Making Use Of What You Don t See: Negative Information In Markov Localization

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1 Making Ue Of What You Don t See: Negative Information In Markov Localization Jan Hoffmann, Michael Spranger, Daniel Göhring, and Matthia Jüngel Department of Computer Science Artificial Intelligence Laboratory Humboldt-Univerität zu Berlin Unter den Linden Berlin, Germany Abtract Thi paper explore how the abence of an expected enor reading can be ued to improve Markov localization. Thi negative information uually i not being ued in localization, becaue it yield le information than poitive information (i.e. ening a landmark), and a enor often fail to detect a landmark, even if it fall within it ening range. We addre thee difficultie by carefully modeling the enor to avoid fale negative. Thi can alo be thought of a adding an additional enor that detect the abence of an expected landmark. We how how uch modeling i done and how it i integrated into Markov localization. In real world experiment, we demontrate that a robot i able to localize in poition where otherwie it could not and quantify our finding uing the entropy of the particle ditribution. Exploiting negative information lead to a greatly improved localization performance and reactivity. Index Term Negative Information, Negative Evidence, Mobile Robot, Markov Localization, Monte Carlo Localization, Entropy I. INTRODUCTION The claic example of negative information wa decribed in the Sherlock Holme cae Silver Blaze. In thi cae, a houe ha been broken into. Under uch circumtance, one would expect the watch-dog to bark. The curiou incident of the non-barking of the dog in the nighttime provide Holme with the information that the dog mut know the burglar, allowing him to olve the cae. Applied to mobile robot localization, thi mean that concluion can be drawn from expected but actually miing enor meaurement [5]. Markov localization method, in particular Monte Carlo localization, have proven their power in numerou robot navigation tak, e.g. in office environment [1], in the mueum tour guide Minerva [14], in the highly dynamic RoboCup environment [8], and outdoor application in le tructured environment [10]; an evaluation of the variou algorithmic approache i given in [3]. Our work i focued on localization baed on landmark. Whenever a robot ene a landmark, the localization etimate i updated uing the enor model. Thi enor model i acquired before the actual run. It decribe the probability of the meaurement z given a tate (poition, orientation, etc.) The project i funded in part by the German Reearch Foundation (DFG), SPP 1125 Cooperative Team of Mobile Robot in Dynamic Environment. of the robot. Senor update only occur when landmark are detected. If no landmark i detected, the tate etimation i updated uing (only) the motion model of the robot. Example. Conider a robot driving down a corridor a hown in fig. 1a-1d. The robot ha a enor to detect door when it i tanding in front of one. Let u aume further that the robot i moving to the right but i obliviou of it tarting poition. A it tart to move to the right it pae and ene a door. Given thi information, it could be tanding in front of either of the door (tate left and right ). A it move on, it doe not pa another door for ome time. At time t = t 3, if left had been the true poition, the robot would have had paed another door by now. Uing the negative information of not perceiving a door, the belief baed on left can be ruled out. A Thrun, Bugard, and Fox put it quite graphically, not eeing the Eiffel Tower in Pari implie that it i unlikely that we are right next to it [13]. We preent a localization approach that incorporate uch negative information. To our knowledge, no explicit tudy of uing negative information in Markov localization ha been publihed. One difficulty i brought about by the fact that, generally peaking, ening a landmark contitute a greater information gain than not ening one imply becaue there are many poition within the robot environment from where the landmark cannot be perceived. A landmark i, by definition, omething that tand out in an environment. The other difficulty in implementing a ytem that ue negative information on a real robot i that there are two main reaon for the abence of an expected enor reading: the target may not be there or the enor may imply be unable to detect the target (due to occluion, enor imperfection, imperfect image proceing, etc.). Differentiating the two cae i not a trivial tak and require careful enor modeling. We addre thi problem by conidering the field of view of the robot and by uing obtacle detection to etimate occluion. Negative information modeling ha been applied to object tracking (ee [12] for an introduction and [5] for an overview). The event of not detecting an object i treated a evidence that can be ued to update it probability denity function [6]. In the RoboCup domain, not eeing the ball on the field

2 can be ued to delete Monte Carlo particle in that region a long a occluion are conidered [7]. Negative information i alo mentioned in the context of imultaneou localization and mapping (SLAM) where it i ued to adjut the confidence in landmark candidate [10]. Outline. In ection II we will how how negative information can be incorporated into Monte Carlo localization. We will then extend the enor model by alo modeling the probability of non-detection event. In ection III the poitive impact on localization will be hown in imulation and real world experiment uing the Sony Aibo ERS-7 robot. II. EXPLOITING NEGATIVE INFORMATION A. Iterative Bayeian Updating Thi work i baed on Markov localization for mobile robot a decribed in [1], [13], [11]. The belief tate of the robot Bel( t ) at time t to be in tate t i determined by all previou robot action u t and obervation z t. Uing Baye law and the Markov aumption, Bel( t ) can be written a a function depending only on the previou belief Bel( t 1 ), the lat robot action u t 1, and the current obervation z t : Bel ( t ) p( t t 1, u t 1 )Bel( t 1 )d t 1 (1) Bel( t ) ηp(z t t )Bel ( t ) (2) with normalizing contant η. Equation 1 how the a priori belief Bel ( t ) which propagate the previou belief uing the motion model of the robot. The meaurement i then incorporated into the belief a decribed in (2) uing the enor model ( enor updating ). In Markov localization, given an initial belief Bel( 0 ) at t = t 0, the robot firt update it belief uing odometry and then incorporate new enor information. The belief i updated iteratively in thi fahion for every following time tep. In the abence of enor reading, no enor updating i performed and the belief i updated olely uing odometry. B. The Notion Of Negative Information Negative information decribe the abence of a enor reading in a ituation where a enor reading i expected given the current poition etimate. To integrate negative information, imagine a binary enor being added that fire whenever the primary enor doe not detect a particular landmark l. It probability of it firing i given by: p(z l,t t ) (3) Thi enor model can be ued to update the robot belief whenever it fail to detect a landmark, i.e. when negative evidence i acquired. Fig. 2 how the probability p(z t x t, y t ) of not ening a landmark on a RoboCup field at poition (x t, y t ) ummed over all poible robot orientation. Thi figure alo how that it i mot likely for the robot to ene a landmark when it i tanding in the middle of the field. The Bel*( t )? Fig. 1a. (t = t 0 ) Illutration of a robot localizing in an office hallway. The robot ha a enor to detect door. At the beginning, the robot doe not know it poition in the hallway (uniform belief ditribution Bel ( t)). At thi time, no ening of the world take place. p(z t t ) Bel*( t )! ening action Bel*( t-1 ) Fig. 1b. (t = t 1 ) The robot ha moved down the hallway and now ene a door p(z t t) which reult in the hown belief Bel ( t). It ha two peak ince the robot could be tanding in front of either door. The previou ditribution i illutrated by the dahed line. p(z t * t ) Bel*( t ) Bel( t ) Bel*( t-1 ) Fig. 1c. (t = t 3 ) The robot move on. There are no door nearby o the door enor doe not ene a door. The enor update ditribution i hown in p(zt t). Thi negative information i of negligible ue at thi poition: it doe not help differentiate between the peak. p(z t * t ) Bel*( t ) Bel( t ) negative info. ued negative info. not ued Fig. 1d. (t = t 4 ) The robot move on and the door enor till doe not ene a door. Bel ( t) how the belief if negative information i taken into account, wherea Bel( t) how the belief without uing negative information to better illutrate the cae. A can be een from the diagram, uing negative information allow the robot to rule out the left peak.

3 p max p min Fig. 2. Probability of not ening a landmark for a robot on a RoboCup occer field. For a robot located around the center of the field, it i hard to mi landmark. likelihood of not ening a landmark i highet for poition at the edge of the field a the robot may be facing outward. Thi rather coare way of incorporating negative information can be refined by taking into account the ening range r t of the robot enor and poible occluion o t of landmark. The ening range i the phyical volume that the enor i monitoring. In cae of a tationary robot, r t = r 0 i contant, for a mobile robot with a pan-tilt camera it i not. By o t we denote a mean of detecting whether or not occluion have occurred. In practice, thi can be calculated from a map of the environment, directly ened by a enor uch a a laer range finder, or derived from a model of moving object in the environment. Combining the two yield the probability of not ening an expected landmark l at time t: p(z t,l t, r t, o t ) (4) Whenever a landmark i not detected, it can be ued in the enor update tep of the Iterative Bayeian Updating (ee Algorithm 1). C. Senor Modeling For The Sony Aibo 1) Field of View: The ERS-7 i a legged robot with a camera mounted in it head. The camera ha a horizontal opening angle of 55 o and the robot head ha 3 degree of freedom (neck tilt, head pan, head tilt). We abbreviate gaze direction by ϕ = (ϕ tilt1, ϕ pan, ϕ tilt2 ). The ening range i calculated by conidering the field of view (FOV) of the robot: 2) Occluion: In order to account for occluion, we opted for an approach that ha been ued uccefully for detecting obtacle, referred to a viual onar [4], [9]: The camera image i canned in vertical can line and unoccupied pace in the plane of the field i detected ince it can only be of green or white color (field line). Scanning for thee color tell the robot where obtacle are and where there i free pace which in turn can be ued to determine if the viibility of the landmark i impaired, i.e. if it i occluded by other robot or ome other obtacle. More pecifically, if the expected Algorithm 1 Iterative Bayeian updating incorporating negative evidence 1: Bel ( t ) p( t t 1, u t 1 )Bel( t 1 )d t 1 2: if (landmark l detected) then 3: Bel( t ) ηp(z t t )Bel ( t ) 4: ele 5: Bel( t ) ηp(z t,l t, r t, o t )Bel ( t ) 6: end if landmark lie in an area where the robot ha detected free pace, the likelihood of the correponding poe etimate i decreaed. If it lie outide of the detected free pace, no inference can be made. Taking FOV and occluion into account, the enor model for not perceiving an expected landmark (equation 4) become: p(z t,l t, z t,ob ) (5) Where z t,ob decribe the current obtacle percept and t = (x t, y t, ϑ t, ϕ t ) the robot tate coniting of the robot poe (poition x t, y t, and orientation ϑ t ) and the current gaze direction ϕ t. III. EXPERIMENTAL RESULTS The RoboCup Sony 4-Legged League erve a a tet bed for our work. In the 4-Legged League, team of 4 Sony Aibo ERS-7 robot play occer againt each other in a color coded environment (ee the official RoboCup web ite for detail: Colored beacon (4 uniquely color coded beacon plu a blue and a yellow goal) and the field line (imilar to the real occer field line) erve the robot for localization. In our experiment, unle otherwie tated, only landmark were ued for localization to emphaize the effect of uing negative information. A. Monte Carlo Localization, Implementation Thi work i baed on the Monte Carlo localization decribed in [11] which alo erve a a bae line implementation. Senor updating wa extended to account for FOV and occluion a decribed. Thi alo require enor updating to be triggered by new camera image regardle of whether or not there wa a percept. Before re-ampling, the weight of an individual particle i calculated a follow: Of all landmark L, the ubet of landmark L i detected, the ubet L i expected but not detected, and latly the ubet L i not detected but wa alo not expected: L = L L L and L L =. The probability of a particle p i i calculated by multiplying all the likelihood of all gathered evidence: p i = l L l (α mead, α expd ) }{{} detected l L l (ϕ, α expd ) }{{} expected and not detected The function l i an approximation of the enor model and return the likelihood of ening the landmark l at angle α mead for a particle p i that expect thi landmark to be at (6)

4 * * field of view 1) 2) Fig. 3. Incorporating negative information. White (outlined) arrow denote particle that receive negative information and are therefore le likely than other, i.e. their weight are being updated by negative evidence. In (1), the effect of uing negative information i hown for a robot that i well localized and frequently ee landmark. (2) Ditribution hortly after the robot ha been diplaced (kidnapped): particle facing the goal are le likely and will eventually be eliminated from the ditribution. Fig. 4. Experimental etup: Robot i tanding at the poition hown in the photo. It perform a canning motion with it camera. α expd. Function l model the probability of not ening the expected landmark l L given the current ening range a determined by ϕ, the robot poe aociated with p i, and the btacle percept z ob. B. Preliminary Experiment For illutration purpoe, we conducted a preliminary experiment in imulation. In thi experiment, the robot tart out being well localized and i then diplaced to a poition where it i not able to get any new enor information (fig. 3). It i imilar to the kidnapped robot problem, but here we emphaize the moment right after the robot i diplaced rather than invetigating how fat it can recover. The effect of the diplacement on the Monte Carlo particle ditribution i the following: particle which repreent the previou belief become le likely when negative information i taken into account (i.e. the information that the landmark i not detected where it i expected). The ditribution diverge toward particle which were le likely prior to the diplacement. Particle repreenting the previou belief are eventually eliminated from the ditribution becaue they are inconitent with the current (negative) enor data. Particle which differ from the previou belief jut enough to be compatible with the current enor data are favored; particle remain cloe to where the robot wa lat able to localize. Thi doe, in mot cae, better repreent what ha happened to the robot than ditributing the particle uniformly over the entire field. C. Localization Experiment The following experiment i a localization tak uing the real robot. The robot i placed on the field at the location indicated in fig. 4, facing outward. The robot perform a canning motion with it head (pan range [ 45 o, 45 o ]) but doe not move otherwie. From it poition, it can only ee one landmark. A panorama compoed of actual robot camera image i hown in fig. 5. The a priori belief i aumed uniform. Thi poition wa choen becaue it i a Fig. 5. A panorama view generated from actual camera image, ingle camera image highlighted. The robot can only ee one landmark. particulary difficult pot for the robot to localize given the limited enor information. Two quantitie can be ued when a landmark i een: it ize in the camera image can be ued to etimate the ditance to the landmark d l and the relative angle to the landmark (bearing, α l ) can be calculated from it poition within the image. In practice we only ue the bearing becaue the ditance meaurement i error prone. Uing jut the bearing, only the orientation of the robot can be inferred. Note that thi differ from triangulation where ditance are ued. In the following paragraph, the baic localization not uing negative information and localization incorporating negative information are compared. We firt qualitatively analyze the particle ditribution and then how how the entropy of the ditribution decreae when negative information i conidered. 1) Particle Ditribution: The baic experiment wa conducted uing 100 particle for Monte Carlo localization. It wa repeated on a log file containing camera image, robot joint angle, and odometry data uing an increaed particle count of 2000 to get a better repreentation of the probability ditribution. Not uing negative information. Without uing negative information, the robot i unable to localize (fig. 6). Only the orientation of the particle i adjuted according to the enor reading. The apparent clutering in the mall ample et in fig. 6 i not table and, even after coniderable time, the particle do not converge. The ditribution for the larger ample et i uniform (w.r.t. poition). Note that the ditribution i not circular becaue the ditance

5 Fig. 6. Particle ditribution not uing negative information, initial uniform ditribution and ditribution after 10. Solid arrow indicate Monte Carlo particle (100). The experiment wa repeated uing 2000 particle (haded line) to better repreent the actual probability ditribution. The actual robot poition i indicated by the white ymbol, the etimated robot poe by the olid ymbol. Not uing negative information and only uing the bearing to the landmark, the robot i unable to localize. Some cluter of particle form but they do not converge. A one would expect, the poition ditribution i almot uniform but the relative angle i quite ditinct. to the landmark wa not ued. Intead, only the bearing to the landmark wa ued. Thi reult in a radial ditribution reembling magnetic field line. Incorporating negative information. The negative information gained in thi experiment i not eeing but one landmark within the pan range (pardon the double negation). Incorporating thi information, the robot i able to localize quickly. On average, the robot i reaonably well localized after about 10 ec with a poe error of le than p = (25 cm, 25 cm, 20 o ). 2) Entropy: We ue the expected entropy H a an information theoretical quality meaure of the poition etimate Bel( t ) [2]: H p ( t ) = t Bel( t ) log(bel( t )) The um run over all poible tate. The entropy of the particle ditribution become zero if the robot i perfectly localized in one poition, maximal value of H mean that Bel( t ) i uniformly ditributed. Fig. 8 how the progreion of the ditribution entropy over time for the above localization experiment calculated from the 100 particle ditribution. Not uing negative information. The experiment tart with a uniform particle ditribution which equal to maximum entropy. When the landmark come into view, a decreae in entropy i oberved. Thi information gain i due to the robot being able to now infer it relative orientation w.r.t. the landmark. Since there are no contraint on the robot poition, the entropy remain at a relatively high level. Thi i eaily een by eparately calculating the entropy of the angle and poition ditribution. Note that even though there i a drop in entropy, the poe etimate itelf i till highly uncertain. Fig. 7. Particle ditribution when negative information i incorporated, initial uniform ditribution and ditribution after 10. When incorporating negative information, the robot i able to localize quickly. Incorporating negative information. When uing negative information, the entropy decreae even before the firt enor reading. The information gain i much maller than that caued by perceiving a landmark but neverthele noticeable. A oon a there i a percept, the negative information in combination with the knowledge of the robot orientation reult in a quick convergence toward the actual robot poe. Thi i remarkable ince without uing negative information, localization wa not poible. Uing field line for localization. The previou experiment wa repeated uing field line for localization in addition to landmark. Thi enable the robot to localize quickly at the actual robot poe even when uing the baic localization (fig. 8, right). Adding negative information, however, greatly increae the rate of convergence and the overall level of entropy i reduced even further. The decreae of entropy when incorporating negative information i not obcured by the uage of line for localization although field line offer a much greater information content than negative information. Kidnapped Robot. The kidnapped robot problem i a commonly ued benchmark for the flexibility and robutne of localization algorithm [3]: a localized robot i diplaced and the time for it to recover i meaured. Our kidnapped robot experiment underlined and confirmed the already tated finding. The robot i able to recover from diplacement without uing negative information a oon a it ucceively ee three landmark. In region where thi wa not guaranteed, the cae i different. Wherea without uing negative information, the robot doe not have enough evidence to update it belief, incorporating negative information allow the robot to localize quickly and reliably in uch region. The ability to localize more quickly uing negative information i highly beneficial in real world application where the robot i trying to actually perform a tak rather than to localize perfectly. Such tak often require the robot to focu it attention on object other than landmark and the

6 H H max t (ec) 0 t (ec) 1) 2) H H max Fig. 8. Expected entropy of the belief in the localization tak with ( ) and without (thin line) uing negative information. 1) At firt the robot doe not ee the landmark. A oon a the landmark come into the robot view (indicated by the dahed vertical line), the entropy drop. Uing negative information, the quality of the localization i greatly improved and the entropy continue to decreae over time. 2) Additionally uing field line for localization enable the robot to localize even without negative information. Incorporating negative information, however, yield a higher rate of convergence and the entropy i ignificantly lowered. ening trategy may keep it from eeing a much of the world a it potentially could. Integrating negative evidence thu allow for more efficient ening and improve overall robot performance. IV. CONCLUSION We demontrate the power of integrating negative information the abence of an expected enor reading into Markov localization. Becaue enor are more likely to overlook obervable landmark than hallucinate one that are not viible, extra care ha to be taken in deigning the enor model. To avoid fale negative, the model need to take into account the enor ening range and poible occluion of landmark. We preent how uch modeling can be achieved in general and pecifically for a Sony Aibo robot in the RoboCup environment. In real robot experiment, we how that uing negative information, a robot i able to localize in poition where it otherwie would not have been able to localize. The robot ene a ingle landmark, and with the additional information of not eeing any other landmark it can limit the area of where it believe it could be. The entropy of the ditribution i greatly reduced when negative information i incorporated and the rate of convergence toward the etimated poition i increaed. Future work will focu on how negative information can be ued for other type of landmark (e.g. field line) and other enor. Performance evaluation will be continued in more complex ituation and will probe the poibilitie of reducing the number of particle neceary for robut Monte Carlo localization. REFERENCES [1] D. Fox, W. Burgard, F. Dellart, and S. Thrun. Monte Carlo Localization: Efficient Poition Etimation for Mobile Robot. In Proc. of AAAI, [2] D. Fox, W. Burgard, and S. Thrun. Active Markov Localization for Mobile Robot. In Robotic and Autonomou Sytem, [3] J.-S. Gutmann and D. Fox. An Experimental Comparion of Localization Method Continued. Proceeding of the 2002 IEEE/RSJ International Conference on Intelligent Robot and Sytem (IROS), [4] J. Hoffmann, M. Jüngel, and M. Lötzch. A Viion Baed Sytem for Goal-Directed Obtacle Avoidance. In 8th International Workhop on RoboCup 2004 (Robot World Cup Soccer Game and Conference), Lecture Note in Artificial Intelligence. Springer, [5] W. Koch. On Negative Information in Tracking and Senor Data Fuion. In Proceeding of the Seventh International Conference on Information Fuion, page 91 98, [6] W. Koch. Utilizing Negative Information to Track Ground Vehicle Through Move-top-move Cycle. In Proceeding of the SPIE, volume 5429, page , [7] C. Kwok and D. Fox. Map-baed Multiple Model Tracking of a Moving Object. In 8th International Workhop on RoboCup 2004 (Robot World Cup Soccer Game and Conference), Lecture Note in Artificial Intelligence. Springer, [8] S. Lener, J. Bruce, and M. Veloo. CMPack: A Complete Software Sytem for Autonomou Legged Soccer Robot. In AGENTS 01: Proceeding of the fifth international conference on Autonomou agent, page ACM Pre, [9] S. Lener and M. Veloo. Viual Sonar: Fat Obtacle Avoidance Uing Monocular Viion. In Proceeding of IROS 03, [10] M. Montemerlo and S. Thrun. Simultaneou Localization and Mapping with Unknown Data Aociation Uing FatSLAM [11] T. Röfer and M. Jüngel. Viion-Baed Fat and Reactive Monte-Carlo Localization. In Proceeding of the IEEE International Conference on Robotic and Automation (ICRA-2003), Taipei, Taiwan, page , [12] S. Särkkä, T. Tamminen, A. Vehtari, and J. Lampinen. Probabilitic Method in Multiple Target Tracking, Reearch Report B36. Technical report, Laboratory of Computational Engineering Helinki Univerity of Technology, [13] S. Thrun, W. Burgard, and D. Fox. Probabilitic Robotic, page 231. MIT Pre, [14] S. Thrun, D. Fox, and W. Burgard. Monte Carlo Localization with Mixture Propoal Ditribution. In Proc. of the National Conference on Artificial Intelligence, page , ACKNOWLEDGMENTS Program code ued wa developed by the GermanTeam, a joint effort of the Humboldt Univerity of Berlin, Univerity of Bremen, Univerity of Dortmund, and the Technical Univerity of Darmtadt. Source code i available for download at Freek Stulp pointed out Silver Blaze to u.