Mobile Robot Localization Using Optical Flow Sensors

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1 Intenational Jounal of Contol, Automation, Mobile Robot and Localization Sstems, vol. Using 2, no. Optical 4, pp. Flow , Sensos Decembe Mobile Robot Localization Using Optical Flow Sensos Sooong Lee and Jae-Bok Song Abstact: Open-loop position estimation methods ae commonl used in mobile obot applications. Thei stength lies in the speed and simplicit with which an estimated position is detemined. Howeve, these methods can lead to inaccuate o uneliable estimates. Two position estimation methods ae developed in this pape, one using a single optical flow senso and a second using two optical sensos. The fist method can accuatel estimate position unde ideal conditions and also when wheel slip pependicula to the ais of the wheel occus. The second method can accuatel estimate position even when wheel slip paallel to the ais of the wheel occus. Location of the sensos is investigated in ode to minimize eos caused b inaccuate senso eadings. Finall, a method is implemented and tested using a potential field based navigation scheme. Estimates of position wee found to be as accuate as dead-eckoning in ideal conditions and much moe accuate in cases whee wheel slip occus. Kewods: Mobile obot localization, mobile obot navigation, optical flow, edundant sensing. 1. INTRODUCTION Accuate position estimation is a ke component to the successful opeation of most autonomous mobile obots. In geneal, thee ae thee phases that compise the movement sequence of a mobile obot: localization, path planning, and path eecution. Duing localization, the position and oientation in the efeence coodinate sstem is detemined using etenal sensos. A path is then updated fom the cuent position to the goal if the cuent obot position is deviated fom the pe-planned path. The final phase is the eecution of the planned path. The movement sequence is epeated so that the obot will emain on couse towads the goal. Localization can be futhe decomposed into two tpes, absolute and elative [1]. Absolute localization elies on landmaks, maps, beacons, o satellite signals to detemine the global position and oientation of the obot. Relative localization (o intemediate estimation) is usuall used duing movement, because absolute localization methods ae moe time consuming. Manuscipt eceived June 24, 2004; evised Novembe 8, 2004; accepted Novembe 8, Recommended b Edito Keum-Shik Hong. This eseach was pefomed fo the Intelligent Robotics Development Pogam, one of the 21st Centu Fontie R&D Pogams funded b the Minist of Science and Technolog of Koea. Sooong Lee is with the Depatment of Mechanical and Sstem Design Engineeing, Hongik Univesit, 72-1 Sangsu- Dong, Mapo-Gu, Seoul , Koea ( sooong@ hongik.ac.k). Jae-Bok Song is with the Depatment of Mechanical Engineeing, Koea Univesit, Anam-dong, Seongbuk-gu, Seoul , Koea ( jbsong@koea.ac.k). Commonl, dead-eckoning (open-loop estimation) is used fo intemediate estimation of position duing path eecution. Dead-eckoning is often used when wheel encodes ae available fo dive wheel position measuement. Howeve, due to eos in kinematic model paametes, wheel slip, o an uneven suface, poo position estimates ma occu. Poo estimates in position duing path eecution equie moe fequent localization, incuing eta ovehead and possibl slowing the movement of the obot. A wose scenaio is one whee poo estimates would cause a collision, impeding the opeation of the obot. It is theefoe impotant to minimize eos in estimated position duing the path eecution phase. Dead-eckoning usuall fails (causes poo estimates) in the pesence of wheel slip. Howeve, using the methods descibed in this pape, accuate estimates of position can be maintained even when wheel slip occus. Indeed, when eithe sstematic eos (eos elated to obot popeties o paametes) o non-sstematic eos (andom eos caused b the envionment) occu, dead-eckoning usuall fails to accuatel estimate position. Deadeckoning onl poduces accuate estimates when all kinematic constaints ae upheld. Two methods ae developed, implemented and tested using inepensive optical flow sensos. The placement of the optical sensos affects estimation eos. An optimal placement scheme (in the sense of minimizing estimation eos) is poposed. Additionall, path planning is discussed and implemented. Optical flow sensos can be used to accuatel estimate the position of the obot b utilizing the methods descibed. In most movement schemes, dead-eckoning eos ae an accepted pat of the movement sequence. These

2 486 Sooong Lee and Jae-Bok Song eos ae usuall counteacted b making fequent localization stops. This is unfotunate, because in man cases dead-eckoning poves to be inaccuate. If a moe accuate method wee available, less intemediate localization would be necessa. This would in tun fee computational esouces that could be used to accomplish highe level tasks. Othe eseaches have implemented simila deadeckoning coection techniques. A [1] towed obot (called a taile), which has accuate wheel encodes and a ota encode on the connection link, is used to detemine the elative movement and diection of the taile with espect to the obot. This infomation allows an accuate estimated position to be maintained. This method educed dead-eckoning eos b an ode of magnitude o moe. Howeve, the added bulk of the taile can complicate the movement of the obot making it difficult to navigate in close quates, especiall when moving backwads. Anothe method of coecting dead-eckoning eos in navigation uses optical flow. In [2], optical flow was used to aid in the navigation of an omnidiectional obot. A CCD camea was positioned at a 45 o downwad angle to the gound in font of the obot. The optical flow obtained was combined with the esults of dead-eckoning via maimum likelihood technique. The method used to calculate optical flow is quite comple, equiing a lage numbe of computations to obtain good esults. GPS has man applications to mobile obot navigation [3]. GPS has been used to coect position estimations b adjusting kinematic paametes. In [4] GPS was used to coect fo heading and step size in a pedestian navigation sstem. When GPS is available the paametes ae adjusted such that when GPS sevice is unavailable, a good estimate of position is maintained. This method is easil potable to mobile obots. Howeve, GPS accuac is limited, so when fine positional contol is necessa it can pove ineffective. GPS is futhe limited b the fact that it will onl wok in outdoo envionments whee lineof-sight to at least 3 satellites is possible. Bashan and Duant-Whte developed inetial navigation methods fo mobile obots in [5]. A seies of solid state gos, acceleometes and tilt sensos wee emploed in conjunction with an etended Kalman filteing method to estimate position and oientation. Using acceleometes to detemine position and oientation, howeve, has seveal dawbacks such as 1-8 cm/s dift ate. Also, the minimum detectable acceleation can sometimes be too lage to detect small motion. Inetial methods can be quite computationall intensive, epensive and comple. fo optical flow measuement. These sensos ae inepensive, eliable, accuate, and ve fast. Two methods of estimating the location and oientation of the obot ae investigated in this section. The fist uses a single senso and a constaint on the kinematics of the obot. The second method uses two sensos and no kinematic constaints Single optical senso Unless the optical flow senso is placed at the point of inteest on the obot, measuements diectl fom the optical senso will not be useful. Additionall, because the optical senso onl povides displacements in the and diections, infomation about the angula displacement of the obot is lost. As a esult, anothe method must be used to detemine the angula velocit of the obot. Fig. 1 shows the coodinates used fo the igid bod method. The obot can be viewed as a igid-bod whee the velocit at the senso ( / t and / t) is known. The kinematic constaints of a diffeential dive obot allow the calculation of movement, given this velocit. Specificall, the cente of the obot is assumed to move onl in a diection pependicula to the wheel ais. The following equation elates the velocit of a point on the ais of otation of a igid bod (obot cente) with a point not on that ais of otation (the senso location): = + ω, (1) s s/ whee is the velocit of the cente of the obot, s is the senso velocit, ω is the angula velocit of the obot, and s / is the vecto fom the location of the senso to the obot cente (Fig. 1). Rewiting in mati fom: 2. SENSOR INTERPRETATION In this pape, commecial optical mice wee used Fig. 1. Rigid-bod model fo senso intepetation.

3 Mobile Robot Localization Using Optical Flow Sensos 487, s, =, + s, ω ω. (2) It should be noted that the senso ma not be oiented along the and obot coodinates. Denoting the oientation of the senso as β, and the senso coodinates as and, the following tansfomation is made to obot coodinates: s, cos( β) sin( β) s, = s, sin( β) cos( β). (3) s, With the assumption that, = 0, ω and, ae obtained fom the following two equations: s, ω =, (4), = s, ω = s, + s,. (5) The obot's velocit can now be easil tanslated to the global coodinate sstem as follows: θ = ( ω ) dt, (6) X = (, sin( θ)) dt, (7) Y = ( cos( θ )) dt. (8), A simila appoach to using the kinematic constaint = is to use the weighted pseudo-invese. This, 0 method gives one possible solution to the undedetemined case, whee thee vaiables ae detemined fom onl two equations. Rewiting the igid bod equation in mati fom:, s, 1 0, = s, 0 1 ω. (9) The undedetemined pseudo-invese takes the fom:, T T s,, = W A ( AW A ) s, ω whee W is a weighting mati and, (10) 1 0 A =. (11) 0 1 If we heavil weight the velocit in the diection to be small, neal an identical solution to the constained case emeges. A suitable weighting mati follows: W = (12) Fig. 11 in Section 4 shows how vaing the weighting mati changes the appaent movement of the obot using epeimental data. The single senso method will give bette esults when wheel slip pependicula to the wheel ais occus athe than dead-eckoning. In fact, as long as the kinematic constaint, = 0 is not violated, the method will suppl accuate position estimates. If multiple sensos ae used, the constaint can be emoved, allowing pecise positional estimates in all kinematic conditions. This is the topic of the following subsection Multiple optical sensos Given a second senso, thee ae at least two appoaches that could be used to intepet the data. Fist, the additional senso could be viewed as a edundant senso, which would lead to data fusion methods. Data fusion should give bette esults than a single senso given data eo. Howeve, it would still povide inaccuate esults if the kinematic constaint,, = 0 wee violated. Altenativel, the velocit infomation fom the second senso can be used to detemine the motion of the igid-bod without the constaint,, = 0, that was necessa using onl a single senso. Looking again at the igid-bod model, two sensos at diffeent locations give ample infomation to detemine the motion of the igid-bod without an kinematic constaints. In this case, the igid-bod model leads to the following fou equations: = ω, (13), s1, s1, = + ω, (14), s1, s1, = ω, (15), s2, s2, = + ω, (16), s2, s2, whee, and, ae the velocities of the cente of the obot, ω is the angula velocit of the obot, si, and si, ae the senso velocities and, si and, si ae the and distances fom the i th senso position to the obot cente. To solve this sstem of equations fo the angula

4 488 Sooong Lee and Jae-Bok Song and linea velocities of the obot, the sstem is witten as 1 0 s1, s1,, 0 1 s1, s1,, 1 0 =. (17) s2, s2, ω 0 1 s2, s2, This ovedetemined sstem can be solved using the pseudo-invese [6]. Simila to one senso case, the obot's velocities ae tanslated to the global coodinates as θ ( ω ) =, (18) dt (, θ, sinθ ) (, θ, cosθ ) X = dt, (19) Y = + dt. (20) The least squaes ovedetemined solution can also be weighted similal to the undedetemined case. Howeve, the weightings would be of the sensed velocities ( s1,, s1,, s2,, s2, ). It is not eadil appaent which of these velocities should eceive a highe impotance than the othe. This avenue of eseach was not investigated. Although multiple sensos do not incease accuac when compaed to a single senso, the kinematic constaint can now be emoved. This ields a poweful method to detemine intemediate estimates of the obot position and oientation. 3. SENSOR PLACEMENT 3.1. Optimal senso location Anothe impotant issue to conside is minimizing an eo. Using the method descibed in the peceding section, seveal possible souces of an eo ae pesent. These include eos in the position and oientation of the sensos and eos in the sensed velocities. Minimizing these eos will lead to bette estimates of obot position. In ode to detemine the best position fo a single senso, the eo in the measuement of the velocit must be minimized. The maimum absolute deviation F,,, is defined as: of a function ( ) o 1 n d ω = d + d, (22) 1 2 d = d + 1 d + + d. d 2 (23) Eos in senso oientation ae ignoed because calibation of the sensos can easil be caied out using a staight line path. Senso oientation can be tuned such that the sensed path closel matches the actual path. Additionall, the position of the senso is known within a few millimetes and is theefoe assumed to be eactl known. (In epeiments, the sensos wee placed at 20cm fom the cente of the obot, and measuement eos ae on the ode of 0.1cm.) This leads to a futhe simplified equation: 1 dω = d, (24) d = d + 1 d. (25) Plots of fist ode deviations of these equations ae shown in Figs. 2 and 3. As can be seen, the optical senso should be located as fa awa as possible fom the cente of the obot along the -ais, because the global minima is located at = 0. Ideall, the eo in the detemination of the obot's position will be zeo fo = 0 and =. Howeve, this is impactical both phsicall and mathematicall. Looking at (4) if = then ω F F df = d0 + + dn. (21) 0 n Using this definition and the peviousl given single senso igid-bod model, the maimum absolute deviations ae as follows: Fig. 2. Eo of ω vesus.

5 Mobile Robot Localization Using Optical Flow Sensos 489 Fig. 3. Eo of vesus,. Fig. 5. Eo of, vesus senso 2 position. Fig. 4. Eo of, vesus senso 2 position. Fig. 6. Eo of ω vesus senso 2 position alwas equals zeo, which is unacceptable. To find the optimal position using two sensos, again the maimum absolute deviations of the functions ae used. Because of the lage numbe of paametes in each equation, visualizing the deviations is difficult. Assuming again that the positions of the sensos elative to the obot's cente can be measued eactl, the onl eo pesent is in the senso velocities. The fist obsevation is that thee is a ange of positions whee the eos become minimal. To minimize the eo in the measuement of the angula velocit ( ω ) the sensos should be located as fa fom the cente of the obot as possible. Looking at Fig. 5, if the eo in -diection velocit, is minimal, the -positions of the sensos have the same value with diffeent signs. The same is obseved fo the eo of the velocit in -diection,. The fist ode deviations of and ω when senso 1 is placed at 1, = 10 and 1, = 0 ae shown in Figs. 4, 5, and 6. The location of the sensos is impotant because the sensos povide onl the linea velocities d and d, but not the angula velocit, dθ. The change in oientation is cleal impotant when updating the position. Theefoe, an eos in d o d will geatl affect the accuac of eithe igid-bod method. As indicated in Fig. 3, the lage the, the smalle the eo in ω. Howeve, it is impactical to have a long am with a senso mounted because the am ma be bent and also it ma cause collision with neab obstacles. The -position of a senso is not as sensitive as the -position eithe in eo of no ω. Theefoe, the font senso is attached at s1, = 40mm and s 1, = 60mm. The ea senso is at the smmetic location at 1, = 40mm and 2, = 60mm. s s 3.2. Gound cleaance Anothe impotant aspect egading the placement of the optical sensos is focal length. Commecial optical flow sensos have a naow band of opeation

6 490 Sooong Lee and Jae-Bok Song coesponding to the focal length. This is because in ode to popel detemine the movement of the senso, the coespondence between the numbe of piels in the image and a eal measuable length must be known. Changing the focal length will va this elationship, causing eos. If this constant focal length is not maintained, eos in distance will accumulate quickl. The sensos used in the epeimental section of this pape have a nominal focal length of 2.4mm. Accuate data ae obtained onl if the focal length is popel maintained. If the focal length is inceased even a few tenths of a millimete, inaccuate d and d data esults. This was ovecome b focing the sensos to the gound, which tended to significantl incease fiction. Howeve, an incease in fiction can cause the wheels to slip, making it difficult to move. It is desiable to educe fiction and at the same time maintain the 2.4mm focal length ecommended b the chip manufactue. Fig. 7. Mobile obot with optical sensos. 4. EXPERIMENTAL ALIDATION 4.1. Senso specifications The optical flow sensos used wee the Agilent ADNS This senso allows fast, accuate, optical sensing of micoscopic images. The senso is capable of 800 counts pe inch while moving at up to 14 inches pe second. Successive images ae used to calculate the and values at up to 2300 fames pe second. A micocontolle is used that communicates diectl with the ADNS This chip communicates with the ADNS-2051, setting modes and communicating with the PC o othe devices using the PS-2 standad. The optical flow senso uses successive images to intepet the movement between images. Images ae taken of a point on the gound diectl beneath the senso. The images ae piels and epesent a micoscopic aea Robot specifications In ode to test the algoithms pesented in this pape, a obot sstem was designed and built. A modula design appoach was implemented. Each module is esponsible fo one pat of the oveall opeation of the obot. This tpe of design pemits testing of vaious configuations, as well as allows eas eplacement of an single sstem Hadwae The mobile obot includes a 12 inch, ound plastic base, two 1 amp 12 olt DC geaed motos, two casto wheels, two 6 inch diamete ubbe wheels, and two encodes attached to the dive wheel ales. The diffeential diven wheels allow tuns to be Fig. 8. Inteaction between objects in Java. made in place. This smmetic design offes high maneuveabilit. The maimum staight line speed is appoimatel 78 feet pe minute (50 evolutions pe minute of the dive wheels). The obot is shown in Fig. 7. Two optical flow sensos ae used but onl the font one is shown in the figue. The obotic base consists of a micocontolle cicuit with vaious communication and electonic chips, two motos, two 1 amp moto contolles, two HEDS-5500 encodes and two Agilent HCTL-2020 encodedecode chips. The senso sstem consists of a contolle and two optical flow sensos. The contolle includes a micocontolle, seial communication module. The micocontolle intefaces with the two sensos and tansmits the data to the PC using seial communication Softwae The softwae consists of thee independent sstems that must opeate conguousl in ode to function.

7 Mobile Robot Localization Using Optical Flow Sensos 491 These sstems ae the obot sstem, the senso sstem and a PC based contolle. The obot and senso sstems ae based on PIC 16F877 micocontolles unning at 10 MHz. The PC contolle is implemented using Java. The opeation of the sstem is outlined in Fig. 8. Softwae design equiements fo the obotic base wee to contol the speed of two motos to desied velocities and output the position (o velocit) of both the left and ight wheels. The obotic base eceives wheel commands fom the PC and contols the diffeence in wheel positions between successive inteupts Intemediate localization Epeiments wee pefomed compaing intemediate localization (positional estimates) using dead-eckoning, the single senso and the multiple senso igid-bod method. Epeiments wee pefomed whee no kinematic violations occued to test the accuac of localization. Epeiments wee also pefomed whee kinematic violations wee foced. In epeiments whee kinematic constaints wee upheld (, = 0 and no wheel slip) as in Fig. 9, little pefomance diffeence can be seen between the methods. Thee ae thee diffeent estimated obot paths in this figue. The fist one is fom the encode data, (so called dead-eckoning). The obot configuation (position/oientation of the obot) is estimated fom the obot fowad kinematics with the measued encode data at each sampling time. The second one is estimated with an optical flow senso that is fied in font of the obot, fom (5)-(9). The thid one is with two optical flow sensos using (17)- (20). When the kinematic constaints wee intentionall violated with an outside distubance as in Fig. 10, howeve, onl the multiple senso method gave good esults. The esults of the single senso method ae inteesting. It would seem that when kinematic distubances ae encounteed, the method gives uneliable esults. Howeve, this should be epected because the kinematic constaint is equied fo a solution to eist in the fist place. Additionall, if the undedetemined pseudoinvese solution is used (see Section 2), thee is little accuac gained. This solution does not use the constaint, but simpl weights the solution so that velocit in the diection is educed. This method was investigated to detemine if an accuate estimate would esult if the constaint, = 0 is emoved. Fig. 11 shows how changing the weighting of, effects the estimated path compaed to the dual-senso method. Fig. 9. Localization methods compaed with kinematics upheld. Fig. 10. Localization methods compaed with kinematic constaints. Fig. 11. Weighted pseudo-invese fo the undedetemined single senso case Potential field based navigation In ode to test the effectiveness of the intemediate

8 492 Sooong Lee and Jae-Bok Song Fig. 12. Navigation with wheel slip. whee k v and k ω ae popotional constants and potential is the potential velocit geneated b the potential field method. Using this appoach, esults wee satisfacto. Also, obstacles wee assumed not to be pesent, but could easil be added. In tests whee no wheel slip o kinematic violations occued, all thee methods wee similal accuate. The lagest pefomance diffeence of the multiple-senso method can be seen in the pesence of kinematic violations, such as wheel slip. Fig. 12 indicates an actual test un whee wheel slip was foced. As one can see, the obot has a sudden change in oientation at the beginning of movement. The multiple-senso method is able to detect this movement, which allows the potential field based navigation method to adjust its couse accodingl. Even when kinematic constaints ae violated, as in Fig. 13 whee the obot was pushed off couse, the multiple senso method still detects the pope change in position and oientation so that the obot successfull eaches its goal. 5. CONCLUSIONS Fig. 13. Navigation with kinematic violation. estimation method descibed, navigation tests wee pefomed. The single and multiple senso igid-bod models and dead-eckoning wee compaed unde vaious conditions. A potential field based appoach was used to geneate velocit commands fo the mobile obot to follow. An online method was used whee the desied and ω wee geneated depending upon the cuent obot location/oientation and the location of the goal point. A slight modification to the conventional potential field based method was used. This is because of the non-holomonic constaints that ae pesent with a diffeential dive mobile obot. The method was to make the obot tun towads the goal point befoe appoaching it. The following elationships wee used:, = k cos( α), (26) ω desied v potential, desied = k α, (27) ω potential Using optical flow sensos, we have deived a method that can accuatel povide intemediate position estimates. The location of the sensos has been investigated in ode to minimize potential eos intoduced b incoect senso eadings. Epeimentall, the multiple senso igid-bod technique has poven to be moe accuate and moe obust than dead-eckoning. Both sstematic and nonsstematic eos can be detected and a good estimate of location and oientation can be maintained. REFERENCES [1] J. Boenstein and L. Feng, Measuement and coection of sstematic odomet eos in mobile obots, IEEE Tans. on Robotics and Automation, vol. 12, no. 6, pp , [2] K. Nagatani, S. Tachibana, M. Sofne, and Y. Tanaka, Impovement of odomet fo omnidiectional vehicle using optical flow infomation, Poc. of IEEE/RSJ Intenational Confeence on Intelligent Robots and Sstems, vol. 1, pp , Octobe [3] B. W. Pakinson and J. J. Spilke, Global Positioning Sstem: Theo And Application, vol. 2, Ameican Institute of Aeonautics and Astonautics, [4]. Gaaj, F. Cecelja, and W. Balachandan, A method fo dead eckoning paamete coection in pedestian navigation sstem, Poc. of the 18th IEEE Instumentation and Measuement Technolog Confeence, vol. 3, pp , Ma 2001.

9 Mobile Robot Localization Using Optical Flow Sensos 493 [5] B. Bashan and H. F. Duant-Whte, Inetial navigation sstems fo mobile obots, IEEE Tans. on Robotics and Automation, vol. 11, no. 3, pp , June [6] W. L. Bogan, Moden Contol Theo, Pentice Hall, Inc., Uppe Saddle Rive, New Jese, [7] G. Ramiez and S. Zeghoul, A new local path planne fo nonholonomic mobile obot navigation in clutteed envionments, IEEE Intenational Confeence on Robotics and Automation, vol. 1, pp , Apil [8] B. Hon, Robot ision, MIT Pess, [9] L. G. Shapio and G. C. Stockman, Compute ision, Pentice-Hall Inc., [10] N. Molton, S. Se, J. M. Bad, D. Lee, and P. Pobet, A steeo vision-based aid fo the visuall impaied, Image and ision Computing, vol. 16, no. 4, pp , Apil Sooong Lee eceived the B.S. and M.S. degees in Mechanical Engineeing fom Seoul National Univesit, Seoul, Koea in 1989, and 1991, espectivel, and the Ph.D degee fom MIT, Cambidge, MA, in He woked as a Senio Reseach Scientist at KIST and then as an Assistant Pofesso in the Depatment of Mechanical Engineeing at Teas A&M Univesit. He joined Hongik Univesit, Seoul, Koea in 2003 and is cuentl an Assistant Pofesso in the Mechanical and Sstem Design Engineeing Depatment. His cuent eseach includes mobile obot localization and navigation, and active sensing. Jae-Bok Song eceived the B.S. and M.S. degees in Mechanical Engineeing fom Seoul National Univesit, Seoul, Koea, in 1983 and 1985, espectivel, and the Ph.D. degee in Mechanical Engineeing fom MIT, Cambidge, MA, in Fom 1992 to 1993 he woked as a Reseach Associate at MIT. He joined the facult of the Depatment of Mechanical Engineeing, Koea Univesit, Seoul, Koea in 1993, whee he has been a Full Pofesso since His cuent eseach inteests ae obot navigation, and design and contol of the obotic sstems including haptic devices and field obots.

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