign of the rotational speed of therobot: negative, positive and null rotational velocities.

In door-crossing behavior, the current action of the robot is effected by the pre-vious action. Therefore, this research modifies the Bayesian network structure intoa dynamic Bayesian network. The new structure can use this to continue its taskreliably. It enables the robot to adapt its behavior in response to the last and presentactions as well as its sensor values.

A dynamic Bayesian network is implemented according to Fig. 4 to implementthis behavior. The arcs are included to make the relationship between actions at twotime steps.

The action of the robot is computed from (4) using sensor values:

p(Ct = v|S1 = s1, . . . , S13 = s13,Ct−1 = v′)

= p(Ct = v|Ct−1 = v′)

× p(S7 = s7|C = v) × p(S13 = s13|C = v)

× p(S1 = s1|S2 = s2, S8 = s8,C = v)

×6∏

i=2

p(Si = si |Si+1 = si+1,C = v)

×12∏

i=8

p(Si = si |Si+1 = si+1,C = v). (3)

The experiments with these two models show that none of them can tolerate thesensor fault and will produce unsatisfactory results when some of the sensors get

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corrupted. This is due to the wrong detection of the robot state from the faulty sensordata generating undesirable action and behavior. To solve this problem, we need amodel that detects faults and faulty sensors, and then eliminates this fault from themodel. Therefore, a new model that is robust against sensor faults is introduced.

4.2. Fault Tolerant Bayesian Network Framework

In this section we propose a fault tolerant Bayesian network model (FTBN) that canperform the desired action in the environment with faulty sensors. The proposedmethod is able to work properly by detecting the fault and removing its effects onthe performance of the mobile robot.

The proposed Bayesian network framework is shown in Fig. 5. This networkincludes four separate Bayesian networks: action model network, fault detectionnetwork, door detection network and diagnosis network.

The action part is similar to the network shown in Fig. 3. It determines the actionof the robot among three possible actions (rotate left, rotate right and go straight).The fault detection network detects the faulty sensor based on a new approach de-scribed in Section 4.2.2.

The door detection network detects the desired door based on the training dataand sensor values.

The diagnosis network fuses the door detection network and the fault detectionnetwork. It is used to recognize the faulty sensor and to change the structure of theaction network based on this identification.

4.2.1. Action Model StructureWe use the same structure as shown in Fig. 3 for training the actions of the robot.The training data are collected with a series of actions in 1925 different trajectoriesfor door crossing. The robot reaction is learned using (2).

4.2.2. Fault Detection Network StructureAny fault occurring in robot sensors would make a sensor value different from itsexpected value. We use a simple model of the environment to predict unreliable

Figure 5. Proposed structure (FTBN).

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Figure 6. Piecewise modeling of the environment.

(a) (b)

Figure 7. Fault detection: (a) threshold for fault and (b) structure.

data from sensors. We assumed that the environment does not have a strange shapeand we could assume that all three points sensed by three adjacent sensors form aline (Fig. 6). The value of one of the sensors such as sensor b can be verified byusing the other two sensors. We use two points (sensed by sensors a and c at Fig. 6)to determine the line and then by using this line the third point (that is expected tobe sensed by sensor b at Fig. 6) is predicted.

Here, it is assumed that the sensor values are propagated around the predictedvalue with a Gaussian distribution. The mean of the Gaussian distribution (μ) is thepredicted value and the variance (σ 2) of this distribution depends on the precisionof the sensor. We use this Gaussian distribution to determine the probability of asensor being faulty. This probability is calculated from the distance between thesensor value and predicted value. This probability is compared with a threshold todetermine the fault (Fig. 7a). The threshold is selected depending on the varianceof the Gaussian distribution.

A sensor value that is in the shaded region is accepted and out of this region isdetected as a faulty sensor. We used (μ ± σ ) for the threshold. This threshold isobtained by a practical test.

This structure (Fig. 7b) will fail when the faulty sensor is in front of a door ordiscontinuity of the walls. For solving this problem, a separate Bayesian network

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is used for door detection. If the robot detects a door with this network, then thesensor value is not considered as a fault.

4.2.3. Door Detection Network StructureThe door detection network structure is given in Fig. 8. It applies sonar readings todetect the door. This network produces a probability value for every sensor. Thisvalue shows the probability of that sensor being in front of the middle of the door.This network selects one of the sensors based on the maximum likelihood of beingthe nearest sensor to the middle of the door. The output from this network is usedfor the diagnosis network.

In the proposed method, the middle of the door is a major point and the doordetection structure (Fig. 8) has been learned to determine which sensor is preciselyin front of it. When a sensor of the robot is located in front of the door, the poste-rior probability of its state at the door detection structure becomes maximized andwith the maximum likelihood method this state is selected as the result of this part.Equation (5) is used for door detection:

p(door detection = δ|S1 = s1, . . . , S13 = s13)

= p(S1 = s1|door detection = δ)

× p(S2 = s2|door detection = δ) × · · ·× p(S13 = s13|door detection = δ), (4)

where si (i = 1, . . . ,13) stands for the value of sonar sensors (Si; i = 1, . . . ,13) ateach step and δ shows the value of doordetection variable having 13 values. This

Figure 8. Door detection network structure.

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Figure 9. Door detection network detected sensor 7 in front of the door.

equation calculates the posterior probability of each sensor being in front of thedoor. Then, by the maximum likelihood of the posterior probabilities, the sensorthat is in front of the door is detected (Fig. 9).

4.2.4. Diagnosis Network StructureWhen a sensor is reported to be faulty by the fault detection network, the doordetection probability is used according to (6) to determine the probability of it beingreally a faulty sensor:

p(diagnosis sensor i = faulty)

= p(door detection = sensor i|S1 = s1, . . . , S13 = s13)

× p(fault detection sensor i = faulty|Si = si,prediction = μ). (5)

After diagnosis of a faulty sensor, the action structure is changed to eliminate thefaulty sensor node and its arcs, and the CPD of the action structure is refreshed.For instance, if we assume that the S4 sensor was faulty, then the modified structureafter elimination would be as shown in Fig. 10.

Using this graph p(S3|C,S4) has to change to P(S3|C) because S4 is eliminated.For example, suppose that S3, S4 and C have CPD values according to Table 1.

After S4 is removed, these values will change to the CPD values of Table 2.The value of every cell in Table 2 is calculated from two columns in Table 1 that

have the same C values. As the sum of columns in the CPD table must be 1, everycell is divided to 2.

5. Experimental Results

Two separate experiments have been performed to verify the proposed method. Thefirst sets of experiments were conducted in the MATLAB simulation environmentby using a simulated robot and simulated sonar data. The second experiment wasconducted by using a real differential drive robot and data from a rotary laser scan-ner.

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Figure 10. Action structure after faulty sensor elimination.

Table 1.P(S3|C,S4)

P (S3|C,S4) C = 0, S4 = 0 C = 0, S4 = 1 C = 1, S4 = 0 C = 1, S4 = 0

S3 = 0 0.95 0.85 0.65 0.4S3 = 1 0.05 0.15 0.35 0.6

Table 2.P(S3|C)

P (S3|C) C = 0 C = 1

S3 = 0 (0.95 + 0.85)/2 = 0.9 (0.65 + 0.4)/2 = 0.525S3 = 1 (0.05 + 0.15)/2 = 0.1 (0.35 + 0.6)/2 = 0.475

The purpose of the experiments is to show that our proposed model can learn thecomplex behavior in different environments with faulty sensors.

5.1. Simulation Environment

A simulated robot is located in the environment that consists of a room with fourwalls and an open door. Figure 11 shows the environment used for training theBayesian network.

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Figure 11. Simulated environment including the robot, door and walls (Map1).

The robot consists of two driving wheels and one non-driving wheel. It isequipped with 13 sonar sensors spaced at 15◦ angular intervals in front of the robotwith a beam aperture of 30◦. Sensor 1 is located in front of the robot, sensors 2–7are placed at the left side of the robot and sensors 8–13 are placed at the right sideof the robot. The range resolution of the sonar data is 40 cm.

The simulated robot is 6 cm wide and 8 cm long. The map is 190 × 190 cm andthe door is 20 cm wide. The middle of the door is at x = 86 cm and y = 138 cm asshown in Fig. 11. In the simrobot simulator each timing stage is 1 s.

For collecting the training data and learning the action, the robot is driven to dif-ferent points of the environment with different directions. For each of the points anddirections, the action is selected by the supervisor based on the difference betweenthe direction of the robot and the middle of the door.

For training the Bayesian network, 75 000 entries were used. Each entry includedan action and readings for 13 sonar sensors. Depending on the data to be used forthe Bayesian network variable nodes, it is necessary to discretize it. In general, it isnot convenient to use a variable with more than 20 different values, even if it is adiscrete one. In this paper, 20 discrete values were collected for each sonar sensor.The door was supposed to be completely open during the experiments.

The robot was expected to follow the shortest path and cross the door withoutany collision with the walls. The initial position and direction of the robot wereselected arbitrarily with a direction ranging from 0 to 180◦. The robot received anerror penalty when it could not cross a door in specified time range or it collided tothe wall.

The robot was guided to cross the door using the Bayesian network of Fig. 3 andthe dynamic Bayesian network of Fig. 4. In the first experiment, the sensors were

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supposed to work without any fault; in the other experiment, one of the sensors wasrandomly selected to be faulty and produce random values in each path. Figure 12compares the performance of the Bayesian network and dynamic Bayesian networkin these experiments.

Figure 12 shows the total error penalty gained by the robot when it starts fromdifferent initial directions at different starting points. Experimental results showthat in the first experiment in which the sensors are without fault, both the Bayesiannetwork and dynamic Bayesian network structures work well, with the error beingless than 9%. It also shows that at the initial angles, where many sensors can sensethe door (such as 60◦, 90◦ and 120◦), the dynamic Bayesian network structure hasbetter performance.

Figures 13 and 14 show the effects of the robot initial position on the generatedpath for the dynamic Bayesian network structure. The robot produces a smooth andshort path when the number of sensors sensing the door increases; otherwise, therobot may take a longer path to cross a door or the robot may even get lost in theenvironment.

Figure 12. Comparison of two different networks for door-crossing behavior on Map1.

Figure 13. Trajectory of the robot when many of the sensors are sensing the door.

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Figure 14. Trajectory of the robot when a few sensors are sensing the door.

Figure 15. Comparison of three different networks errors.

Figure 16. Different maps to test the proposed method.

To show the performance of the proposed model when there is a sensor faultin the mobile robot, we repeated the experiment on map1 using FTBN. Figure 15shows the result for FTBN and compares it with the Bayesian network and dynamicBayesian network results. To show the learning ability of the proposed method, itwas experimented on different maps of Fig. 16, while it was trained using onlydata from Map1. Figures 17 and 18 show that FTBN can guide the robot in anunseen environment with an acceptable accuracy. The proposed model has betterperformance than both methods in the presence of a fault. The results show that theproposed structure is robust against faults and decreases the errors of behavior from

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(a)

(b)

(c)

Figure 17. Performance of the new proposed structure (FTBN) for Map1–6 of Figs 11 and 16.

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(d)

(e)

(f)

Figure 17. (Continued.)

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(a)

(b)

Figure 18. Comparison of three different network errors for Map1–6 of Figs 11 and 16.

21 to 12% on Map1. These show that FTBN is not very sensitive to changing themap of the room. However, the Bayesian network and dynamic Bayesian networkare very sensitive to changing the map and in the presence of the fault.

In the other test, the optimality of the trajectories in all three models was com-pared. To do this, from 75 000 entries in which the robot was trained, trajectorieswhose optimality was lower than a threshold were removed (about 50 000 entriesremained). In this paper, the threshold is defined as two lines that are connectedbetween two sides of the robot to two sides of the door at each step (Fig. 19). If therobot defects from this region at each step, the trajectory is not optimal. The result

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(c)

(d)


is shown in Table 3, indicating that if we remove the non-optimal trajectories fromthe training data, the performance of FTBN improves.

The results show that the average error for unseen maps is larger than for thetrained map, but it is almost the same for different maps.

5.2. Sourena Robot

The Sourena robot (Fig. 20) is a three-wheeled differential drive robot. The robotconsists of two parts: a base and a body. The base has a size of 35 cm × 60 cm ×

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(e)

(f)


40 cm and the total height of the robot is 150 cm. In the real environment exper-iments, the robot is located inside a 5 m × 6 m room with an 80-cm open door.The robot is equipped with a rotary laser scanner that can scan the environment5 times/s. The resolution of sampling was reduced to 15◦ to make it comparablewith the sonar data used in the simulation.

The program that we used for the real robot is the same as the simulated robot.In the simulation test, the output of the program was sent to the simulated robot;however, in the real test, this output is sent to the Sourena robot to perform thebehavior.

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(a) (b)

Figure 19. Region for optimality testing: (a) on t1 and (b) next action on t2.

Table 3.Comparing the Bayesian network and dynamic Bayesian network and FTBN with sensor faults

Bayesian network Dynamic Bayesian FTBNerrors (%) network errors (%) errors (%)

Map1 21 27 12Average Map2–6 41 44 16Door crossing with optimal trajectory 23 30 10

in Map1Door crossing with optimal trajectory 50 52 14

in Map2–6 (average)

For training the proposed FTBN framework, 500 entries were used. Each entryincluded an action and readings for 13 sensors value.

For testing the proposed FTBN framework, the robot was located at 100 differ-ent starting positions in the room with arbitrary directions. The robot could crossthe door in 82 test runs successfully. The same experiment was repeated by usingthe Bayesian network structure for robot guidance, that caused 73 successful door-crossing behaviors. This experiment also showed the superiority of FTBN to theconventional Bayesian network.

6. Conclusions

In this work, a new Bayesian network has been successfully applied for door-crossing behavior by a robot domain with faulty sensors. We proposed a newstructure for simultaneously performing behavior and detecting faults.

The performance of new proposed real-time method has been tested successfully.Using this method, the robot can be trained in an environment without faults andthen used in a real environment in which a fault might occur in the sensors. By using

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Figure 20. Sourena robot.

this method, the influence of a sensor fault on the behavior of the robot decreasesgreatly.

In forthcoming works, we will apply this method to more complex and realisticproblems, such as avoiding static and moving obstacles, and consider the noise onsensor values.

Acknowledgement

The authors would like to express their sincere thanks to Mr. H. Vatankhah for hisinvaluable help in the experiments with the real robot.

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About the Authors

Alireza Rezaee received his BS degree in Control Engineering from Sharif Uni-versity of Technology, Iran (2002) and the MS degree in Electrical Engineeringfrom Amirkabir University of Technology (2005). He is currently a PhD studentin Electrical Engineering at the Amirkabir University, Iran. His field of research ismachine learning, Bayesian networks and robotics.

Abolghasem A. Raie received his BS degree in Electrical Engineering from SharifUniversity of Technology, Iran (1973) and his MS and PhD degrees in ElectricalEngineering from University of Minnesota, USA (1979 and 1982, respectively).From 1983 till now, he is a member of the Faculty of the Electrical EngineeringDepartment at Amirkabir University of Technology, Iran. His research interestsare algorithm design and performance analysis, machine vision, sensor fusion,and mobile robot navigation.

Abolfazl Nadi received the BS degree in Software Engineering from the FerdowsiUniversity of Mashhad. Currently, he is an MS student of Artificial Intelligenceat the Computer Engineering Department of Amirkabir University of Technology,Iran. His research interests include mobile robots, humanoid and robot navigation,machine learning, and Bayesian networks.

Saeed Shiry Ghidary received his BS degree in Electronic Engineering and MSin Computer Architecture from Amirkabir University of Technology, in 1990and 1994, respectively. He studied robotics and artificial intelligent systems inKobe University, and got his PhD, in 2002. He has been an Assistant Professorat Amirkabir University of Technology, since 2004. His research interests includeintelligent robotics, machine learning, machine vision, cognitive science and brainmodeling.

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sensor fault tolerance method by using a bayesian network for robot behavior

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