Multi-Robot Simultaneous Localization and Mapping (Multi-SLAM)

Transcription

1 Muli-Robo Simulaneous Localizaion and Mapping (Muli-SLAM) Kai-Chieh Ma, Zhibei Ma Absrac In his projec, we are ineresed in he exension of Simulaneous Localizaion and Mapping (SLAM) o muliple robos. By definiion, SLAM is he problem where he robo needs o incremenally build a map of his environmen while using his map o esimae is absolue posiion simulaneously. We successfully implemened boh single-robo SLAM and muli-robo SLAM using paricle filers. By comparison beween hese wo approaches, we showed ha he resuls from muli-robo SLAM ouperform he single-robo SLAM in erms of localizaion and mapping qualiy. I. INTRODUCTION Localizaion and mapping are wo imporan opics in mobile roboic applicaions. Robo localizaion is he problem of esimaing a robo s pose while mapping is he problem of consrucing or learning a map which can be used laer for he robo o localize iself. Ineresingly, hese wo problems can acually be done simulaneously. In lieraure, i s known as he simulaneous localizaion and mapping problem (SLAM). I has been a ho opic in roboics for many years [9]. Moivaed by he fac ha SLAM problems are ypically formulaed as a single robo problem, we wan o invesigae he possibiliies of muli-robo SLAM (Muli-SLAM). In he projec, we implemened he paricle-based filering algorihms for boh single-slam and Muli-SLAM and showed ha, in erms of robo pose error and map qualiy, he algorihm performs beer han he counerpar algorihm of single SLAM. The deails of he approaches, implemenaion and experimens are documened comprehensively in his repor accordingly. II. RELATED WORK SLAM also known as Concurren Mapping and Localizaion (CML) is one of he fundamenal challenges of roboics, dealing wih he building he map and deermining he locaion of he robo simulaneously. In he beginning, boh he map and he vehicle posiion are unknown, and he robo has a known kinemaic model hrough he unknown environmen, in which here are several landmarks. Several research groups and researchers have worked and are currenly working in SLAM, and he mos commonly used sensors can be caegorized ino laser-based, sonar-based, and vision-based sysems [1]. Roboic map-building can be raced back o 25 years ago, and since he 1990s probabilisic approaches (i.e. Kalman Filers (KF), Paricle Filers (PF) and Expecaion Maximizaion (EM)) have become dominan in SLAM. The hree The auhors are wih he Deparmen of Compuer Science a he Universiy of Souhern California, Los Angeles, CA 90089, USA. {kaichiem, zhibeima}@usc.edu echniques are mahemaical derivaions of he recursive Bayes rule. The main reason for his probabilisic echniques populariy is he fac ha robo mapping is characerized by uncerainy and sensor noise, and probabilisic algorihms ackle he problem by explicily modeling differen sources of noise and heir effecs on he measuremens [8]. Many approaches have been proposed o ackle he single- SLAM problem. Kalman filers are Bayes filers ha represen poseriors using Gaussians. Kalman filers are based on he assumpion ha he sae ransiion and he measuremen funcions are linear wih added Gaussian noise. There are wo ypes variaions of KF in SLAM: he Exended Kalman Filer (EKF) and is relaed Informaion Filering (IF). Los of SLAM approaches are based on EKF [2]. EKF could handle nonlineariies from he real world, by approximaing he robo moion model using linear funcions while he IF could propagae he inverse of he sae error covariance marix. There are several advanages ha he IF filer has over he KF: 1. The daa is filered by simply summing he informaion marix and vecor, providing more accurae esimaes, raher han he approximaion [10]; 2. IF are more sable han KF. 3. EKF is quie slow when esimaing high dimensional maps. Beyond hese wo approaches where poseriors are represened using Gaussians, an paricle-based filering approach was proposed. In lieraure, i s called Paricle Filer (PF), which is a recursive Bayesian filer ha is implemened in Mone Carlo simulaions. I does he esimaion by a se of random poin paricles represening he Bayesian poserior. The paricles make i possible o handle highly nonlinear sensors and non-gaussian noise. However in dealing wih SLAM problems, one fundamenal drawback of he classic PF is ha each ime i deecs a landmark, he compuaional complexiy will grow, which is no suiable for map-building. However, here are sill several works proposed o deal wih he SLAM problem by using a varian of PF, such as FasSLAM [5] and FasSLAM2.0 [6]. The comparison of differen filering algorihms are shown below. Advanages and Disadvanages of Filering Approaches Filer Pros Cons KF high convergence Gaussian assumpion handle uncerainy slow in high dimension sable and simple daa associaion problem IF accurae need sae esimae PF handle nonlineariies growh in complexiy handle non-gaussian noise There are few works which have been done o invesigae

2 on Muli-SLAM. The mos famous one is from Andrew Howard [3], i describes an on-line algorihm for Muli- SLAM wih paricle filers. III. PROBLEM DEFINITIONS In is secion, we concisely give he formal definiions of he localizaion, mapping, SLAM and Muli-SLAM problems, respecively. A. Localizaion Localizaion is he problem of esimaing a robo s coordinaes relaive o an exernal reference frame. Formally, le x = [x, y, θ] T be he pose of a 2D robo in he exernal reference frame. Given he conrol inpu u 1: and he ses of measuremens, z 1:, where z = {z 1, z 2,..., z N } is he se of N measuremens a ime and he known map m, he localizaion problem is o find he poserior disribuion of robo poses, p(x 0: u 1:, z 1:, m), where x 0: is essenially he rajecory of he robo. B. Mapping Mapping is he problem of consrucing he map m given he ses of measuremens z 1: and he rajecory of he robo defined hrough he sequence of all poses, x 1:. Noe ha in mapping problems, he rajecory is assumed o be known and fully observable so ha conrols u 1: play no role in mapping. Mahemaically, i s equivalen o finding he poserior over he map, p(m z 1:, x 0: ) C. SLAM and Muli-SLAM From he definiions of he individual localizaion and mapping problem. We can see ha an accurae map is needed for localizaion while a precise pose esimae is needed for mapping. Therefore, SLAM is inherenly a harder problem han eiher localizaion or mapping since i manages o solve he boh problems simulaneously. For single-slam problems, i s finding he join poserior disribuion of he map and robo poses, ha is, p(x 1:, m z 1:, u 1: ), where x 0 is he iniial pose of he robo. The exension o muliple robos is as follows: p(x 1 1:, x 2 1:, m z 1 1:, u 1 1:, x 1 0, z 2 1:, u 2 1:, x 2 0), where he superscrips denoes he robo number. (For noaional simpliciy, from now on, we will only use wo robos in formulaions) IV. APPROACHES AND METHODS In our problem seings, we are dealing wih 2D ground robos which are conrolled by forward velociy and angular velociy commands. The pose sae of he robo is represened by is 2D posiion and orienaion. The map we are consrucing is landmark-based. Here we represen he whole map as m which acually conains he 2D posiion of each landmark in our environmen. In he secion, we firs mahemaically describe he moion and measuremen model for he robos used in our projec, and hen we presen he algorihms for boh Single and Muli SLAM. A. Moion Model In our projec, he velociy moion model is used. I assumes ha we can conrol a robo hrough wo velociies, a roaional and a ranslaional velociy. Le he ranslaional velociy a ime be v, and he roaional velociy. Hence, we have u = [v, ] T. Assume ha he robo pose a ime is given by x = [x, y, θ] T, and afer ime of moion, he ideal robo will be a x +1 = [x, y, θ ] T. Using simple kinemaics and rigonomery, one can easily show ha x y θ x v sin θ + v sin(θ + ) = y + v cos θ v cos(θ + ) (1) θ By ideal we mean he robo moion is noise-free, bu in realiy, robo moion is subjec o noise. Therefore he acual velociies always differ from he commanded ones by a noise erm. More precisely, we assume he acual velociies are given by [ ] [ ] [ ] ˆv v ɛα1v = + 2+α2ω2 (2) ˆ ɛ α3v 2+α4ω2 Here ɛ b 2 is a zero-mean Gaussian error wih variance b 2. Thus in his model, he rue velociy equals he commanded velociy plus some small, addiive error (noise). Here we assume he sandard deviaion of he error is proporional o he commanded velociy. The parameers α 1 o α 4 (wih α i 0 for i = 1,..., 4) are robo-specific error parameers. Inuiively, he larger he noise, he larger hese parameers should be. The moion equaion given above implies he radius of he circular segmen and he disance raveled is influenced by he conrol noise. However, he fac ha he rajecory is circular is sill no affeced. The assumpion of circular moion can lead o a degeneracy [9]. Therefore, o generalize our moion model accordingly, we assume he robo also performs a roaion ˆγ a is final pose. Thus, he θ in Eq. (1) is replaced by θ = θ + ˆ + ˆγ (3) wih ˆγ = ɛ α5v 2. Again, α +α6ω2 5 and α 6 are he robospecific parameers deermining he variance of he addiional roaional noise. In sum, he final moion model is as follows: y = θ x x y θ + B. Measuremen Model ˆv ˆ sin θ + ˆv ˆ sin(θ + ˆ ) ˆv ˆ cos θ ˆv ˆ cos(θ + ˆ ) (4) ˆ + ˆγ In our projec, he feaure-based measuremen model is used. I assumes he feaures have been exraced from he raw measuremens and all laer calculaion are based on hese feaures. The key advanage of his model is he reducion of complexiy since he feaure space is usually lowdimensional. In paricular, he feaures used in our projec are called landmarks. They are physical objecs in he workspace for robo navigaion. The deails of feaure exracion will be discussed in V-A. Here we simply assume he feaure we ge conains he range and he bearing of he landmark relaive

3 o he robo s local coordinae frame. We also assume ha he correspondence of landmarks is known and exac afer feaure exracion (Tha is, no daa associaion issues in our implemenaion.). Recall ha he map we are consrucing is a se of N feaures, m = {m 1, m 2,..., m N }, where m i is he coordinae in he global frame. The relaion beween he local frame feaure and he global coordinae can be derived using sandard geomeric laws. Specifically, he measuremen model of i-h feaure a ime wih is corresponding i-h landmark in he map is given by [ ] [ ] [ ] r i (mi,x x) = 2 + (m i,y y) 2 ɛσ 2 r + aan2(m i,y y, m i,x x) θ ɛ (5) σ 2 φ φ i Similar o previous secion where he model is subjec o noise, he model is added wih zero-mean Gaussian noise, ɛ σ 2 r, ɛ σ 2 φ wih variances σr 2 and σφ 2, respecively. Noe ha σr 2 and σφ 2 are also par of robo-specific parameers. C. Single FasSLAM Algorihms In his subsecion, we briefly describe he FasSLAM algorihm for single SLAM problems [7]. I s based on Rao- Blackwellized paricle filer, which is a varian of PF. Concepually, Rao-Blackwellized paricle files uses paricles o represen he poserior over some variables, along wih Gaussians (or some oher parameric disribuions) o represen all oher variables. Concreely, FasSLAM uses paricle filers for esimaing he robo pah while using muliple EKF o esimae map feaures locaions individually. The advanage of FasSLAM over oher SLAM algorihms arises from he fac ha hey can cope wih non-linear robo moion models. This advanage is more imporan when he kinemaics are highly non-linear, or when he pose uncerainy is relaively high. One oher key propery of FasSLAM is ha i solves boh he full SLAM problem and he on-line SLAM problem. Tha is, he FasSLAM is formulaed o calculae he full pah poserior and i also esimaes one pose a-a-ime. Now we describe how a paricle is represened and updaed in deails. Each paricle conains an esimaed robo pose, denoed by x [k], a se of Kalman filers wih mean µ [k] i, and covariance Σ [k] i,, one for each feaure m i in he map, and a weigh w [k]. Here [k] is he index of he paricle. Wih his paricle represenaion, he basic seps of he FasSLAM algorihm are as follows. (Assuming here are M paricles in oal.) Do he following M imes: 1) Rerieval: Rerieve a pose x [k] 1 paricle se Y 1. from he previous 2) Predicion: Sample a new pose x [k] p(x x [k] 1, u ). 3) Measuremen updae: For each observed feaure, z, i incorporae i ino he EKF by updaing he mean µ [k] i, and covariance Σ [k] i,. 4) Imporance weigh: Calculae he imporance weigh w [k] for he new paricle. Resampling: Sample, wih replacemen, M paricles, where each paricle is sampled wih a probabiliy proporional o w [k] The key propery o he successful approximaion of poseriors lies in he sep of calculaing imporance weigh and resampling. Inuiively, he imporance weigh is calculaed o represen he likelihood of he paricle based on he curren measuremens. In he resampling sep, paricles wih higher weighs are more likely o be preserved while paricles wih lower weighs are more likely o be eliminaed. In his way, we are coninuously approximaing he poseriors wih hose mos likely paricles. This propery also implies ha wih larger number of paricles, we can approximae he poseriors more accuraely. D. Muli FasSLAM Algorihms In his subsecion, we show how he FasSLAM can be exended o handle muliple robos. In fac, provided ha he iniial robo poses are known, he single SLAM algorihm can be generalized o handle muliple robos. The goal is o simulaneously esimae he poseriors over wo robo rajecories and one common map. Mahemaically, i s p(x 1 1:, x 2 1:, m z 1 1:, u 1 1:, x 1 0, z 2 1:, u 2 1:, x 2 0) (6) = p(x 1 1:, x 2 1: z 1 1:, u 1 1:, x 1 0, z 2 1:, u 2 1:, x 2 0) (7) p(m x 1 1:, x 2 1:, z 1 1:, u 1 1:, x 1 0, z 2 1:, u 2 1:, x 2 0) = p(x 1 1: z 1 1:, u 1 1:, x 1 0, z 2 1:, u 2 1:, x 2 0) (8) p(x 2 1: z 1 1:, u 1 1:, x 1 0, z 2 1:, u 2 1:, x 2 0) p(m x 1 1:, x 2 1:, z 1 1:, u 1 1:, x 1 0, z 2 1:, u 2 1:, x 2 0) = p(x 1 1: z 1 1:, u 1 1:, x 1 0)p(x 2 1: z 2 1:, u 2 1:, x 2 0) (9) p(m x 1 1:, x 2 1:, z 1 1:, u 1 1:, x 1 0, z 2 1:, u 2 1:, x 2 0) = p(x 1 1: z 1 1:, u 1 1:, x 1 0)p(x 2 1: z 2 1:, u 2 1:, x 2 0)p(m x 1 0:, x 2 0:) (10) From Eq. (6) o Eq. (7), he basic propery of condiional probabiliy is applied o decouple m from he oher erms. From Eq. (7) o Eq. (8), we assume ha hese wo rajecories are independen. From Eq. (8) o Eq. (9), we assume ha he moion conrols, measuremens and he iniial pose of one robo do no depend on he pose of he oher. From Eq. (9) o Eq. (10), he Markov assumpion is applied. Markov assumpion posulaes ha pas and fuure daa are independen if one knows he curren sae x. Therefore, z1:, 1 u 1 1:, z1:, 2 x 2 0 are discarded given ha x 1 0:, x 2 0: are known. Based on he derivaion, he paricle filer for Muli-SLAM can be consruced as follows. Now each paricle is a uple conaining (x 1[k], x 2[k] C. The predicion sep is now generalized o predic boh, m [k], w [k] ). Following he framework in IV- x 1[k] and x 2[k]. The measuremen updae sep remains he same excep ha we now have wo ses of measuremens coming from wo robos. As for he imporance weighs, since we have facored he poserior of he join probabiliy, he imporance weigh is simply he muliplicaion of each erm in single-slam cases. The deailed algorihm is pseudo coded in in Alg. IV-D. For he deailed derivaion of he EKF updaes on each landmark, please refer o he book [9].

4 Algorihm 1 Muli-SLAM Algorihm 1: procedure MULTI-SLAM(Z 1, Z 2, u 1, u 2, Y 1 ) 2: for k = 1 o M do 3: rerieve x 1[k] 1, x2[k] 1, µ [k] 1, 1, Σ[k] [k] 1, 1,..., µ // N is number of landmarks p(x 1 x 1[k] 1, u[1] ) p(x 2 x 2[k] 4: x 1[k] 5: x 2[k] 1, u[2] ) 6: for each feaure z in Z 1 do 7: if feaure z never seen before hen 8: µ [k] i, = h 1 (z, x 1[k] 9: H = h (x 1[k] ), µ [k] i, ) 10: Σ [k] i, = H 1 Q (H 1 ) T 11: w 1[k] = p 0 12: else 13: ẑ = h(µ [k] i, 1, x1[k] 14: H = h (x 1[k] ), µ [k] i, 1 ) 15: Q = HΣ [k] i, 1 HT Q 1 + Q 16: K = Σ [k] i, HT Q 1 17: µ [k] i, = µ[k] i, 1 18: Σ [k] i, + K(z ẑ) = (I KH)Σ[k] i, 1 19: w 1[k] = 2πQ 1 2 exp( 1 2 (z ẑ) T Q 1 (z ẑ)) 20: end if 21: end for 22: for each feaure z in Z [2] do 23: // similar o he above 24: end for 25: for all oher unobserved landmarks i do 26: µ [k] i, = µ[k] i, 1 27: Σ [k] i, = Σ[k] i, 1 28: end for 29: end for 30: Y = 31: for i = 1 o M do 32: draw random k wih probabiliy w 1[k] w 2[k] 33: add x 1[k] 34: end for 35: end procedure A. SLAM Daase, x 2[k], µ [k] 1,, Σ[k] 1, V. IMPLEMENTATION,..., µ [k] N,, Σ[k] N, In our projec, we use he open daase accquired from [4]. I includes daase which are suiable o do experimens on single-slam and muli-slam. Each daase conains odomery (insead of conrol inpus, odomery may be a misused of erms in heir descripion of he daase) and (range and bearing) measuremen daa from 5 robos, as well as accurae groundruh daa for all robo poses and 15 landmark posiions. Each robo and landmark has a unique idenificaion number encoded as a barcode (wih known dimensions). Images capured by he camera on each robo (a a resoluion of ) are recified and processed o deec he barcodes. The encoded idenificaion number N, 1, Σ[k] N, 1 (a) (b) Fig. 1. (a) The environmen where he daase was colleced; (b) Robo plaforms used o collec he daase. as well as he range and bearing o each barcode is hen exraced. The camera on each robo is convenienly placed o align wih he robo body frame. The daase is colleced in he indoor environmen shown in Fig. 1(a). Robos move o randomly prese waypoins in a 15m 8m indoor space while logging odomery daa, and range-bearing observaions o landmarks and oher robos. Fig. 1(b) shows he experimenal robo. This robo is he irobo Creae wih 34cm in diameer. B. ROS Considering he possibiliy of exending our work o simulaions or real robos, we decided o use ROS as he developmen ools and he infrasrucure of our sysem. The Robo Operaing Sysem (ROS) is a se of sofware libraries and ools ha help build robo applicaions. From drivers o saeof-he-ar algorihms, and wih powerful developer ools. And i s all open source. The node diagram of our projec is shown in Fig. 2. The saring node is daa reader, which reads he daa from he open daase, and publishes he processed daa o slam runner, in which muliple SLAM algorihms are implemened and run. Finally, slam runner publishes he resuls of SLAM algorihms o poins and lines for posprocessing and hen poins and lines publishes a mos 5 groundruh pahs and 5 SLAM pahs o rviz for dynamic visualizaion. C. Visualizaion For convenience, we use he rviz ool for our final visualizaion. Rviz (ROS visualizaion) is a 3D visualizer for displaying sensor daa and sae informaion from ROS. We use nav msgs/p ah in rviz o show he pahs, visualizaion msgs/m arkerarray o show he

5 (a) Fig. 2. The node srucure of our projec shown by using he rq graph command landmarks, and geomery msgs/p osearray o show he paricles. VI. RESULTS AND EVALUATION We conduced several experimens o validae boh Single- SLAM and Muli-SLAM algorihms, all of which were implemened in C++. The experimens were performed on a sysem wih an Inel i5 2.2GHz processor and 4GB RAM. A. Dead-reckoning mehod vs. Single-Robo SLAM The rajecory resuls of Single-SLAM w/o incorporaing measuremens are shown in Fig. 3. The blue dos are groundruh landmarks. The green pah is he groundruh pah of he robo, while he purple one is he pah ha we calculaed from he single-slam. The ligh-blue cluser is he approximaed disribuion of he robo pose esimaed using paricles. Fig. 3(a) shows he resul of he rajecory wihou incorporaing he measuremen informaion. We can see ha wihou doing i (also known as he dead-reckoning mehod), he error from he noisy robo moion evenually accumulaes unboundedly compared o he Single-SLAM algorihm shown in Fig. 3(b). The numerical comparison is also shown in Fig. 4(a). To show he applicabiliy of Single- SLAM, he numerical error of Single-SLAM is furher shown in Fig. 4(b). The average error over 1400 frames (roughly 5 mins in real ime) is 0.6m, which is accepable considering robo s diameer is 0.34m. We also measured he mapping qualiy in erms of he landmark posiion error(he disance beween our esimaed landmark posiion and he groundruh landmark posiion) in Fig. 4(c). The average error over 15 landmarks is abou 0.6m and we can see ha as ime goes by, he error gradually converges. B. Single-SLAM vs. Muli-SLAM The experimens on muli-slam are also conduced. Fig. 5 is he resul of 3 robos SLAM pah. We can see ha he resuling rajecories of each robo are sill close o he groundruh rajecories. Fig. 6(a) shows he numerical rajecory error beween Single-SLAM and Muli-SLAM. The performance on muli-slam is beer han single-slam in (b) Fig. 3. (a) Single-robo rajecory wihou incorporaing measuremens (dead-reckoning mehod); (b) Single-robo SLAM wih measuremens incorporaed erms of he average error over he whole rajecory. For Muli-SLAM, i s abou 0.42m, while i s 0.6m roughly for Single-SLAM. The Muli-SLAM also performs beer on he map consrucion, which is shown in Fig. 6(b). The converged error in Muli-SLAM is only 0.5m compared o 0.7m in Single-SLAM. From he experimen, we ve shown ha muli-slam s performance is beer han single-slam s performance. VII. STRENGTHS AND WEAKNESSES A. Srenghs and weaknesses of he Muli-SLAM algorihm From he derivaion in secion IV-D, we see ha he algorihm is an exac exension from single-slam algorihm wihou approximaions. The experimen resuls in secion VI also show ha he muli-slam can help improve he individual localizaion and mapping. However, here are assumpions which migh no always be rue in real world and have o be aken ino accoun. For example, he assumpion ha he measuremens of one robo do no depend on oher poses of robos may no hold anymore if one robo can parially occlude he measuremens and affec he accuracy of daa associaion of he measuremens. Forunaely in he daase, he issue does no happen because he ideniy of each measuremen is deeced using barcodes, and herefore can be reaed as exac values. Anoher issue ha migh arise from he algorihm is ha if one robo s uncerainy is oo

6 (a) (b) (c) Fig. 4. (a) Comparison of pah error beween dead-reckoning mehod and single-robo SLAM; (b) Single-robo SLAM pah error; (c) Map qualiy in erms of landmark posiion error. large, he performance could be worse because he pollued informaion is incorporaed. However his can acually be miigaed by uning he robo-specific parameers described in secion IV-A and secion IV-B o be larger in order o reflec he level of uncerainy of his paricular robo. B. Srenghs of our projec Fig. 5. Muli-robo SLAM pah. We successfully implemened boh single-robo SLAM and muli-slam, and use rviz o do he visualizaion. Our resul is accepable wih small deviaed from he groundruh. Our projec is based on ROS, which is readily exensible for our fuure work, such as he simulaion(gazebo) and real robos, The visualizaion of our projec is clear and easy o undersand. The links of our demos are in he APPENDIX II. C. Weaknesses of our projec In our experimen, we only use he he same parameer in moion model and measuremen mode due o he ime pressure. I would be beer if we could do more experimens wih differen parameers. (a) VIII. SUMMARY (b) Fig. 6. (a) Comparison of pah error beween single-slam and Muli- SLAM; (b) Comparison of landmark error beween single-slam and Muli- SLAM. In our projec, we implemened paricle-based filering algorihms for Single and Muli SLAM and showed ha, in erms of robo pose and map (landmark-based) qualiy, he Muli-SLAM algorihm performs beer han he counerpar algorihm of Single-SLAM. For fuure work, we wan o do daa-driven parameer opimizaion for boh moion model and measuremen model in order o improve he performance of SLAM algorihms. Acive exploraion could be also anoher fuure work we can work on. Currenly, he pahs raversed by he robos in he daase are randomly prese, meaning he mapping space is no acually explored in an efficien way. To achieve full auonomy, he robo should auonomously plan a suiable moion policy in order o visi unknown areas while minimizing he uncerainy on is pose. Therefore, acive exploraion planning algorihms are also promising as a direcion of research.

7 APPENDIX I CODE Kai-Chieh Ma, Zhibei Ma, 2016, Gihub reposiory, hps://gihub.com/markcsie/slam_projec APPENDIX II VIDEOS All he demos of our projec are creaed by rviz in ROS. The demo of single-robo SLAM: hps:// 322l1n7eunbn6/single.mp4?dl=0 The demo of muli-robo SLAM wih 3 robos: hps:// s1870vq3u35576/muli3.mp4?dl=0 The demo of muli-robo SLAM wih 5 robos: hps:// 7n0uvcxir6ca9rc/muli5.mp4?dl=0 APPENDIX III RESPONSIBILITY Kai-Chieh Ma: Single SLAM, Muli Robo SLAM, ROS. Zhibei Ma: Daa collecion, Single SLAM, RVIZ Visualizaion. REFERENCES [1] J. Aulinas, Y. Peillo, J. Salvi, and X. Lladó. The slam problem: A survey. In Proceedings of he 2008 Conference on Arificial Inelligence Research and Developmen: Proceedings of he 11h Inernaional Conference of he Caalan Associaion for Arificial Inelligence, [2] A. J. Davison and D. W. Murray. Simulaneous localizaion and mapbuilding using acive vision. IEEE Trans. Paern Anal. Mach. Inell., 24(7): , July [3] A. Howard. Muli-robo simulaneous localizaion and mapping using paricle filers. In Proceedings of Roboics: Science and Sysems, Cambridge, USA, June [4] K. Y. Leung, Y. Halpern, T. D. Barfoo, and H. H. Liu. The uias mulirobo cooperaive localizaion and mapping daase. The Inernaional Journal of Roboics Research, 30(8): , [5] M. Monemerlo, S. Thrun, D. Koller, and B. Wegbrei. FasSLAM: A facored soluion o he simulaneous localizaion and mapping problem. In Proceedings of he AAAI Naional Conference on Arificial Inelligence, [6] M. Monemerlo, S. Thrun, D. Koller, and B. Wegbrei. FasSLAM 2.0: An improved paricle filering algorihm for simulaneous localizaion and mapping ha provably converges. In Proceedings of he Sixeenh Inernaional Join Conference on Arificial Inelligence (IJCAI), [7] M. Monemerlo, S. Thrun, D. Koller, B. Wegbrei, e al. Fasslam: A facored soluion o he simulaneous localizaion and mapping problem. In Aaai/iaai, pages , [8] S. Thrun. Roboic mapping: A survey. In G. Lakemeyer and B. Nebel, ediors, Exploring Arificial Inelligence in he New Millenium. Morgan Kaufmann, o appear. [9] S. Thrun, W. Burgard, and D. Fox. Probabilisic Roboics. Inelligen roboics and auonomous agens. MIT Press, [10] S. Thrun and Y. Liu. Muli-robo slam wih sparse exended informaion filers. Springer, 2003.