Effective Team-Driven Multi-Model Motion Tracking

Transcription

1 Effecive Team-Driven Muli-Model Moion Tracking Yang Gu Compuer Science Deparmen Carnegie Mellon Universiy 5000 Forbes Avenue Pisburgh, PA 15213, USA Manuela Veloso Compuer Science Deparmen Carnegie Mellon Universiy 5000 Forbes Avenue Pisburgh, PA 15213, USA ABSTRACT Auonomous robos use sensors o perceive and rack objecs in he world Tracking algorihms use objec moion models o esimae he posiion of a moving objec Tracking efficiency compleely depends on he accuracy of he moion model and of he sensory informaion Ineresingly, when he robos can acuae he objec being racked, he moion can become highly disconinuous and nonlinear We have previously developed a successful racking approach ha effecively swiches among objec moion models as a funcion of he robo s acions If he objec o be racked is acuaed by a eam, he se of moion models is quie more complex In his paper, we repor on a racking approach ha can use a dynamic muliple moion model based on a eam coordinaion plan We presen he muli-model probabilisic racking algorihms in deail and presen empirical resuls boh in simulaion and real robo es Our physical eam is composed of a robo and a human in a real Segway soccer game scenario We show how he coordinaed plan allows he robo o beer rack a mobile objec hrough he effecive ineracion wih is human eammae Caegories and Subjec Descripors I210 [Arificial Inelligence]: Vision and Scene Undersanding Modeling and recovery of physical aribues, Moion General Terms Algorihms, Experimenaion, Human Facors Keywords Team-Driven, Muli-Model, Moion Modelling, Tracking 1 INTRODUCTION There have been considerable invesigaions ino he problem of racking moving arges eg [8] Wihin he roboics Permission o make digial or hard copies of all or par of his work for personal or classroom use is graned wihou fee provided ha copies are no made or disribued for profi or commercial advanage and ha copies bear his noice and he full ciaion on he firs page To copy oherwise, o republish, o pos on servers or o redisribue o liss, requires prior specific permission and/or a fee HRI 06, March 2 3, 2006, Sal Lake Ciy, Uah, USA Copyrigh 2006 ACM /06/0003 $500 communiy, here has been a similar ineres in racking arges from robo plaforms eg [11] When racking is performed by a robo execuing specific asks acing over he arge being racked, such as a Segway RMP soccer robo grabbing and kicking a ball, he moion model of he arge becomes dependen on he robo s acions [10] The robo s acic provides valuable informaion in erms of he arge behavior We have inroduced he acic-based moion modelling and racking in such scenarios [9] However, for he environmens in which he Segway RMP soccer robo operaes in, here are muliple arges, besides he ball, eg he eammae and he opponens, which need o be racked properly All he players on he field can also acuae over he ball, namely grab and kick he ball according o he rules which makes he moion model of he ball even more complex When he robo is playing a game as a member of a human-robo eam, he eam coordinaion knowledge provides furher informaion ha can be incorporaed ino he moion modelling and racking process In his paper, we presen an exension o he acic-based racking scheme inroduced in [9] o solve a plan-dependen muli-arge racking problem The paper is organized as follows We firs give a brief descripion of he Segway RMP soccer robo Nex we show he eam-driven play-based moion modelling for muliple arges and we incorporae he eam coordinaion knowledge ino he moion modelling We hen describe he mulisensor muli-model racking algorihm for muliple arges, leading o our experimenal resuls, relaed work, conclusions and fuure work 2 SEGWAY RMP SOCCER ROBOT The Segway plaform is unique due o is combinaion of wheel acuaors and dynamic balancing Segway RMP, or Robo Mobiliy Plaform, provides an exensible conrol plaform for roboics research [12] I imbues he robo wih he novel characerisics of a fas plaform and ravel long ranges, able o carry significan payloads, able o navigae in relaively igh spaces for is size, and provides he opporuniy o moun sensors a a heigh comparable o human eye level In our previous work, we have developed a Segway RMP robo base capable of playing Segway soccer (Figure 1) We briefly describe he wo major componens of he conrol archiecure, he sensor and he robo cogniion, which are highly relaed o our moion modelling for efficien muliarge racking

2 ball no seen Search Ball ball los ball seen Aim a Ball ball los ball is close Grab Ball eammae los Kick Aim a Teammae eammae found Search Teammae Figure 2: Skill sae machines (SSMs) for an example acic: CachKickToTeammae Eachnodeis a skill and he edges show he ransiion beween skills Figure 1: The Segway RMP soccer robo equipped wih a kicker, a cacher, infrared sensors, and a camera mouned on a cusom pan-il uni 21 Vision Sensor and Infrared Sensor Over he years, a lo of differen sensors such as vision sensors, infrared and ulrasound sensors have been used in he roboics communiy For environmens he Segway RMP operaes in, here are few sensors ha can compee wih color vision for low cos, compac size, high informaion volume and hroughpu, relaively low laency, and promising usage for objec recogniion [7] Thus, we choose vision as he primary sensor In our work wih he Segway RMP plaform, we have been exploring echniques o enable a vision-cenric robo o be able o play soccer in oudoor environmens where illuminae is variable [5, 6] Furhermore, as he ask is adversarial and highly dynamic, he combinaion of robo speed and ball speed means ha i is essenial ha he vision algorihms be boh robus, and exremely efficien Indeed, only a fracion of he CPU resources can be devoed o vision processing as he remainder of he CPU resources mus be used for cogniion in order o ge low-laency robo behaviors We have developed a new echnique for fas color-objec recogniion ha is suiable for use in robo plaforms like he Segway For more deails of his approach, see our paper [6] The goal of vision is o provide as many valid esimaes of arges as possible Tracking hen fuses his informaion o rack he mos ineresing arges (he ball and he eammae, in his paper) of relevance o he robo We do no discuss he localizaion of he robo in he sense ha a lo of soccer asks (known as acics and plays in laer secions) can be done by he Segway RMP robo independenly of knowing where i is in he world Also we use global reference in his paper (global posiion and velociy) which means i is relaive o he reference poin where he robo sars o do dead reckoning Recenly, we have equipped each robo wih infrared sensors o reliably deec he objec which is in he cachable area of he robo Is measuremen is a binary value indicaing wheher or no an objec is in ha area In mos cases, his is he blind area of he vision sensor Therefore, he infrared sensor is paricularly useful when he robo is grabbing he ball 22 Robo Cogniion A conrol archiecure, called Skills-Tacics-Plays, was proposed in [3] o achieve he goals of responsive, adversarial eam conrol The key componen of STP is he division beween single robo behavior and eam behavior Aplay,P, is a fixed eam plan which consiss of a se of applicabiliy condiions, erminaion condiions, and N roles, one for each eam member Each role defines a sequence of acics T 1,T 2, and associaed parameers o be performed by ha role in he ordered sequence Assignmen of roles o eam members is performed dynamically a run ime Upon role assignmen, each robo i is assigned is acic T i o execue from he curren sep of he sequence for ha role Aacic, T, encapsulaes a single robo behavior Each robo i execues is own acic as creaed by he curren play P A acic T i deermines he skill sae machine SSM i o be execued by he robo i A skill, S, is a focused conrol policy for performing some complex acion Each skill is a member of one, or more, skill sae machines SSM 1,SSM 2, Each skill S deermines wha skill i ransiions o S based upon he world sae, he ime skill S has been execuing for, and he execuing acic for ha robo We consruc he robo cogniion using a similar archiecure Plays, acics, and skills, form a hierarchy for eam conrol Plays conrol he eam behavior hrough acics, while acics encapsulae individual robo behavior and insaniae acions hrough sequences of skills Skills implemen he focused conrol policy for acually generaing useful acions Figure 2 shows he SSMs and ransiions for an example acic: CachKickToTeammae, which conains six skills The acic sars from SearchBall, andwhenheballisvisible hen ransis o he skill AimABall If he ball is los, he sae machine ransis back o SearchBall Else if he skill GrabBall is successfully execued, he sae rasis o SearchTeammae, AimATeammae and he final Kick skill Segway soccer is a eam spor, and herefore he building of our game sraegy required no only execuion of single robo behavior, bu also coordinaion wih he eammae, he human player The curren coordinaion is simple and basically based upon wo fixed plays for offensive and defensive siuaion respecively Our offensive play is shown as follows, in which he erminaion condiion is eiher play abored or he siuaion changed (a urn-over of ball posses-

3 sion announced by he referee) There are wo roles in his play, one passes he ball o he oher who posiions down field and wais for receiving a pass PLAY Naive Offense APPLICABLE offense DONE abored!offense ROLE 1 pass 2 none ROLE 2 posiion_down_field receive_pass none Our curren coordinaion is purely observaion based Each player assigns role from his own eyesho wihou communicaion For example, should he robo hink he eammae is closer o he ball, he robo would choose o posiion and receive he ball (ROLE 2) from is eammae (ROLE 1) Furhermore, he robo knows which side gains possession of he ball from he referee announcemen (whisle), herefore i ells offensive from defensive siuaion clearly and hus i has deerminisic idea of which play he eam is using The robo makes an assumpion ha is eammae is performing he same game play as iself The robo can infer wha acic he eammae is execuing from he eam play For insance, afer receiving he ball from he eammae, as a passer, he robo would assume he eammae go forward o a acically advanageous posiion o receive a pass The predefined play for eam coordinaion provides useful informaion for moion modelling, which will be furher discussed in secion 3 3 PLAY-BASED MOTION MODELLING In his secion, we ake a muli-arge racking problem as a deailed example o show he exension of he acic-based moion modelling mehod in general when he eam coordinaion knowledge (play) is incorporaed Firs we give an inroducion of he environmen and arges under he Segway soccer seup Second, we describe deailed moion models for boh he ball and he eammae Third, we exend he acic-based moion modelling o he play level when boh he ball and he eammae are included ino he racking We show how we model he play-dependen ineracions beween he eammae, he robo and he ball and se up a base for giving he eam-driven muli-model racking algorihm in he nex secion 31 Tracking Scenario In a Segway soccer game, here are muliple moving arges on he field eg, he ball, he human eammae and he wo opponens Each eam is idenified by heir disinc color The ball is in orange [4] We consruc wo single arge rackers in he sysem, for he ball and he eammae respecively We use wo separae rackers insead of one muli-arge racker for boh of hem because we can differeniae he ball wih he eammae hanks o he color-based vision sysem The general parameerized sae-space sysem for he kh arge x k, a ime is given by: x k, = fk m (x k, 1, u m k, 1, vk, 1) m (1) z k, = h m k (x k,, n m k,) (2) where f m k and h m k are he parameerized sae ransiion and measuremen funcions for he mh model of he kh arge; x, u, z are he sae, inpu and measuremen vecors; v, n are he process and measuremen noise vecors of known saisics; m is he model index ha can ake any one of N k values, where N k is he number of models of he kh arge being racked (ball/eammae); 32 Ball Moion Modelling In our Segway RMP soccer robo environmen, we define five models o model he ball moion (for he res of his paper, for simpliciy, we use x o represen he ball sae, and use x o represen he eammae sae) Free-Ball The ball is no moving a all or moving sraigh wih a consan speed decay d which depends on he environmen surface x = F x 1 + v 1 1 (3) z = H x + n 1 (4) where x =(x,y, ẋ, ẏ ) T, z =(x,y ) T ; x,y are he ball s x, y posiion in he global coordinae a ime ; and ẋ, ẏ are he ball s velociy in x and y direcion in he global coordinae The superscrip 1 indicaes he model index F and H are known marices as follows: F k = [ ] d 0, H k = d where is he ime inerval beween vision frames Robo-Grab-Ball The ball is grabbed by he robo s cacher In he case of robo grabbing ball, no vision is needed o rack he ball, because we assume he ball moves wih he robo Therefore he ball has he same velociy as he robo (bu plus he noise) and is global posiion a ime is jus he robo s global posiion plus heir relaive posiion, which is assumed o be a consan, plus he noise Human-Grab-Ball The ball is held by he eammae we can infer he ball posiion similarly if we know he eammae posiion well Robo-Kick-Ball The ball is kicked by he robo herefore is velociy is equal o a predefined iniial speed plus he noise The ball is supposed o move oward eiher he human eammae or he goal Human-Kick-Ball The ball is kicked by he eammae and i is supposed o be eiher a pass o he robo or a shoo a he goal 33 Teammae Moion Modelling We define four models o model he human eammae s moion Random Walk The eammae is wondering in he field So he sae a he new ime is he sae a he curren ime wih some addiive zero-mean (assumed Gaussian) noise

4 m 1 m 2 m n m 1 h 1,1 h 1,2 h 1,n Human Kick Human Grab Random Walk P osiioning m 1 m 2 m 1 mh 2 1,1 m 2,1 h 1,2 m 2,2 h 1,n h 2,n m 2 h 1,1 m 2,1 h 1,2 m 2,2 h 1,n h 2,n m n m h 2,1 h n,1 2,2 m n,2 h 2,n h n,n m n m n,1 m n,2 h n,n <P a, v b> Robo Kick Free (a) Robo Grab Hold Ball (b) Acc m n h n,1 h n,2 h n,n m 1 m 2 m <P 1, v 1> n <P 2, v 1> Figure 3: Play-Based moion modelling, where m 1,m 2,,m n are n models, P a is he eam play, v b is he addiional informaion h i,j is he ransiion probabiliy from model m i o model m j given m i, and P a,v b Each layer in he graph is condiioned on a paricular combinaion of he play execued and he addiional informaion obained Holding Ball The eammae is holding he ball wihou moving and waiing for he robo o receive he ball Should he robo know he ball posiion well, i can infer he eammae posiion by he ball posiion in a similar way as Robo-Grab-Ball for ball moion modelling Acceleraing The eammae dashes and obains a velociy in a shor ime Posiioning The eammae is going o a predefined acical posiion wih a consan speed This case happens mosly afer he eammae passing he ball o he robo and moving down he field oward opponen s goal 34 Play Based Model Transiions Given he knowledge of he eam coordinaion plan (he play P 1 a ime 1), he robo can infer wha acic he eammae is execuing (T 1), which provides valuable informaion abou he moion model of he eammae (m ) Boh he robo and he eammae ac over he ball in a Segway soccer game The moion model of he ball (m )is herefore affeced by wha acic he robo (T 1) andhe eammae (T 1) are execuing From he previous subsecion, we know ha he model index m deermines he presen model being used For our eammae racking example, m = i, i =1,, 4 In our approach, i is assumed ha he eammae moion model index, m, condiioned on he previous acic execued T 1 by he eammae, and oher useful informaion v (such as ball sae), is governed by an underlying Markov process, such ha, he condiioning parameer can branch a he nex ime-sep wih probabiliy p(m = i m 1 = j, T 1,v )=h i,j (5) where i, j =1,,N m Since T 1 can be deermined by P 1, wege h i,j = p(m = i m 1 = j, P 1,v ) (6) Figure 4: Objec moion modelling based on he play: Naive Offense Each node is a model Models ransi o one anoher according o he predefined probabiliies (no shown in he figure) (a) Ball moion model (b) Human eammae moion model Since we can draw p(m = i m 1 = j) inann m N m able, we can creae a able for Equaion 6 wih a hird axis which is defined by he uple P a,v b as shown in Figure 3 Here he play P a, is he primary facor ha deermines wheher m i ransis o m j and wha he ransiion probabiliy is, while he informaion v b deermines he prior condiion of he ransiion Each layer in he graph is condiioned on a paricular combinaion of he acic execued and he addiional informaion obained For our ball racking example, m = i, i =1,, 5 Similarly, h i,j = p(m = i m 1 = j, T 1,T 1,v ) (7) where i, j =1,,N msincet 1,T 1 can be deermined by P 1, wege h i,j = p(m = i m 1 = j, P 1,v ) (8) Suppose he curren eam play is he Naive Offense in Secion 22, we can obain he corresponding moion model ransiions for boh he ball and he eammae using he play-based mehod (Figure 4) 4 MULTI-SENSOR MULTI-MODEL TRACKING Following he play-based moion model given in he previous secion, we can use dynamic Bayesian neworks (DBNs) o represen he whole sysem for eammae and ball racking in a naural and compac way as shown in Figure 5 and Figure 6 respecively In his graph, he sysem sae is represened by variables (play P,acicT, infrared sensor measuremen s, ball sae x, ball moion model index m, vision sensor measuremen of ball z, eammae sae x, eammae moion model index m, vision sensor measuremen of eammae z ), where each variable akes on values in some space The variables change over ime in discree inervals, so ha eg x is he ball sae a ime Furhermore, he edges indicae dependencies beween he variables For insance, in Figure 6 he ball moion model index m depends on m 1,T 1,T 1,s and x 1, hence here are edges coming from he laer five variables o m Noe ha we use an approximaion here We assume he measuremen of he infrared sensor is always he rue value, so i does no depend on he ball sae Under his assumpion, here is no edge from x 1 o s,whichgrealysimplifies he ball-racking DBN and he sampling algorihm as well

5 Play P k- 2 Vision Measuremen Teammae Tacic T' k-2 Teammae Moion Model m' k-1 Sae x' k-1 z' k-1 h a v 0 L P k-1 T' k-1 m' k x' k z' k Figure 7: Tes seup for esimaing he ball speed decay d The ball rolls off he ramp (wih heigh h) wih speed v 0 and i sops afer i ravels a disance of L P k T' k m' k+1 x' k+1 z' k+1 Figure 5: A dynamic Bayesian nework for eammae racking wih a Segway RMP robo Filled circles represen deerminisic variables which are observable or are known as he acic or he play ha he robo is execuing For he res of his secion, we give he ball-racking algorihm following Figure 6 The eammae-racking algorihm can be obained similarly following Figure 5 We use he sequenial Mone Carlo mehod o rack he moion model m and he objec sae x Paricle filering is a general purpose Mone Carlo scheme for racking in a dynamic sysem I mainains he belief sae a ime as a se of paricles p (1),,p (Ns),whereeachp (i) is a full,p (2) insaniaion of he racked variables {p (i),w (i) }, w (i) is he weigh of paricle p (i) and N s is he number of paricles In our case, p (i) = x (i),m (i) The equaions below follow from he ball-racking DBN m (i) p(m m (i) 1, x(i) 1,s,T 1,T 1) (9) x (i) p(x m (i), x (i) 1 ) (10) Noe ha T 1 and T 1 are inferred deerminisically from P 1 insead of sampling Also noe ha in Equaion 10, he ball sae is condiioned on he ball moion model m (i) sampled from Equaion 9 Then we use he Sample Imporance Resampling (SIR) algorihm o updae he sae esimaes The sampling algorihm is as follows: [{x (i),m (i) 01 for i =1:N s 02 draw m (i) 03 draw x (i) 04 se w (i),w (i) } Ns i=1 ]=SIR[{x(i) 1,m(i) 1,w(i) 1 }Ns p(m m (i) 1, x(i), x (i) 1 ) p(x m (i) 1,s,T 1,T 1 ) = p(z x (i) ) 05 end for 06 Calculae oal weigh: w = [{w i}ns i=1 ] 07 for i =1:N s 08 Normalize: w i = wi /w 09 end for 10 Resample i=1, z,s,t 1,T 1 ] The inpus of he algorihm are samples drawn from he previous poserior x (i) 1,m(i) 1,w(i) 1, he presen vision and infrared sensory measuremen z,s, he robo s acic T 1, and he eammae s acic T 1 The oupus are he updaed weighed samples x (i),m (i),w (i) In he sampling algorihm, firs, a new ball moion model index, m (i), is sampled according o Equaion 9 a line 02 Then given he model index, and previous ball sae, a new ball sae is sampled according o Equaion 10 a line 03 The imporance weigh of each sample is given by he likelihood of he vision measuremen given he prediced new ball sae a line 04 Finally, each weigh is normalized and he samples are resampled Then we can esimae he ball sae based on he mean of all he x (i) Similarly he sae of he eammae x can be obained from he eammae racker 5 EXPERIMENT In his secion, we design experimens o esimae he ball speed decay in (ime inerval beween vision frames) on differen surfaces We profile he sysem and measuremen noise Finally we evaluae he effeciveness of our racking sysem in boh simulaed and real-world ess 51 Ball Moion Profiling From previous work we know he iniial speed and accuracy of he ball velociy afer a kick moion And we use he seup shown in Figure 7 o esimae he ball speed decay d Indeail,wepuheballonheopof a ramp and le i roll off he ramp wih iniial speed v 0 = 2gh wihou aking he fricion on he surface of he ramp ino accoun, where g is he graviy and h is he heigh of he ramp We record he disance he ball ravelled (L) fromhe posiion he ball rolls off he ramp o he posiion i sops Obviously, he ball speed decay can be approximaed as d =1 v0 L where 0033 sec Following he es resul, we use d = 099 for he cemen surface From he es, we noe ha he faser he ball s speed, he smaller he sysem noise, hence he more he ball s rajecory forms a sraigh line Based on he daa we colleced from experimens, we herefore model he sysem noise when he moion model is Free-Ball o be inverse proporional o he ball speed 52 Measuremen Noise Profiling In order o profile he measuremen noise, we pu he ball on a series of known posiions, read he measuremen from vision sensor, and hen deermine he error in ha measuremen From he resuls, we know ha he nearer he ball, he smaller he observaion noise Therefore we choose

6 Play P k- 2 Teammae Tacic Robo Tacic T k-2 Ball M o io n Model Infrared Sensor s k- 1 Sae Vision Measuremen T' k-2 m k-1 x k-1 z k-1 P k-1 T k-1 s k T' k-1 m k x k z k P k T k s k+ 1 T' k m k+1 x k+1 z k+1 Figure 6: A dynamic Bayesian nework for ball racking wih a Segway RMP robo Table 1: The average RMS error of posiion esimaion and velociy esimaion from human-rackers Moion Model Single Model Muli-Model Posiion Es RMS (m) Velociy Es RMS (m/s) Table 2: The average RMS error of posiion esimaion and velociy esimaion from ball-rackers Moion Model Single Model Muli-Model Posiion Es RMS (m) Velociy Es RMS (m/s) o approximae he error disribuion as differen Gaussians based on he disance from he robo o he ball 53 Simulaion Experimens Because i is difficul o know he ground ruh of he objec s posiion and velociy in he real robo es, we do he simulaion experimens o evaluae he precision of racking Experimens are done following he Naive Offense play, in which he robo acs as he receiver and he human eammae acs as he passer Noises are simulaed according o he model profiled in he previous secion In he beginning, he eammae holds he ball Afer a fixed amoun of ime, he ball is kicked owards he robo, and he eammae moves forward o a predefined locaion We implemen boh a single model racker and a playbased muli-model racker for he ball and he eammae We simulae he experimen for 50 runs, and hen compare he performance of he wo rackers wih differen implemenaions The average RMS error of posiion esimaion and velociy esimaion are shown in Table 1 and 2 respecively The resuls show ha he play-based muli-model scheme performs much beer han he single model especially in erms of velociy esimaion Because wih he play-based moion model, when he ball is being kicked, mos paricles evolving using he ransiion model deermined by he play will change is moion model m (i) from Free-Ball o Human-Kick-Ball, and a velociy will be added o he ball accordingly Figure 8 and Figure 9 show he ball velociy esimaion and he eammae velociy esimaion during a shor erm for a given simulaion es In boh figures, The lef graph shows he x-componen of he velociy (v x) esimaion hrough single model racking and play-based muli-model racking The righ graph shows he y-componen of he velociy (v y) esimaion The doed line wih x-mark represens he rue value, he solid line wih circle represens he he velociy esimaion hrough play-based muli-model racking, he solid line wih cross represens he he velociy esimaion hrough single model racking We noe ha he velociy esimaion wih muli-model rackers he rue velociy in erms v x and v y much more consisen han wih single model rackers 54 Team Cooperaion Tes In he real-world es, we do experimens on he Segway RMP soccer robo execuing he offensive play and coordinaing wih he human eammae The es seup is demonsraed in Figure 10, in which he digis along he lines show he sequence of he whole sraegy, he filled circle a posiion B represens he robo, he unfilled circle a posiion E represen an opponen player, and he shaded circle represen he human eammae When each run begins, he human eammae is a posiion A Wih his eam cooperaion plan (play), he robo chooses he acic CachKickToTeammae o execue, in which he robo sars wih he skill Search-Ball When he robo finds he ball, he eammae passes he ball direcly o he robo and chooses a posiioning poin o go o eiher a C or D The robo grabs he ball afer he ball is in he cachable

7 Table3: Theaverageimeakenoverallhesuccessful runs v x (m/s) rue muli model esimae single model es ime (sec) v y (m/s) rue muli model esimae single model es ime (sec) Figure 8: Ball velociy esimaion The lef figure shows he x-componen of he velociy (v x)esimaion hrough single model racking and play-based muli-model racking The righ figure shows he y- componen of he velociy (v y) esimaion The doed line wih x-mark represens he rue value, he solid line wih circle represens he he velociy esimaion hrough play-based muli-model racking, he solid line wih cross represens he he velociy esimaion hrough single model racking Moion Model Single Model Muli-Model Mean Time (sec) ' C ;; E A 1 3 3' B Figure 10: A demonsraion of a naive eam cooperaion plan in offensive scenario The digis along he lines show he sequence of he whole plan The filled circle a posiion B represens he robo The unfilled circle a posiion E represen an opponen player The shaded circle represen he human eammae 2' D area and is deeced by he infrared sensor (skill Grab-Ball) Nex he robo searches for he eammae holding he ball wih is cacher (skill Search-Teammae) Afer he robo finds he eammae, he robo kicks he ball o is eammae and he eammae shoos a he goal(skill KickToTeammae, compleing he whole offensive play Each run ends in one of he following condiions v x (m/s) rue muli model esimae single model es ime (sec) v y (m/s) rue 015 muli model esimae single model es ime (sec) Figure 9: Human eammae velociy esimaion The lef figure shows he x-componen of he velociy (v x) esimaion hrough single model racking and play-based muli-model racking The righ figure shows he y-componen of he velociy (v y)esimaion The doed line wih x-mark represens he rue value, he solid line wih circle represens he he velociy esimaion hrough play-based mulimodel racking, he solid line wih cross represens he he velociy esimaion hrough single model racking succeed if he human receives he ball from he robo or he human does no receiver he ball bu he pass canbeconsideredasa good one fail if he robo is in searching for he ball or he eammae for more han 30 seconds fail if he ball is ou of he field before he robo caches i In he experimen over 15 runs, we keep rack of he successful rae and he mean ime aken in each successful run (lised in Table 3) The robo wih single model rackers fails 5 of he oal and has an average running ime of 334 seconds in he 10 successful runs While he robo wih play-based muli-model rackers only fails 2 of he oal and has an average running ime of 226 seconds in he 13 successful runs Using play-based muli-model racking saves 323% ime in erms of compleing he whole play over single model racking During he experimen, we noe ha when using he single model racking, mos ime were spen on searching he eammae Incorporaing he eam cooperaion knowledge known as play ino he eammae moion modelling grealy improves he accuracy of he eammae moion model and herefore avoids aking ime in searching a los arge from scrach

8 6 RELATED WORK Tracking moving objecs using a Kalman filer is he opional soluion if he sysem follows a single model, f and h in Equaion 1 and 2 are known linear funcions and he noise v and n are Gaussians [1] Muliple model Kalman filers such as Ineracing Muliple Model (IMM) are known o be superior o he single Kalman filer when he racked objec is maneuvering [2] For nonlinear sysems or sysems wih non-gaussian noises, a furher approximaion is inroduced, bu he poserior densiies are herefore only locally accurae and do no reflec he acual sysem densiies Since he paricle filer is no resriced o Gaussian densiies, a muli-model paricle filer is inroduced However, his approach assumes ha he model index, m, is governed by a Markov process such ha he condiioning parameer can branch a he nex ime-sep wih probabiliy p(m = i m 1 = j) =h i,j where i, j =1,,N mbuhe uncerainies in our objec racking problem do no have such a propery due o he ineracions beween he robo and he racked objec In his moivaion, a acic-based moion modelling mehod is proposed in [9] Based on ha approach, we furher inroduce he play-based moion modelling mehod when eam coordinaion knowledge is available In [10], an approach were proposed for racking a moving arge using Rao-Blackwellised paricle filer In heir experimens, he discree saes are he non-linear moion of he observing plaform and he differen moion models for he arge Bu hey use a fixed ransiion able beween differen models Our ransiion model is dependen on he play ha he robo is execuing and he addiional informaion ha maers This play-based moion modelling can be flexibly inegraed ino our exising skills-acics-plays archiecure 7 CONCLUSIONS AND FUTURE WORK Moivaed by he ineracions beween a eam and he racked objec, we conribue a mehod o achieve efficien racking hrough using a play-based moion model and combined vision and infrared sensory informaion The eamdriven moion modelling mehod gives he robo a more exac ask-specific moion model when execuing differen acics over he racked objec (eg he ball) or collaboraing wih he racked objec (eg he eammae) I improves he accuracy of he objec racking by swiching he objec s moion model according o he curren eam sraegy wihou communicaion among he eammaes, which is applicable o human-robo cooperaion ask Then we represen he sysem in a compac dynamic Bayesian nework and use paricle filer o keep rack of he moion model and objec sae hrough sampling The empirical resuls from he simulaed and he real experimens show he efficiency of he eam-driven muli-model racking over single model racking If he eammae is a human, no a robo, he cerainy ha he eammae is execuing he expeced play or acic could be reduced Tha is, he human eammae could fail o execue he desired play or acic Fuure work will ake such uncerainy ino accoun Anoher ineresing work is o model he muli-arge moion when each arge has muliple hypohesis, which is caused by incorrec measuremens originaing from he cluer We would like o see how he informaion from he acic and he play can help o eliminae false alarms and achieve efficien resampling under he framework of he paricle filer 8 ACKNOWLEDGMENTS We would like o hank Bre Browning for developing he whole archiecure and vision sysem and Brenna Argall for developing he skill and game play for he Segway robos This work was suppored by Unied Saes Deparmen of he Inerior under Gran No NBCH The conen of he informaion in his publicaion does no necessarily reflec he posiion or policy of he Defense Advanced Research Projecs Agency (DARPA), US Deparmen of Inerior, US Governmen, and no official endorsemen should be inferred 9 REFERENCES [1] S Arulampalam, S Maskell, N Gordon, and T Clapp A uorial on paricle filers for on-line non-linear/non-gaussian bayesian racking IEEE Transacions on Signal Processing, 50(2): , Feb 2002 [2] Y Bar-Shalom, X-R Li, and T Kirubarajan Esimaion wih Applicaions o Tracking and Navigaion John Wiley & Sons, Inc, 2001 [3] B Browning, J Bruce, M Bowling, and M Veloso STP: Skills, 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