research article implementation of a tour guide robot

Research ArticleImplementation of a Tour Guide Robot SystemUsing RFID Technology and Viterbi Algorithm-Based HMMfor Speech Recognition

Neng-Sheng Pai Hua-Jui Kuang Ting-Yuan Chang Ying-Che Kuo and Chun-Yuan Lai

Department of Electrical Engineering National Chin-Yi University of Technology No 57 Section 2 Zhongshan RoadTaiping District Taichung 41170 Taiwan

Correspondence should be addressed to Neng-Sheng Pai paimailncutedutw

Received 3 January 2014 Accepted 1 March 2014 Published 24 March 2014

Academic Editor Her-Terng Yau

Copyright copy 2014 Neng-Sheng Pai et alThis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper applied speech recognition and RFID technologies to develop an omni-directional mobile robot into a robot with voicecontrol and guide introduction functions For speech recognition the speech signals were captured by short-time processing Thespeaker first recorded the isolated words for the robot to create speech database of specific speakers After the speech pre-processingof this speech database the feature parameters of cepstrum and delta-cepstrum were obtained using linear predictive coefficient(LPC) Then the Hidden Markov Model (HMM) was used for model training of the speech database and the Viterbi algorithmwas used to find an optimal state sequence as the reference sample for speech recognitionThe trained reference model was put intothe industrial computer on the robot platform and the user entered the isolated words to be tested After processing by the samereference model and comparing with previous reference model the path of the maximum total probability in various models foundusing the Viterbi algorithm in the recognition was the recognition result Finally the speech recognition and RFID systems wereachieved in an actual environment to prove its feasibility and stability and implemented into the omni-directional mobile robot

1 Introduction

For speech recognition the dissimilarity between the sig-nal characteristic values and the characteristic values inthe database was calculated in early stages to identify theminimum difference as the recognition result However thismethod has a problem of poor recognition effect due todifferent talking speeds Afterwards some scholars proposedthe dynamic timewarping (DTW) to improve the recognitioneffect [1 2]Thismethod assumes two speech signal segmentsto be compared and the short-time feature parameters ofthe two segments of speech are extracted namely separatedinto a string of frames to determine a group of parametersfrom each frame The comparison between two segmentsof speech is indeed the comparison between two sequencefeature parametersTheDTW can adjust the speech length toreduce the errors in the speech time span In the recognition

system followingDTW the Artificial Neural Network (ANN)and HMM algorithms were proposed

The ANN is a method often used in the artificial intel-ligence domain [3 4] The ANN does not need to knowthe mathematical model of the system in experimental datamodeling and highly complex recognition of images lettersor sound so that it can replace system models Knowing thetype of outputs generated from the type of input could achievegood recognition effect after learning and repeated trainingHowever the ANN updates weights and bias iteratively andthe amount of calculation is large so it consumes a lot ofcomputer resources The HMM uses probability model todescribe the pronunciation in statistics [5ndash7] A continuousstate transition in Markov model can be regarded as thephonation of a short speech segment namely a string ofconnected HMM which is the representative for segmentof speech The HMM is a method mostly used in speech

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 262791 7 pageshttpdxdoiorg1011552014262791

2 Mathematical Problems in Engineering

Industrialcomputer

Bluetoothdongle

PIC

Motorencoder

Encoderboard

DCmotor

Motordriver

Bluetooth serial

adapter

RFID reader

Computer side

Omnidirectionalmobile robot side

User side

RS232

RS232

RS232

PWM

RF

USB

Wirelesshandset

Bluetooth

Transform to

RFIDtag

RFIDtag

RF

lead acid battery

lead acid battery

Powercircuit

Ultrasonicseneor

9V

9V

9V

110V

5V

5V

5V

5V

24V

24V

5V 9V 24V

12C12V

500W

IO

IO

IO

power inverter

microcontroller

PIC microcontroller

Figure 1 Robot system hardware link

recognition in recent years This paper uses the HMM as thespeech recognition core

2 Hardware Design

The direction of the voice controlled guide type omnidirec-tional mobile robot is controlled by voice and the robothas the RFID guide system and infrared image trackingand ultrasonic obstacle avoidance functions [8] All of theproposed robot systems are configured with three subsys-tems they are omnidirectional mobile robot side computerside and user side and shown in Figure 1 The PeripheralInterface Controller (PIC) microcontroller is the core onthe omnidirectional mobile robot side its main functionincludes signal process of peripheral devices and motor drivecontrol for three wheelsThe computer side uses an industrialcomputer processing speech recognition calculation RFIDguide system and infrared image trackingThe user side usesa wireless headset and the RFID active tag as voice controlequipments

3 HMM-Based Speech Recognition System

31 Preprocessing and Feature Parameter Extraction Thespeech signals are preprocessed before speech recognitionThe speech preprocessing contains sampling frame endpointdetection preemphasis and windowing After the speechsignal preprocessing the characteristic feature parameters

are identified for subsequent recognition calculation Inthis paper the Linear Predictive Coefficient (LPC) is usedto deduce the cepstrum and delta-cepstrum as the mostimportant feature parameters

The concept of linear prediction originates from that theamplitude of a sampling point is related to the amplitudeof an adjacent sampling point during pronunciation If thepostsampling sequence of speech signals is 119878(119899) the presentsample of speech signal that is 119878(119899) is the sample values oftime 119899 If 119878(119899) is the predicted value of 119878(119899) since there mustbe an error between the predicted value and the actual valuethe predicted error can be expressed as 119890(119899) as follows

119890 (119899) = 119878 (119899) minus 119878 (119899) = 119878 (119899) minus

119897

sum

119895=1

119886119895119878 (119899 minus 119895) (1)

where 119886119895 is the linear predictive coding and 119897 is the ordernumber of linear prediction The coefficient 119886119895 is adjustedas long as the squared error value of (1) is minimizedan optimal linear predictive coefficient 119886119895 can be obtainedThe autocorrelation is determined before solving the linearpredictive coefficient and then the wanted linear predictivecoefficient is obtained from the obtained autocorrelationusing the Durbin algorithm

After determining the LPC the cepstrum coefficient isdeduced from the LPC [9]The cepstrum coefficient separatesthe vocal tract model from excitation signal and it can calcu-late the vocal tract parameters more precisely so as to control

Mathematical Problems in Engineering 3

Yes

Enter verbal command on direction

Speech recognition system

Robot movement control

Tag in users hand is read

Introduce the site

Fixed tag is read

Start

RFID actives tag transmits signal

Whether RFID reader receives

tag signal or not

RFID reader continues detection

No

No

Yes

Tag ID recognition

End

Introduce or not(speech recognition

system)

Figure 2 System operation flow of voice controlled guide type omnidirectional mobile robot

Figure 3 Omnidirectional mobile robot

the speech spectrum characteristicsThe cepstrum coefficient119888119895 is determined from the linear predictive coefficient 119886119895where 119897 is the order number of linear prediction shown asfollows

1198881 = 1198861

119888119895 = 119886119895 +

119895minus1

sum

119896=1

(1 minus119896

119895) sdot 119886119896 sdot 119888119895minus119896 (1 lt 119895 le 119897)

119888119895 =

119901

sum

119896=1

(1 minus119896

119895) sdot 119886119896 sdot 119888119895minus119896 (119895 gt 119897)

(2)

In a practical environment the external noise influencesthe speech receiving so that the tone in the spectrum isdisturbed and distorted The delta-cepstrum can reduce thisnoise effect The delta-cepstrum parameter Δ119888119895(119905) is shownin (3) where 120591 is the number of related former (minus119870) or latterframes (119870)The cepstrum and delta-cepstrumparameters areto be used as feature parameters for recognition

Δ119888119895 (119905) =119889119888119895 (119905)

119889119905=

sum119870

120591=minus119870120591 sdot 119888119895 (119905 + 120591)

sum119870

120591=minus1198701205912

(3)

32 HMM and Training Reference Model

321 Build the Initial Model The states and frames areseparated averagely from the audio part of a segment ofspeech according to the preset HMM state number and thefeature vectors in the frames are used to calculate the meanvalue 119872119895 and variance Var119895 as shown in (4) where 119860 is astate of HMM 119894 is the frame 119895 is the feature parameter 119879 isthe number of frames in a state and 119902 is the number of featurevectors of cepstrum and delta-cepstrum This paper uses 15


(a) (b)

(c) (d)

Figure 4 User using speech to control robot to move forward and turn left (a) User commands robot to move forward (b) User commandsrobot to stop (c) User commands robot to turn left (d) Robot turns left and moves on

cepstrum and 15 delta-cepstrum as characteristic values and119902 is 30

119872119895 =sum119879

119894=1119860 (119894 119895)

119879 1 le 119895 le 119902

Var119895 =sum119879

119894=1[119860 (119894 119895)]

2

119879minus (119872119895)

2

1 le 119895 le 119902

(4)

322 Viterbi Algorithm In order to obtain the correct rela-tionship between frame andHMM state more accurately thispaper uses a Gaussian probability function [10] to determinethe similarity probability value of state and frame A higherprobability value indicates a higher similarity between thecorresponding frame and the state as shown in (5) where119866119894(119909119879) is the probability value of each state corresponding toits frame 119889 is the feature vector dimension 119909119879 is the featurevector 120591119877119894 is the mean value of states 119877119894 is the covariance


(a) (b)

(c) (d)

Figure 5 Robot guide experiment (a) User commands robot to move forward (b) Robot detects tag and asks user whether he needs anyintroduction to the place or not (c) User says YES (d) Robot plays video

matrix of the density function and 119866119894(119909119879) is the probabilityvalue of similarity between the feature vector 119909119879 and state 119894

119866119894 (119909119879)=1

radic(2120587)119889 1003816100381610038161003816119877119894

1003816100381610038161003816

exp minus1

2(119909119879minus 120591119877119894)

119879119877119894minus1

(119909119879 minus120591119877119894)

(5)

The HMM can be represented by

120582 = 120587 119860 119861 119878 119881 (6)

where 119878 = 1199041 1199042 119904119873 is the state sequence 119873 is thestate number 119881 is the observed results 120587 = 120587119894 is theinitial state probability 119860 = 119886119894119895 is the state transitionprobability 119861 = 119887119895(119874119905) is the state observation probability119874119905 = 1198741 1198742 119874119879 is the observation sequence and 119879 isthe sequence length

TheGaussian probability density function determines theprobability value between frame and state The HMM hasmany optional paths for state transition and the pathwith themaximum total probability value among all possible paths is


required to be found This paper uses the Viterbi algorithm[11 12] as shown in (7)ndash(10) where 120575119894(119894) is the probability ofstaying in state 119894 at time 119905 120595119905(119894) is the probability of reachingstate 119894 at time 119905 119901 is the final probability value of the Viterbialgorithm and 119878119879 is the optimal state sequence

Step 1 Initializing

120575119905 (119894) = 120587119894119887119894 (1199001) 1 le 119894 le 119873

120595119905 (119894) = 0

(7)

Step 2 Recursing

120575119905+1 (119895) = max1le119894le119873

[120575119905 (119894) sdot 119886119894119895] sdot 119887119895 (119900119905+1)

120595119905+1 (119895) = arg max1le119894le119873

[120575119905 (119894) sdot 119886119894119895]

1 le 119905 le 119879 minus 1 1 le 119895 le 119873

(8)

Step 3 Terminating

119901 = max1le119894le119873

[120575119905 (119894)]

119878119879 = arg max1le119894le119873

[120575119905 (119894)]

(9)

Step 4 Path backtracking

119878119905 = 120595119905+1 (119878119905+) 119905 = 119879 minus 1 119879 minus 2 119879 minus 3 1 (10)

323 Reevaluation After the new relationship between stateand frame is obtained using the Viterbi algorithm themean value and variance in old state are updated and theGaussian density function is used to determine the updatedprobability between state and frame again The new totalprobability value is obtained using the Viterbi algorithmTheupdate continues until the maximum total probability valueis converged and this is the reference model after training

33 Speech Recognition The needed commands are trainedinto models which serve as reference database of speechrecognition The feature parameters are determined accord-ing to previous procedure during recognition The referencemodels of database are compared using the Viterbi algorithmto determine the probability value of each model and findthe optimal state sequence The time warping of speechsignals is solved automatically when corresponding to asequence of frames to the state sequence The key point inthe speech training procedure is to identify the correlationbetween frame and stateThe relationship between frame andstate should be updated by continuous path backtracking ofViterbi until the path with the maximum total probabilityis determined The most important step in the recognitionprocedure is to compare the reference models of trainingand obtain the maximum total probability value in referencemodels

Table 1 Recognition rates for the speaker dependent and speakerindependent

Speaker dependent Recognition ratesChun-Yuan 967Jian-Min 933Yi-Chung 90Wei 967Hung-Hui 933Average recognition rates 94Speaker independent Recognition ratesJason 667Ian 733Andy 90Momo 833Apple 50Average recognition rates 747

4 Experiment Results

Figure 2 shows the system operation flow of the voice con-trolled guide type omnidirectional mobile robot In the RFIDguide system the Reader captures Tag data and then attachesenvironmental information to the Tags of different ID codesor starts up the speech function Figure 3 shows the pictureof the proposed omnidirectional mobile robot

We place the robot in the actual environment and test var-ious moving actions (forward backward turn left turn rightstop and turn back) The voice control of speaker dependentand speaker independent are tested by five users respectivelyand the experimental results of speech recognition rates areshown in Table 1 Figure 4 shows the experiment of the userusing speech to control the robot to move forward and turnleft Figure 5 shows the user using speech to control the robotto move forward receiving the Tag of the classroom whenpassing by the classroom the user can use Yes orNo to choosewhether accessing detailed information on the site The siteis introduced in the video format so that the user can getacquainted with the environment quickly

5 Conclusions

This paper used the HMM-based speech recognitionmethodto complete a voice controlled guide type omnidirectionalmobile robot The first convenience of voice control is thatthe operation does not require manual operation whichmakes the robot more user-friendly The guide system basedon RFID technology enables the users to know the infor-mation of an unfamiliar environment quickly Finally therobot movement experiment and the robot guide systemexperiment proved the feasibility and stability of this voicecontrolled guide type omnidirectional mobile robot

Conflict of Interests

The authors declare no conflict of interests


Acknowledgment

The financial support of this research by the National ScienceCouncil of Taiwan underGrant no NSC-100-2221-E-167-004is greatly appreciated

References

[1] H Sakoe and S Chiba ldquoDynamic programming algorithmoptimization for spoken word recognitionrdquo IEEE Transactionson Acoustics Speech and Signal Processing vol 26 no 1 pp 43ndash49 1978

[2] C Kim and K-D Seo ldquoRobust DTW-based recognition algo-rithm for hand-held consumer devicesrdquo IEEE Transactions onConsumer Electronics vol 51 no 2 pp 699ndash709 2005

[3] D P Morgan and C L Scofield Eds Neural Networks andSpeech Processing Kluwer Academic Publishers 1991

[4] C-F Juang C-T Chiou and C-L Lai ldquoHierarchical singleton-type recurrent neural fuzzy networks for noisy speech recogni-tionrdquo IEEE Transactions on Neural Networks vol 18 no 3 pp833ndash843 2007

[5] L R Rabiner ldquoA tutorial on hiddenMarkovModels and selectedapplications in speech recognitionrdquo IEEE T Acoust Speech vol77 pp 257ndash286 1978

[6] S YoshizawaNWadaNHayasaka andYMiyanaga ldquoScalablearchitecture for word HMM-based speech recognition andVLSI implementation in complete systemrdquo IEEE Transactionson Circuits and Systems I Regular Papers vol 53 no 1 pp 70ndash77 2006

[7] J-H Im and S-Y Lee ldquoUnified training of feature extractor andHMM classifier for speech recognitionrdquo IEEE Signal ProcessingLetters vol 19 no 2 pp 111ndash114 2012

[8] S F Huang Design and Implementation of an AutonomousFollowing Omni-Directional Mobile Robot National DigitalLibrary of Theses and Dissertations Taipei Taiwan 2008

[9] Y Yuan P Zhao andQ Zhou ldquoResearch of speaker recognitionbased on combination of LPCC and MFCCrdquo in Proceedingsof the IEEE International Conference on Intelligent Computingand Intelligent Systems (ICIS rsquo10) pp 765ndash767 Xiamen ChinaOctober 2010

[10] L Liu and J He ldquoOn the use of orthogonal GMM in speakerrecognitionrdquo inProceedings of the IEEE International Conferenceon Acoustics Speech and Signal Processing (ICASSP rsquo99) pp845ndash848 Phoenix Ariz USA March 1999

[11] C C Wen EdMultimedia Applications for Speech RecognitionSystem National Digital Library of Theses and DissertationsTaipei Taiwan 2008

[12] D F Tseng ldquoRobust decoding for convolutionally coded sys-tems impaired by memoryless impulsive noiserdquo IEEE Transac-tions on Communications vol 61 pp 4640ndash4652 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Industrialcomputer

Bluetoothdongle

PIC

Motorencoder

Encoderboard

DCmotor

Motordriver

Bluetooth serial

adapter

RFID reader

Computer side

Omnidirectionalmobile robot side

User side

RS232

RS232

RS232

PWM

RF

USB

Wirelesshandset

Bluetooth

Transform to

RFIDtag

RFIDtag

RF

lead acid battery

lead acid battery

Powercircuit

Ultrasonicseneor

9V

9V

9V

110V

5V

5V

5V

5V

24V

24V

5V 9V 24V

12C12V

500W

IO

IO

IO

power inverter

microcontroller

PIC microcontroller

Figure 1 Robot system hardware link

recognition in recent years This paper uses the HMM as thespeech recognition core

2 Hardware Design

The direction of the voice controlled guide type omnidirec-tional mobile robot is controlled by voice and the robothas the RFID guide system and infrared image trackingand ultrasonic obstacle avoidance functions [8] All of theproposed robot systems are configured with three subsys-tems they are omnidirectional mobile robot side computerside and user side and shown in Figure 1 The PeripheralInterface Controller (PIC) microcontroller is the core onthe omnidirectional mobile robot side its main functionincludes signal process of peripheral devices and motor drivecontrol for three wheelsThe computer side uses an industrialcomputer processing speech recognition calculation RFIDguide system and infrared image trackingThe user side usesa wireless headset and the RFID active tag as voice controlequipments

3 HMM-Based Speech Recognition System

31 Preprocessing and Feature Parameter Extraction Thespeech signals are preprocessed before speech recognitionThe speech preprocessing contains sampling frame endpointdetection preemphasis and windowing After the speechsignal preprocessing the characteristic feature parameters

are identified for subsequent recognition calculation Inthis paper the Linear Predictive Coefficient (LPC) is usedto deduce the cepstrum and delta-cepstrum as the mostimportant feature parameters

The concept of linear prediction originates from that theamplitude of a sampling point is related to the amplitudeof an adjacent sampling point during pronunciation If thepostsampling sequence of speech signals is 119878(119899) the presentsample of speech signal that is 119878(119899) is the sample values oftime 119899 If 119878(119899) is the predicted value of 119878(119899) since there mustbe an error between the predicted value and the actual valuethe predicted error can be expressed as 119890(119899) as follows

119890 (119899) = 119878 (119899) minus 119878 (119899) = 119878 (119899) minus

119897

sum

119895=1

119886119895119878 (119899 minus 119895) (1)

where 119886119895 is the linear predictive coding and 119897 is the ordernumber of linear prediction The coefficient 119886119895 is adjustedas long as the squared error value of (1) is minimizedan optimal linear predictive coefficient 119886119895 can be obtainedThe autocorrelation is determined before solving the linearpredictive coefficient and then the wanted linear predictivecoefficient is obtained from the obtained autocorrelationusing the Durbin algorithm

After determining the LPC the cepstrum coefficient isdeduced from the LPC [9]The cepstrum coefficient separatesthe vocal tract model from excitation signal and it can calcu-late the vocal tract parameters more precisely so as to control


Yes





Introduce the site

Fixed tag is read

Start



tag signal or not


No

No

Yes

Tag ID recognition

End


system)




1198881 = 1198861

119888119895 = 119886119895 +

119895minus1

sum

119896=1

(1 minus119896


119888119895 =

119901

sum

119896=1

(1 minus119896


(2)


Δ119888119895 (119905) =119889119888119895 (119905)

119889119905=

sum119870

120591=minus119870120591 sdot 119888119895 (119905 + 120591)

sum119870

120591=minus1198701205912

(3)




(a) (b)

(c) (d)



119872119895 =sum119879

119894=1119860 (119894 119895)

119879 1 le 119895 le 119902

Var119895 =sum119879

119894=1[119860 (119894 119895)]

2

119879minus (119872119895)

2

1 le 119895 le 119902

(4)



(a) (b)

(c) (d)



119866119894 (119909119879)=1

radic(2120587)119889 1003816100381610038161003816119877119894

1003816100381610038161003816

exp minus1

2(119909119879minus 120591119877119894)

119879119877119894minus1

(119909119879 minus120591119877119894)

(5)


120582 = 120587 119860 119861 119878 119881 (6)





Step 1 Initializing

120575119905 (119894) = 120587119894119887119894 (1199001) 1 le 119894 le 119873

120595119905 (119894) = 0

(7)

Step 2 Recursing

120575119905+1 (119895) = max1le119894le119873

[120575119905 (119894) sdot 119886119894119895] sdot 119887119895 (119900119905+1)

120595119905+1 (119895) = arg max1le119894le119873

[120575119905 (119894) sdot 119886119894119895]

1 le 119905 le 119879 minus 1 1 le 119895 le 119873

(8)

Step 3 Terminating

119901 = max1le119894le119873

[120575119905 (119894)]

119878119879 = arg max1le119894le119873

[120575119905 (119894)]

(9)










5 Conclusions





Acknowledgment


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Yes





Introduce the site

Fixed tag is read

Start



tag signal or not


No

No

Yes

Tag ID recognition

End


system)




1198881 = 1198861

119888119895 = 119886119895 +

119895minus1

sum

119896=1

(1 minus119896


119888119895 =

119901

sum

119896=1

(1 minus119896


(2)


Δ119888119895 (119905) =119889119888119895 (119905)

119889119905=

sum119870

120591=minus119870120591 sdot 119888119895 (119905 + 120591)

sum119870

120591=minus1198701205912

(3)




(a) (b)

(c) (d)



119872119895 =sum119879

119894=1119860 (119894 119895)

119879 1 le 119895 le 119902

Var119895 =sum119879

119894=1[119860 (119894 119895)]

2

119879minus (119872119895)

2

1 le 119895 le 119902

(4)



(a) (b)

(c) (d)



119866119894 (119909119879)=1

radic(2120587)119889 1003816100381610038161003816119877119894

1003816100381610038161003816

exp minus1

2(119909119879minus 120591119877119894)

119879119877119894minus1

(119909119879 minus120591119877119894)

(5)


120582 = 120587 119860 119861 119878 119881 (6)





Step 1 Initializing

120575119905 (119894) = 120587119894119887119894 (1199001) 1 le 119894 le 119873

120595119905 (119894) = 0

(7)

Step 2 Recursing

120575119905+1 (119895) = max1le119894le119873

[120575119905 (119894) sdot 119886119894119895] sdot 119887119895 (119900119905+1)

120595119905+1 (119895) = arg max1le119894le119873

[120575119905 (119894) sdot 119886119894119895]

1 le 119905 le 119879 minus 1 1 le 119895 le 119873

(8)

Step 3 Terminating

119901 = max1le119894le119873

[120575119905 (119894)]

119878119879 = arg max1le119894le119873

[120575119905 (119894)]

(9)










5 Conclusions





Acknowledgment


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b)

(c) (d)



119872119895 =sum119879

119894=1119860 (119894 119895)

119879 1 le 119895 le 119902

Var119895 =sum119879

119894=1[119860 (119894 119895)]

2

119879minus (119872119895)

2

1 le 119895 le 119902

(4)



(a) (b)

(c) (d)



119866119894 (119909119879)=1

radic(2120587)119889 1003816100381610038161003816119877119894

1003816100381610038161003816

exp minus1

2(119909119879minus 120591119877119894)

119879119877119894minus1

(119909119879 minus120591119877119894)

(5)


120582 = 120587 119860 119861 119878 119881 (6)





Step 1 Initializing

120575119905 (119894) = 120587119894119887119894 (1199001) 1 le 119894 le 119873

120595119905 (119894) = 0

(7)

Step 2 Recursing

120575119905+1 (119895) = max1le119894le119873

[120575119905 (119894) sdot 119886119894119895] sdot 119887119895 (119900119905+1)

120595119905+1 (119895) = arg max1le119894le119873

[120575119905 (119894) sdot 119886119894119895]

1 le 119905 le 119879 minus 1 1 le 119895 le 119873

(8)

Step 3 Terminating

119901 = max1le119894le119873

[120575119905 (119894)]

119878119879 = arg max1le119894le119873

[120575119905 (119894)]

(9)










5 Conclusions





Acknowledgment


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b)

(c) (d)



119866119894 (119909119879)=1

radic(2120587)119889 1003816100381610038161003816119877119894

1003816100381610038161003816

exp minus1

2(119909119879minus 120591119877119894)

119879119877119894minus1

(119909119879 minus120591119877119894)

(5)


120582 = 120587 119860 119861 119878 119881 (6)





Step 1 Initializing

120575119905 (119894) = 120587119894119887119894 (1199001) 1 le 119894 le 119873

120595119905 (119894) = 0

(7)

Step 2 Recursing

120575119905+1 (119895) = max1le119894le119873

[120575119905 (119894) sdot 119886119894119895] sdot 119887119895 (119900119905+1)

120595119905+1 (119895) = arg max1le119894le119873

[120575119905 (119894) sdot 119886119894119895]

1 le 119905 le 119879 minus 1 1 le 119895 le 119873

(8)

Step 3 Terminating

119901 = max1le119894le119873

[120575119905 (119894)]

119878119879 = arg max1le119894le119873

[120575119905 (119894)]

(9)










5 Conclusions





Acknowledgment


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Step 1 Initializing

120575119905 (119894) = 120587119894119887119894 (1199001) 1 le 119894 le 119873

120595119905 (119894) = 0

(7)

Step 2 Recursing

120575119905+1 (119895) = max1le119894le119873

[120575119905 (119894) sdot 119886119894119895] sdot 119887119895 (119900119905+1)

120595119905+1 (119895) = arg max1le119894le119873

[120575119905 (119894) sdot 119886119894119895]

1 le 119905 le 119879 minus 1 1 le 119895 le 119873

(8)

Step 3 Terminating

119901 = max1le119894le119873

[120575119905 (119894)]

119878119879 = arg max1le119894le119873

[120575119905 (119894)]

(9)










5 Conclusions





Acknowledgment


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgment


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article implementation of a tour guide robot

Documents