Cooperative Localization Based on Visually Shared Objects

Transcription

1 Cooperatve Localzaton Based on Vsually Shared Objects Pedro U. Lma 1,2, Pedro Santos 1, Rcardo Olvera 1,AamrAhmad 1,andJoão Santos 1 1 Insttute for Systems and Robotcs, Insttuto Superor Técnco, Lsboa, Portugal 2 Unversdad Carlos III de Madrd, Avda. Unversdad, 30, Leganés, Span {pal,psantos,aahmad,jsantos}@sr.st.utl.pt, rcardo.olvera@st.utl.pt Abstract. In ths paper we descrbe a cooperatve localzaton algorthm based on a modfcaton of the Monte Carlo Localzaton algorthm where, when a robot detects t s lost, partcles are spread not unformly n the state space, but rather accordng to the nformaton on the locaton of an object whose dstance and bearng s measured by the lost robot. The object locaton s provded by other robots of the same team usng explct (wreless) communcaton. Results of applcaton of the method to a team of real robots are presented. 1 Introducton and Related Work Self-localzaton s one of the most relevant topcs of current research n Robotcs. Estmaton-theoretc approaches to self-localzaton, as well as to self-localzaton and mappng (SLAM) have produced sgnfcant results n recent years, manly for sngle robots, provdng effectve practcal results for dfferent applcatons. One of the research fronters n ths topc concerns now cooperatve localzaton (and possbly mappng) usng a team of multple robots. One of the earler works on cooperatve localzaton [Sanderson, 1996] addresses cooperatve localzaton wthn a Kalman flter framework, where the relatve postons of the robots are the observatons of the flterng part of the algorthm, and the state ncludes the postons of all the robots. Fox et al ntroduced an extended verson of the general Markov Localzaton algorthm [Fox et al., 2000], where two robots use measurements of ther relatve dstance and bearng to nsert an extra step n the belef update algorthm based on the Bayes flter. They used the Monte Carlo Localzaton (MCL) sampled verson of Markov Localzaton algorthm to nfluence the weghts of the partcles of the observed robot from the partcles samplng the nter-robot dstance and bearng measurement model of the observng robot. Other authors address multrobot localzaton usng smlar approaches, so as to provde relatve localzaton of the team members n one of the team robots local frame from nter-robot dstance measurement [Roumelots and Bekey, 2002, Zhou and Roumelots, 2008]. All these works do not use envronment nformaton commonly observed by the team robots to mprove ther localzaton. Other works attempt to take advantage of envronment features and landmarks to help a multrobot team to mprove the pose estmates of ts own team members, whle J. Ruz-del-Solar, E. Chown, and P.G. Ploeger (Eds.): RoboCup 2010, LNAI 6556, pp , c Sprnger-Verlag Berln Hedelberg 2011

2 Cooperatve Localzaton Based on Vsually Shared Objects 351 smultaneously mappng the landmark locatons. Fenwck et al [Fenwck et al., 2002] focus on convergence propertes and performance gan resultng from the collaboraton of the team members on concurrent localzaton and mappng operatons. Jennngs et al [Jennngs et al., 1999] descrbe a stereo-vson-based method that uses landmarks whose locaton s determned by one of the robots to help the other robot determnng ts locaton. The frst approach addresses a general model that does not take advantage of partcular features of the estmaton-theoretc methods used (e.g., partcle flters) to mprove the robustness and to speed up cooperatve localzaton, whle the second s focused on a partcular applcaton. In ths paper, we ntroduce a modfcaton of MCL that changes the partcle spreadng step (used when a robot detects t s lost), usng nformaton provded by other robot(s) of the team on the locaton of an object commonly observed by the lost robot. Ths modfcaton speeds up the recovery of the lost robot and s robust to perceptual alases, namely when envronments have symmetres, due to the extra nformaton provded by the teammates. The ntroduced method enables cooperatve localzaton n a multrobot team, usng vsually shared objects, takng advantage of the specfc features of partcle flter algorthms. Each robot s assumed to run MCL for ts self-localzaton, and to able to detect when the uncertanty about ts localzaton drops below some threshold. An observaton model that enables determnng the level of confdence on the ball poston estmate s also assumed to be avalable at each robot of the team. Though these assumptons are, to some extent, stronger than those assumed by cooperatve smultaneous localzaton and mappng methods, they allow global robot and object localzaton. Though other authors have explored the use of observatons to ntalze and/or reset partcle flters adequately [Lenser and Veloso, 2000, Thrun et al., 2001], the use of shared observatons of common objects to cooperatvely mprove multrobot MCL s novel, to the best of our knowledge. The paper s organzed as follows: n Secton 2, we descrbe our cooperatve localzaton method. Results of experments wth real soccer robots n the RoboCup Mddle- Sze League (MSL), that use the ball as the vsually shared object, are presented n Secton 3. Conclusons and prospects for future work are dscussed n Secton 4. 2 Cooperatve Localzaton Usng a Vsually Shared Object Let us consder a team of N robots, r 1,...,r n. Robot r has pose (poston + orentaton) coordnates l r =(x r,y r,θ r ) n a global world frame, and estmates them usng a MCL algorthm. Each robot can determne the poston of an object o n ts local frame, therefore beng able to determne ts dstance and bearng to that object as well. Robots can also determne f they are lost or kdnapped,.e., f ther confdence n the pose estmate drops below some threshold. If a robot s not lost, t can also determne the object poston n the global world frame usng the transformaton between ts local frame and the global world frame that results from the knowledge of ts pose. The estmate of the object poston n any frame s determned based on a probablstc measurement model that ncludes the uncertanty about the actual object poston. When the global world frame s used, addtonal uncertanty s caused by the uncertan pose of the observng robot.

3 352 P.U. Lma et al. The poston of the object as determned by robot r n the global world frame s denoted by p o =(x o,y o ), whle the dstance and bearng of the object wth respect to the robot, as measured by the robot, are gven by d o and ψo, respectvely. 2.1 Overall Descrpton The orgnal MCL algorthm used by each of the team robots to estmate ts pose s as follows: Algorthm MCL(L(t 1), u(t), z(t), map) statc w slow, w fast L(t) =L(t) = w avg =0 for m =1to M do l [m] (t) =sample moton model(u(t), l [m] (t 1)) w [m] (t) =measurement model(z(t), l [m] (t), map) L(t) = L(t)+ l [m] (t),w [m] (t) w avg = w avg + 1 M w(t)[m] endfor w slow = w slow + α slow (w avg w slow ) w fast = w fast + α fast (w avg w fast ) for m =1to M do wth probablty max{0.0, 1 w fast /w slow } do add random pose to L(t) else draw {1,..., M} wth probablty w [] (t) add l [] (t) to L(t) endwth endfor return L(t) where L(t) s a set of Mpartcles and ther weghts at step t of the teraton process, l [m] (t),w [m] (t), m=1,...,m, L(t) s a set of M unweghted partcles l [m] (t), m= 1,...,M, u(t) are odometry readngs at tme t, z(t) are robot observatons at tme t, concernng ts self-localzaton, map s a map of the robot world (e.g., a set of landmarks or other), and w fast,w slow are auxlary partcle weght averages, wth 0 α slow α fast, such that w slow provdes long-term averages and w fast provdes short-term averages. The algorthm uses a sample moton model and a measurement model to update, at each step, the robot pose, from the odometry u(t) and measurements z(t) nformaton. It keeps addng random partcles to those obtaned n the re-samplng step (where the probablty of clonng an exstng partcle s proportonal to ts weght), n a number whch ncreases wth the devaton of the w fast average from the long-term w short average. In the lmt case, when all partcle weghts tend to zero n the short-term, all partcles are reset accordng to an unform dstrbuton.

4 Cooperatve Localzaton Based on Vsually Shared Objects 353 When cooperatve localzaton n a multrobot team, usng vsually shared objects, s ntended, MCL runnng n a gven robot r must be modfed so as to use nformaton from other robot(s) n the team, when w fast /w slow drops below a gven confdence threshold C threshold, meanng that r s lost or was kdnapped. That nformaton comes n the form of the object poston determned by the other robot(s). Assumng r (the lost/kdnapped robot) can observe the same object, the re-samplng s then based on a spatal probablty dstrbuton whch depends on the dstance and bearng of the lost robot to the object and on the uncertanty assocated to the object poston measurement provded by the other robot(s). Ths way, whle a unform dstrbuton s stll used to keep a certan level of exploraton of the pose space to make the algorthm robust to measurement and moton errors, f those errors nfluence becomes too hgh, the partcles are completely reset accordng to the cooperatve nformaton from teammates about a vsually shared object. The new MCL algorthm used by robot r from the team to estmate ts pose becomes (the subndex r s used for local estmates, odometry readngs, observatons and partcle weghts): Algorthm Cooperatve Shared Object MCL(L r (t 1), u r (t), z r (t), map) statc w slow, w fast L r (t) =L r (t) = w avg =0 for m =1to M do l r [m] (t) =sample moton model(u r (t), l r [m] (t 1)) w r [m] (t) =measurement model(z r (t), l r [m] (t), map) L r (t) = L r (t)+ l r [m] (t),w r [m] (t) w avg = w avg + 1 M w[m] r (t) endfor w slow = w slow + α slow (w avg w slow ) w fast = w fast + α fast (w avg w fast ) f w fast /w slow < C threshold and nfo about object poston n global world frame avalable from teammate(s) r j r and object vsble to r then draw L r (t) accordng to object pose spatal probablty dstrbuton determned from r and r j nformaton else for m =1to M do wth probablty max{0.0, 1 w fast /w slow } do add random pose to L r (t) else draw k {1,..., M} wth probablty w r [k] (t) add l [k] r (t) to L r (t) endwth endfor endf return L r (t)

5 354 P.U. Lma et al. Spatal Probablty Densty Fg. 1. Typcal spatal probablty densty functon from whch partcles are drawn, after a decson to reset MCL In the new algorthm one needs to further detal how to handle the followng ssues: 1. nfo about object poston n global world frame avalable from teammate(s) r j r ; 2. draw L r (t) accordng to object pose spatal probablty dstrbuton determned from r and r j nformaton. Item 1. concerns p j o,.e., the object poston n the global world frame, as determned by r j (n general, r j may be any robot but r, or several such robots, n whch case the object poston results from the fuson of ther nformaton). Furthermore, we assume that, assocated wth p j o, r j provdes a confdence measure regardng that nformaton. That confdence measure depends on r j s object observaton model; self-localzaton estmate uncertanty. Assumng a bvarate Gaussan object observaton model for r j centered on p j o and wth a covarance matrx Σo j(dj o,ψj o ) dependent on the dstance and bearng to the object, ths tem contrbutes to the confdence measure wth Σo j(dj o,ψj o ) 1. The self-localzaton estmate confdence factor s not so smple, snce one must determne t from the partcle flter set. One good approach to ths s to consder the number of effectve partcles n rj eff = 1 Mm=1 [Thrun et al., 2005]. (w r [m] j ) 2 Consderng both factors, the measure of confdence of r j on ts own estmate of object o poston n p j o s gven by CF p j o where η s a normalzaton factor. = η Σ j o (dj o,ψj o ) 1 n rj eff

6 Cooperatve Localzaton Based on Vsually Shared Objects 355 Fg. 2. Computng the orentaton of a partcle representng a robot pose hypothess. On the left, bearng of the object wth respect to the robot. On the rght: relevant angles for the computaton of the robot orentaton hypothess for each partcle. Regardng tem 2., and assumng that the object s vsble to the lost robot r,ths robot determnes the dstance and bearng of the object n ts local frame, (d o,ψ o ).The dstance d o s used to parametrze the spatal probablty densty functon (pdf) from whch partcles representng the robot poston n polar coordnates are drawn, after a decson to reset MCL. Ths bvarate (usng polar coordnates d and ψ centered n the object) pdf s: Gaussan n the d varable, wth mean value d o and varance nversely proportonal to the confdence factor CF p j o ; unform n the ψ varable, n the nterval [0, 2π[ rad. An example of ths pdf s shown n Fgure 1. One can trvally map the polar coordnates onto Cartesan coordnates, thus obtanng the x r,y r poston components of the pose l r for robot r. The orentaton component θ r of l r s computed from the bearng angle ψo of the object,.e., the angle between r longtudnal axs (the one pontng towards ts front ) and the lne connectng ts center wth the object center (see Fgure 2 - left), and the actual angle ψ of ths lne wth respect to the x-axs of a frame centered on the object,.e., the partcle angle n polar coordnates centered on the object (see Fgure 2 - rght). We add some random nose θ rand wth a zero mean Gaussan pdf representng the bearng measurement error model. Hence, from Fgure 2: θ r = ψ + π ψ o + θ rand. In summary, the Cooperatve Shared Object MCL algorthm modfes the plan MCL algorthm, replacng the standard partcle reset, usng a spatally unform pdf, by a partcle reset based on the nformaton about the poston, n the global world frame (determned by one or more teammates), and the dstance and bearng, n the local frame of the lost/kdnapped robot, of an object vsble to all the ntervenng robots. Addtonal nput parameters of ths algorthm are (assumng r as the lost/kdnapped robot and r j as any of the robots provdng nformaton to mprove ts localzaton):

7 356 P.U. Lma et al. C threshold to determne f the robot s lost or was kdnapped; determnant of the object measurement model covarance matrx Σo(d j j o,ψo) j 1 sentbyr j to r when r detects t s lost and requests support from teammates; the number of effectve partcles n n rj eff MCL algorthm sent by r j to r when r detects t s lost and requests support from teammates; dstance and bearng of the object n r local frame, (d o,ψ o ) measured by r when t s lost and receves the above nformaton from teammate(s); varance of the zero mean Gaussan pdf representng the bearng measurement error model at r (see prevous tem). The frst two tems can be combned frst n r j, that sends to r ts confdence factor CF p j o on the object poston n the global world frame. The regular procedure for each of the team robots s to run Cooperatve Shared - Object MCL.Whenw fast /w slow <C threshold at r, ths robot requests help to teammates. One or more teammates r j send the object poston n global world coordnates and the assocated confdence factor. Then, r partcles are spread unformly over a crcle centered on the object, wth nomnal radus equal to the dstance to the object measured by r, added to a Gaussan uncertanty around ths value, wth varance proportonal to r j confdence factor. The orentaton component of the pose results from the bearng ψo of the object measured by r n ts local frame, ncludng an uncertanty proportonal to the varance of the Gaussan representng ths measurement model. A couple of practcal ssues to be consdered are: after a robot detects t s lost and spreads ts partcles over a crcle centered wth the vsually shared object, t should run the regular MCL algorthm n the next steps (a number dependent on the applcaton), so that t does not keep resettng ts partcles over a crcle around the object, whle ts pose estmate has no converged to the actual value; the decson on whch teammates can contrbute wth useful nformaton may be taken by consderng ther own confdence factor and only usng the nformaton provded by robots wth CF p j o above some gven threshold. In general, all teammates can contrbute, but n some cases ther nformaton may be hghly uncertan. 2.2 Partcle Spreadng Valdaton There s a specfc stuaton where the proposed algorthm requres some mprovement, e.g., when a robot s kdnapped to a pose where t observes the object at approxmately the same dstance of where the robot was before. In ths case, when the robot detects t s lost by checkng ts w fast /w slow value, t wll stll spread new partcles over a crcle centered wth the object, ncludng a regon around where the robot wrongly estmates ts pose. To prevent such stuatons, the algorthm must nclude a restrcton that requres all the re-spread partcles to be out of a regon (e.g., a crcle) that ncludes the majorty of the partcles at the MCL step when the robot detected t was lost. Nonetheless, t s mportant to note that partcles may be correct n the old pose, f they just have smlar postons but farly dfferent orentatons. Because of ths, the algorthm must also check f the orentaton hypothess assocated to each partcle s wthn a small range of values around the orentaton at kdnappng detecton tme. If they are not, the restrcton above does not apply.

8 Cooperatve Localzaton Based on Vsually Shared Objects 357 Fg. 3. Cooperatve robot localzaton n RoboCup Soccer MSL: (a) The whte robot determnes the ball poston n ts local frame but ts estmated pose (based on feld lne detecton - lnes observed by robot are dashed and do not concde at all wth the actual sold feld lnes) s ncorrect, because the robot was kdnapped. (b) Teammates (green robots) communcate the ball poston n the global world frame, as well as the correspondng confdence factor. (c) Lost robot measures ts dstance and bearng to the ball and re-spreads the partcles accordng to ths and to the ball poston team estmate. (d) The prevously lost robot regans ts correct pose. 3 Results of Implementaton n Real Soccer Robots We have appled the Cooperatve Shared Object MCL algorthm to real robots n RoboCup Soccer Mddle-Sze League (MSL), n whch the robots use the ball to regan ther pose when they are kdnapped and detect to be lost on the feld. Fgure 3 provdes an example that llustrates the algorthm applcaton n ths scenaro. 3.1 Expermental Setup 1 In ths setup tests were made by kdnappng a robot to nne dfferent postons, n one quarter of the whole soccer feld, as depcted n Fgure 4. The other feld regons would not provde extra nformaton, due to the soccer feld symmetry. One teammate stopped n a random poston always sees the ball and nforms the kdnapped robot of the ball s poston on the global feld frame. Both robots use MCL wth 1000 partcles, as descrbed n a prevous paper [Santos and Lma, 2010]. The standard devaton of the Gaussan used to model the bearng angle measurement error at the kdnapped robot was adjusted expermentally as π/12 rad. We kdnapped the robot fve tmes for each of the nne postons. Kdnappng was carred out by pckng up the robot and movng t to another locaton wth MCL on and after ts convergence to a correct estmate. After kdnappng, the ncrease of unformly dstrbuted partcles was vsble, turnng quckly to a re-spread over crcle centered wth the ball poston, as estmated by the teammate.

9 358 P.U. Lma et al. Fg. 4. Layout of experments. A ) The black numbered spots correspond to the postons to where one of the team robots was kdnapped. The red crcle represents a statc robot, always well localzed, and watchng the ball (smaller yellow crcle). B) The fgure n B s an example snapshot of the global frame nterface whch plots real robot and ball postons as well as partcles used by MCL n real-tme. Here t shows the kdnapped robot spreadng partcles after gettng lost and usng the shared ball. The algorthm runs on a NEC Versa FS900 laptop wth a Centrno 1.6GHz processor and 512Mb of memory, usng mages provded by a Marln AVT F033C frewre camera, and n parallel wth the other processes used to make the robot play soccer. The camera s mounted as part of an omndrectonal doptrc system, usng a fsh-eye lens attached to t. The robots dsposed as n poston 4 are depcted n Fgure 5. Fg. 5. Real robot example for one of the layout locatons: the robot on the left s the robot that nforms about the ball poston, whle the robot on the rght s the kdnapped robot, n locaton 4

10 3.2 Expermental Setup 2 Cooperatve Localzaton Based on Vsually Shared Objects 359 In ths setup, the teammate whch observes the ball tracks and follows the ball by mantanng a fxed orentaton and dstance wth respect to ball. We kdnapped the other robot n the followng 4 cases durng ths setup: Case 1: Both observer robot and the ball movng when the ball s n the feld of vew (FOV) of both robots. Robot kdnapped twce n ths case. Case 2: Observer robot stopped and the ball s movng whle the ball s n the FOV of both robots. Robot kdnapped once n ths case. Case 3: Both observer robot and the ball stopped when the ball s n the FOV of both robots. Robot kdnapped twce n ths case. Case 4: Both observer robot and the ball movng when the ball moves away from the FOV of the kdnapped robot durng the tme of kdnappng and then later reappears n ts FOV. Robot kdnapped once n ths case. The rest of the detals for ths setup s smlar to expermental setup Results and Dscusson Results of experments n setup 1 are shown n Table 1. In the table, successes correspond to the number of experments where the robot could regan ts correct pose after kdnappng occurred. Iteratons to converge refer to the mean value of teratons requred by the algorthm to converge after a kdnappng, over 5 experments for a gven kdnappng locaton. Note that one predcton and one update teraton of MCL take approxmately 0.1s each, therefore the mean value of teratons should be multpled by 0.2 s to have an dea of the tme taken by the algorthm n each case. Overall, the algorthm performed qute well n real stuatons, ncludng cases where we kdnapped the robot to a poston where ts dstance to the ball remaned the same. Some feld locatons are clearly more demandng than others (e.g., 5, 6, 7) causng the robot to fal to regan ts posture n one of the tests, possbly due to perceptual alasng relatvely to other feld postons. In the expermental setup 2 the robot successfully recovers and re-localzes tself n 5 stuatons (3 Cases) and fals n 1. The number of teratons performed by the Table 1. In expermental setup 1 results of kdnappng a robot to 9 dfferent postons on the feld (thrd column s the average of 5 experments per locaton) Feld poston Successes Iteratons to converge

11 360 P.U. Lma et al. Table 2. Results of kdnappng as explaned n expermental setup 2 Case Stuaton Result Iteratons to converge 1 1 Success 17 2 Success Falure Success 15 2 Success Success 61 algorthm to converge are presented n Table 2. In case 4 of ths setup, the robot performs a very hgh number of teratons to converge manly due to the absence of the ball from kdnapped robot s FOV for a whle before t comes n the FOV of both robots. In all the sets of experments, communcaton delay between the robots was consstently montored durng the run-tme of the algorthm. Older data (> 2seconds) was dscarded. A chunk of teratons performed by the robot to converge to the rght posture s attrbuted to ths communcaton delay. 4 Conclusons and Future Work In ths paper we presented a modfed MCL algorthm for cooperatve localzaton of robots from a team, where an object vsually observed by all the team members nvolved n the cooperatve localzaton s used. The algorthm takes advantage of the nformaton on the vsually shared object, provded by teammates, to modfy the partcle reset step when a robot determnes t s lost (e.g., because t was kdnapped). The algorthm was appled to real robots n RoboCup Soccer MSL wth consderable success. The major ssue wth our approach s the confusng stuaton whch can arse due to false postve dentfcaton of the shared object. A proper approach to solve t would be to use a fused nformaton of the shared object, where the fuson algorthm can dscard false postves detected by teammates. Secondly, a fast movng ball creates larger uncertanty about ts poston whch also affects the robustness of our approach to some extent. Future work wll nclude testng the algorthm n more demandng stuaton, such as durng actual games, wth the robots contnuously movng. Furthermore, we plan to mprove the algorthm by modfyng the orgnal MCL such that a fracton of the partcles s always spread over a crcle algorthm, dependng on the rato between the short-term average and long-term average of ther weghts, nstead of checkng when ths rato drops below a gven threshold. Other objects, such as the teammates, can also be shared to mprove cooperatve localzaton, as long as one can determne ther poston and track them. Acknowledgment Ths work was supported by project FCT PTDC/EEA-CRO/100692/2008 (author Aamr Ahmad) and also a Banco de Santander Char of Excellence n Robotcs grant from the U. Carlos III de Madrd (author Pedro Lma).

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