Measuring Cooperative Robotic Systems Using Simulation-Based Virtual Environment

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1 Measurng Cooperatve c Systems Usng Smulaton-Based Vrtual Envronment Xaoln Hu Computer Scence Department Georga State Unversty, Atlanta GA, USA Bernard P. Zegler Arzona Center for Integratve Modelng and Smulaton Unversty of Arzona, Tucson AZ, USA 8572 ABSTRACT Smulaton-based study plays an mportant role n expermentng, understandng, and evaluatng ntellgent robotc systems. Whle robot models can be created and studed n a smulated envronment, replacng some of the robot models wth ther real robot counterparts brngs smulaton-based study one step closer to the realty. It also provdes the flexblty to allow real robots to be expermented wthn a vrtual envronment. Ths capablty of robot-n-the-loop smulaton s especally useful for large-scale cooperatve robotc systems whose complexty and scalablty severely lmt the possblty for study and evaluaton n a physcal envronment wth real robots. Ths paper presents a smulaton-based approach that allows a cooperatve robotc system to be effectvely evaluated n a vrtual envronment wth combned real and vrtual robots. Ths capablty adds to conventonal smulaton-based study to form an ntegrated measurng process. An example of robotc convoy system s presented together wth metrcs to measure the formaton coherence of cooperatve robotc system. Some prelmnary smulaton results are presented. KEYWORDS: Cooperatve c System, Vrtual Envronment, -n-the-loop Smulaton, c Convoy System. INTRODUCTION Cooperatve robotc systems couple computatonal ntellgence to the physcal world. These systems consst of multple homogenous or heterogeneous robots that perceve the envronment, make decsons, and carry out commands to affect the envronment. Communcaton and cooperaton s mportant for theses systems snce ther robots work as a collectve team to fnsh common tasks. Several taxonomes and metrcs have been defned to classfy these systems. For example, Dudek, etc. [] classfes robotc collectves along seven dmensons: sze of the collectve, communcaton range, communcaton topology, communcaton bandwdth, collectve reconfgurablty, processng ablty of each collectve unt, and collectve composton. Balch [2] classfes the performance metrc of multrobot tasks based on tme, subject of acton, resource lmts, group movement, platform capabltes, etc. The ncreasng complexty of collectve robotc systems calls for systematc methods as well as supportng envronments to experment, understand, and evaluate these systems. To serve ths purpose, modelng and smulaton technologes are frequently appled. Wth smulaton-based methods, models of robots can be bult and smulated. Dfferent confguratons can be easly appled to experment and measure the performance of the system under development. To allow smulaton of robotc systems that actvely nteract wth an external envronment, an envronment model needs to be created. Ths envronment model serves as a vrtual envronment to provde sensory nput to robot models and to response to robots actuaton. For example, a vrtual envronment for moble robots smulaton can have vrtual obstacles that can be sensed by robot models, and t responds to robots movements by updatng new sensory nformaton to robot models. Whle robot models can be created and studed n a smulated envronment, replacng some of the robot models wth ther real robot counterparts wll brng smulaton-based study one step closer to the realty and provdes the flexblty to allows real robots to be expermented n a vrtual envronment. Ths capablty of robot-n-the-loop smulaton s especally useful for large-scale cooperatve robotc systems whose complexty and scalablty severely lmt expermentaton n a physcal envronment usng all real robots. Ths paper presents an approach that allows a cooperatve robotc system to be effectvely evaluated n a vrtual envronment wth combned real and vrtual robots. Ths research s an extenson to our prevous work on a smulaton-based software development methodology for cooperatve robotc systems [3, 4]. Ths methodology supports model contnuty so the smulaton models n the desgn stage can be drectly mapped to real robots to control the real robots n executon. It greatly eases the transton from smulaton-based study to real robot mplementaton and

2 Report Documentaton Page Form Approved OMB No Publc reportng burden for the collecton of nformaton s estmated to average hour per response, ncludng the tme for revewng nstructons, searchng exstng data sources, gatherng and mantanng the data needed, and completng and revewng the collecton of nformaton. Send comments regardng ths burden estmate or any other aspect of ths collecton of nformaton, ncludng suggestons for reducng ths burden, to Washngton Headquarters Servces, Drectorate for Informaton Operatons and Reports, 25 Jefferson Davs Hghway, Sute 204, Arlngton VA Respondents should be aware that notwthstandng any other provson of law, no person shall be subject to a penalty for falng to comply wth a collecton of nformaton f t does not dsplay a currently vald OMB control number.. REPORT DATE AUG REPORT TYPE 3. DATES COVERED to TITLE AND SUBTITLE Measurng Cooperatve c Systems Usng Smulaton-Based Vrtual Envronment 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Georga State Unversty,Computer Scence Department,Atlanta,GA, PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 0. SPONSOR/MONITOR S ACRONYM(S) 2. DISTRIBUTION/AVAILABILITY STATEMENT Approved for publc release; dstrbuton unlmted. SPONSOR/MONITOR S REPORT NUMBER(S) 3. SUPPLEMENTARY NOTES Proceedngs of the 2004 Performance Metrcs for Intellgent Systems Workshop (PerMIS -04), Gathersburg, MD on August ABSTRACT see report 5. SUBJECT TERMS 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT a. REPORT unclassfed b. ABSTRACT unclassfed c. THIS PAGE unclassfed Same as Report (SAR) 8. NUMBER OF PAGES 7 9a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescrbed by ANSI Std Z39-8

3 ncreases the confdence that the fnal system mplements the behavor as been developed. Ths research s based on the Dscrete Event System Specfcaton (DEVS) modelng and smulaton framework [5]. The concept of vrtual envronment has been largely used by the technology of vrtual realty (VR), whch has been appled to varous areas such as smulaton of manufacturng plants, the plannng of robotc workcells, and robot teleoperaton systems. Whle the research of VR manly deals wth the nteracton wth human operators, our work focuses on the nteracton between robots and the vrtual envronment. The followng research work s related to our research from ths perspectve. Komorya and Tan [6] developed a vrtual envronment that allows a sngle real robot to be expermented n a vrtual envronment. Wang [7] proposed a smulaton envronment that allow real and vrtual robot to work together. The work of RAVE [8] developed a smulaton envronment that supports multple moble robotc systems. Our research extends these works by developng a welldefned archtecture, an ncremental development process, and by ntegratng expermental frames to measure cooperatve robotc systems wth combned real and vrtual robots n a systematc way. Ths paper s organzed as follows. Secton 2 presents the vrtual measurng envronment from three aspects: the archtecture, the measurng process, and the relatonshp to expermental frames. Secton 3 descrbes a robotc convoy system as an llustratve example. The models of ths system are frst descrbed, several metrcs are then presented, and some prelmnary smulaton data s gven. Secton 4 concludes ths work and provdes future research drectons. 2. A VIRTUAL EVALUATION ENVIRONMENT FOR ROBOTIC SYSTEMS The effectveness of ths smulaton-based vrtual evaluaton envronment s supported by a well-defned archtecture, an ncremental measurng process, and by ntegratng expermental frames to specfy metrcs for performance measurement. Next we present these three aspects respectvely. 2. Archtecture of the Vrtual Evaluaton Envronment In ths research we vew robotc systems as a partcular form of real-tme systems that montor, respond to, or control, an external envronment. Ths envronment s connected to the computer system through sensors, actuators, and other nputoutput nterfaces [9]. A robotc system from ths pont of vew conssts of sensors, actuators and the decson-makng unt. A cooperatve robotc system s composed of a collecton of robots that communcate wth each other and nteract wth an envronment. Ths above descrpton suggests the basc structure for a smulaton-based vrtual envronment for robotc systems: an envronment model, and a collecton of robot models that nclude a decson makng model, sensors, and actuators. The envronment model represents the real envronment wthn whch the robotc system wll be executed. It may nclude vrtual obstacles, vrtual robots, or any other enttes that are useful for smulaton-based study. It forms a vrtual envronment for the robots. The robot model represents the control software that governs the robot s behavor. It also ncludes sensor and actuator nterfaces to brdge the decsonmakng model and the smulaton-based vrtual envronment. In our research, we clearly separate a robot s decson-makng unt, whch s modeled as a DEVS atomc or coupled model, from the sensors and actuators that are modeled as DEVS Actvtes. Couplngs can be added between DEVS Actvtes and the envronment model thus messages can be passed between the decson-makng model and the envronment model through sensor/actuator Actvtes. vrtual obstacle vrtual counterpart of the real robot vrtual robots vrtual envronment wreless communcaton vrtual sensors Control Model HIL actuators computer moble robot Fgure : Archtecture of robot-n-the-loop smulaton The clear separaton between robots decson-makng model and sensor/actuator nterfaces brngs several advantages. Frst, t separates a robot s decson-makng from hardware nteracton, thus makng t easer for the desgner to focus on the decson-makng model, whch s the man desgn nterest. Secondly, the exstence of a sensor/actuator nterface layer makes t possble for the decson-makng model to nteract wth dfferent types of sensors/actuators, as long as the nterface functons between them are mantaned the same. Thus dependng on dfferent expermental and measurng objectves, a robot model can be equpped wth dfferent sensors/actuators to be expermented and measured. Our prevous work [0] has taken advantage of these features to allow drect transferrng of the decson-makng models from smulaton to real robots executon a capablty referred as model contnuty. Durng smulaton, the decsonmakng model nteracts wth a vrtual envronment through vrtual sensors/actuators; durng real executon, the real robots decson-makng models nteracts wth a real envronment through real sensor/actuator nterfaces. An ntermedate stage can also be developed to allow the decson-makng model on a real robot to nteract wth the smulaton-based vrtual envronment. We call ths stage robot-n-the-loop smulaton. It s acheved by confgurng a real robot to use a combnaton of vrtual and real

4 sensors/actuators. For example, Fgure shows an expermental setup where one real moble robot works together wth a vrtual envronment. In ths example, the moble robot uses ts vrtual sensor to get sensory nput from the vrtual envronment and uses ts real motor nterface to move the robot. As a result, ths real robot moves n a physcal feld based the sensory nput from a vrtual envronment. Wthn ths vrtual envronment, the robot can see vrtual obstacles and other vrtual robots that are smulated by computers. Ths capablty of robot-n-the-loop smulaton brngs smulaton-based study one step closer to the realty. It also makes t possble to study and measure several real robots wthn a large robotc system that may nclude hundreds of robots. In ths case, the rest of robots can be provded by the smulaton-based vrtual envronment. One mportant ssue for the robot-n-the-loop smulaton s the synchronzaton between the real robots and the vrtual envronment. For example, n Fgure, when the decsonmakng model ssues a movng command, the real robot wll move a dstance n the physcal envronment. Ths change of poston should also be updated by the vrtual envronment. For ths purpose, each real robot has a vrtual counterpart n the vrtual envronment. When a real robot moves, the poston of ts vrtual counterpart wll be updated. Thus the synchronzaton between the real robot and the vrtual envronment s actually the synchronzaton between the real robot and ts vrtual counterpart. Ideally, an ndependent montorng system s needed to track the movement of the real robots and then nform the vrtual envronment to synchronze the dstance and tme of robots movements. In our current mplementaton, a set of HIL (hardware-n-theloop) sensors/actuators has been developed. These HIL sensors/actuators drve the real sensor/actuators, whle n the meantme are coupled to the vrtual envronment thus messages can be sent to t. For the example shown n Fgure, the HIL motor drves the motor of the robots. In the meantme t catches the movecomplete sgnal returned from the motor and then sends a message to the vrtual envronment to update the poston of ts vrtual counterpart. 2.2 From Model To Real An Incremental Measurng Process Based on ths vrtual measurng envronment, an ncremental measurng process s developed. Ths process ncludes three steps and supports smooth transtons between them. These steps are measurng based on conventonal smulaton, measurng based on robot-n-the loop smulaton, and measurng based on real robot executon. Fgure 2 gves an example wth two robots to llustrate ths process. The frst step s conventonal smulaton, where all components are models and smulated by fast-mode or realtme smulators n one computer. As shown n Fgure 2(a), both robot models are equpped wth vrtual sensors and actuators to nteract wth the vrtual envronment. Couplngs between two robots can also be added so they can send messages to each other. We note that ths s the same setup as the smulatons that most robotc research uses. It has the most flexblty as all components are models and dfferent confguratons can be easly appled to measure the system under development. Model Vrtual Vrtual Model Vrtual Vrtual Vrtual Envronment Model Vrtual Vrtual Real Vrtual HIL Vrtual Envronment Real Real Real Real Envronment (a) (b) (c) Fgure 2: An ncremental measurng process Real Real Real The second step s robot-n-the-loop smulaton where one or more real robots are measured and expermented wthn a vrtual envronment together wth other vrtual robots (robot models) that are smulated by computer. In ths step, the vrtual robots stll use vrtual sensors/actuators. However, dependng on the measurng objectves, the real robots may have a combnaton of vrtual and HIL sensors/actuators. For example, the real robot shown n Fgure 2(b) uses a vrtual sensor and a HIL actuator. The couplngs between the two robots are mantaned the same so the real and vrtual robots can nteract wth each other n the same way as n the frst step. However, the real commutaton n ths step happens across a wreless network, whch s transparent to the robots. Snce real robots are nvolved n the smulaton, robot-n-theloop smulaton has to run n a real-tme fashon. The fnal step s the real system measurement, where real robots are measured n a real physcal envronment. These robots use real sensors and actuators. They communcate n the same way as the frst two steps snce the couplngs between them are not changed through the process. The measurement of ths step s from the realty, thus havng the most fdelty. However, t s also most costly and tme consumng among the three steps. Ths ncremental measurng process brngs smulatonbased study closer and closer to the realty. As the process proceeds, the flexblty (easy to experment dfferent confguratons) and productvty (tme savng and cost savng) of the measurement decreases and the fdelty (loyal to the realty) of the measurement ncreases Specfy Measurng Metrcs Usng Expermental Frame An expermental frame s a specfcaton of the condtons wthn whch the system s observed or expermented [5]. In DEVS-based modelng and smulaton framework, an expermental frame s realzed as a system that nteracts wth the source system, or System Under Test (SUT), to obtan the data of nterest under specfed condtons. It conssts of four major subsectons: nput stmul: specfcaton of the class of admssble nput tme-dependent stmul. Ths s the class from

5 whch ndvdual samples wll be drawn and njected nto the model or system under test for partcular experments. control: specfcaton of the condtons under whch the model or system wll be ntalzed, contnued under examnaton, and termnated. metrcs: specfcaton of the data summarzaton functons and the measures to be employed to provde quanttatve or qualtatve measures of the nput/output behavor of the model. Examples of such metrcs are performance ndces, goodness-of-ft crtera, and error accuracy bound. analyss: specfcaton of means by whch the results of data collecton n the frame wll be analyzed to arrve at fnal conclusons. The data collected n a frame conssts of pars of nput/output tme functons. When an expermental frame s realzed as a system to nteract wth the SUT (or ts model), the four specfcatons become components of the drvng system. For example, a generator of output tme functons mplements the class of nput stmul. Integrate expermental frames nto the vrtual measurng envronment brngs the advantage that measurng metrcs can be formally specfed. More research s on the way to ntegrate them n a structured way. In the meantme a set of measurng metrcs s also under development for cooperatve robotc systems. 3. ROBOT CONVOY: A CASE STUDY EXAMPLE The presented vrtual measurng envronment has supported the development of a robotc convoy system. Below we brefly descrbe the model of ths system, ts measurng metrcs, and some prelmnary results that are collected from smulaton-based study. We note that most results presented n ths paper are collected from smulatons that do not nvolve real robots. But n the next step we plan to measure the system usng robot-n-the-loop smulaton and expect to reach more nterestng results. For example, we plan to use one real robot to run robot-n-the-loop smulaton to check the convoy speed of ths real robot and compare t wth the data collected from the conventonal smulaton. Another result that we plan to check s to use two real robots neghborng to each other and then check the back robot s poston errors based on the poston and drecton of ts front robot n the physcal envronment. 3. System Descrpton and System Model Ths robot convoy system conssts of an ndefnte number of robots, sayng N robots (N>). These robots are n a lne formaton where each robot (except the leader and the ender) has a front neghbor and a back neghbor. The robots used n ths system are car type moble robots wth wreless communcaton capablty. They can move forward/backward and rotate around the center, and have whsker sensors and nfrared sensors. []. One of the basc goals of ths convoy system s to mantan the coherence of the lne formaton and to synchronze robots movements. Synchronzaton means a robot cannot move forward f ts front robot doesn t move, and t has to wat f ts back robot doesn t catch up. To serve ths purpose, synchronzaton messages are passed between a robot and ts neghbors. To acheve coherence of the lne formaton, the movng parameters of a front robot are passed back. Ths allows the back robot to plan ts own movement accordngly based on ts front robot s movement. The system has no global communcaton and coordnaton snce we want to study how global behavor can be acheved usng localzed sensng and communcaton. FReadyIn n FReadyOut BReadyIn FReadyOut FReadyIn 3 BReadyOut BReadyIn FReadyOut FReadyIn 2 BReadyIn BReadyOut Fgure 3: System model of the robotc convoy system BReadyOut Fgure 3 shows the model of ths system. As we can see, ths model ncludes N models (each of them s a DEVS coupled model), whch are correspondng to the N robots n the system. Each ntermedate robot model has two nput ports: FReadyIn, BReadyIn and two output ports: FReadyOut, BReadyOut. These ports are used to send and/or receve synchronzaton messages between robots and to pass movng parameters from a front robot to the back robot. The couplngs between them are shown n Fgure 3. Durng the convoy, the leader robot ( n Fgure 3) decdes the path of convoy. Meanwhle, t wll turn around f ts nfrared sensors ndcate that there are obstacles ahead. All other robots conduct movement based on ther sensory nput and the movng parameters passed back from ther front robots. Specfcally, a robot wll predct where ts front robot s and turn to that drecton. It then moves forward or backward to catch ts front robot. After that t may go through an adjust process to make sure that t does not lose ts front robot. Ths adjust process s necessary because nose and varance exst durng a movement so a robot wll not reach the desred poston and drecton after the movement. Durng adjustment, a robot scans around untl t fnds ts front robot. Then t sends out a synchronzaton message to nform ts front and back neghbors. Thus robots actually go through a basc turn move adjust nform routne. For example, a robot R - wll turn angle α - to the drecton of ts front robot R -2, move dstance d - to catch ts front robot,

6 and then adjust tself wth angle β - to make sure t sees ts front robot R -2. Fgure 4 shows these movng parameters. R α R - a d R D α - δ d - R - β - δ Fgure 4: Movng parameters for robots convoy After the adjustment, R - sends out a synchronzaton message to ts neghbors. Ths synchronzaton message contans nformaton of α -, d -, and β -. Based on ths nformaton and ts sensory data, R plans ts movement. Ths s shown by Fgure 4 and formulated by formula ()-(3). Among these formulas, δ s the angle (drecton) dfference between R and R - ; a s the dstance between robot R and R - and can be calculated from the robot s nfrared sensor data and the sze of the robot. Specfcally, the turnng angle α of R s calculated by formula (); the movng dstance d can be calculated from formula (2), where D s the desred dstance between R and R -. Then the new angle dfference δ ' between R and R - s updated by formula (3), where β s the adjustng angle for R. We note that due to nose and varance, the δ ' calculated from formula (3) wll not be the exact angle dfference between R and R -. However, t seems that ths error does not accumulate as tme proceeds. d *sn( α + δ ) tgα = a + d *cos( α + δ ) () d * sn( α + δ ) d = D snα (2) δ = δ + α + β α β (3) The model of each robot s developed based on the subsumpton archtecture [2]. It has the Avod model to avod collsons wth any objects; the Convoy model to control robot s movement based on the rules as descrbed above. It also has DEVE Actvtes to represent the sensor/actuator nterfaces of the robot. A detaled descrpton of a smlar model can be found at [3]. Fgure 5 shows the Envronment model that we used for ths example. Ths Envronment model ncludes TmeManager models and the SpaceManager model. For each robot, there s a TmeManager correspondng to t. Ths TmeManager models the tme for a robot to conduct a movement. The SpaceManager models the movng space, ncludng the dmenson, shape and locaton of the feld and the objects nsde the feld. It also keeps track of robots (x,y) postons and movng drectons durng smulaton. Such trackng s needed to supply robots wth the correct sensory data. To account for varablty n the real moton, a random number generator provdes a source of addtve nose. Note that n ths example we have gnored the dynamcs of a movement as we treat each movement as an atomc acton so the postons and drectons of robots are updated dscretely. move moven startmove TmeManager t startmove TmeManagerN N tn movecomplete SpaceManager (x, y) N (x, y) movecompleten Obstacles (x, y) Fgure 5: Envronment model sensordata sensordatan Wth all these models, smulaton was run and a graphc user nterface was developed to show robots movements. Fgure 6 shows two snapshots of a robotc convoy system wth 30 robots wthn a feld surrounded by walls. As can be seen n ths system, robots wll not follow the exact track of the leader robot. However, they are able to follow ther mmedate front robots closely, thus formng a coherent team from a global pont of vew. Note that obstacles can also be easly added wthn the feld. () (2) Fgure 6: Snapshot of robots n moton 3.2 Measurng Metrcs and Smulaton Results A good set of measurng metrcs s very mportant to study ths robotc convoy system. Ths secton descrbes several metrcs that we have developed. These metrcs are nether fnal nor complete. However, they serve as a startng pont to analyze and measure ths system. Some prelmnary smulaton results based on these metrcs are also presented and analyzed. Convoy Speed and Number of Adjustment The convoy speed of the team and the number of adjustment for each robot are among the most obvous results that can be obtaned from smulaton-based study. Both them can be vewed as metrcs for the system s performance. In fact, these two metrcs are correlated to each other: the larger the number of adjustment, the slower the convoy speed. Snce

7 robots move n a coordnated way, we defne the convoy speed as the speed of the leader robot. Ths can be calculated by dvdng the movng dstance by the logc tme of smulaton. The number of adjustment can be obtaned drectly from each robot. Formaton Coherence Due to nose and varance n realty, there exsts dfference between a robot s real poston, drecton (angle) and ts desred poston and drecton. Ths dfference s affected by the varance of movement n real executon, whch s modeled by addng nose nto robot s movement n smulaton. On the other hand, even though varance exsts, ths system can stll conduct the convoy wth some level of formaton coherence. Ths s because an adjust process has been mplemented that allows robots to adjust ther postons/drectons based on the feedback from ts nfrared sensors. Apparently the level of formaton coherence s affected by the varance of movement. If ths varance s large enough, even though a adjust process exsts, the system wll eventually fal to mantan ts formaton coherence. To study ths problem, we calculate each robot s poston errors under the effect of dstance nose factor (DNF) and angle nose factor (ANF). These two factors are the rato of the maxmum dstance varance and maxmum angle varance as compared to the robot s movng dstance respectvely. For example, f the angle nose factor s 0. and a robot moves forward 60, after ts movement the robot wll have maxmum 6 degrees varance from ts desred drecton. Once each robot s poston error s known, the average poston error of the team can be derved. Ths average s an ndcator for the convoy system s formaton coherence: the smaller the error s, the more coherent the convoy system s. Formula (4) (7) shows how the average poston error can be calculated. In these formulas, D s the desred dstance between robots and N s the total number of robot. In case the formaton coherence s broken, sayng robot R lose tself, E (t) wll ncrease contnuously, makng the average error E(t) ncrease too. Note that the desred poston (x -desred, y -desred ) of R s calculated from ts front robot R - s poston, not related to any specfc formatons. Thus systems wth dfferent lne formaton shapes may have the same poston errors. E x 2 2 ( t) = ( x ( t) x desred ( t)) + ( y ( t) y desred ( t)) (4) desred( t) = x ( t) D *cosθ ( t) (5) desred ( t) = y ( t) D * snθ ( t) (6) y E t E t = ( ) ( ) (7) N Fgure 7 shows the average poson error for a system wth 30 robots, DNF=0., and ANF=0.08. The system starts wth all robots at ther desred postons. Thus as smulaton proceeds, the poston error ncreases from 0. It then reaches a stable stage where the poston error oscllates around an average value (35.7 In ths example). As we can see, n ths system the poston error does not accumulate over tme. Thus we say that ths system s formaton coherence s mantaned. poston error average poston error wth 30 robots smulaton steps DNF=0., ANF=0.08 Fgure 7: Average poston error wth 30 robots Senstvty Snce the formaton coherence s affected by the nose factors, senstvty analyss s useful to study f the system s robust to nose factors. To conduct senstvty analyss, we run smulatons wth dfferent nose factors and calculate the poston errors. Fgure 8 shows a system wth 30 robots average poston errors under the effect of three sets of DNF and ANF: set has DNF = 0.04, ANF = 0.04; set 2 has DNF =0., ANF = 0.08; set 3 has DNF = 0.2, ANF = 0.. For analyss purpose, we omt the transent stage when the smulatons start. poston errors Poston errors vs. nose factors smulaton steps Seres Seres2 Seres3 Fgure 8: Average poston errors vs. nose factors Fgure 8 shows that dfferent nose factors result n dfferent error patterns. However, for ths system, all three errors are stll mantaned wthn a boundary (they do not accumulate as tme ncreases). By calculatng the average of them, we have average = 35., average2 =35.7, and average3 =36.6. From these data we can see that as the nose factor ncreases, the poston error ncreases too. However, ths change s nsgnfcant as compared to change of the nose factors. Although more analyss s needed to reach any quanttatve concluson, we can say that ths system s nsenstve to the nose factors as long as these factors are wthn a safe boundary. Ths s because the system mpalements an adjust process that allows robots to adjust themselves based on the feedback from ther IR sensors.

8 Scalablty Scalablty refers to the ablty of a system to mantan ts qualty as the scale of the system ncreases. To study scalablty, we change the number of robots and run smulaton to see how that affects system s average poston error (average over number of robots and over tme). Fgure 9 shows the poston errors for the number of robots to be 0, 20, 30, and 40 wth DNF =0. and ANF =0.08. It shows that the average poston error ncreases as the number of robot ncreases. If ths trend holds true wth more robots, the system s not scalable n the sense that t wll eventually break as more robots are added nto the system. poston error Poston error vs. number of robots number of robots DNF=0., ANF=0.08 Fgure 9: Average poston errors vs. number of robots 4. CONCLUSION Ths paper presents a smulaton-based vrtual evaluaton envronment for cooperatve robotc systems. Ths vrtual envronment allows a combnaton of real and vrtual robots to work together for a system-wde study and measurement. An ncremental measurng process s developed to transton smulaton-based study closer to realty as the process proceeds. Based on ths vrtual envronment, a robotc convoy system was developed and presented n ths paper as an llustratve example. Coherence metrcs for ths system were defned and prelmnary smulaton results were dscussed. We note that most results presented n ths paper are collected from smulatons that do not nvolve real robots. But n the next step we plan to measure the system usng robot-nthe-loop smulaton and expect to gather more nterestng results. In the meantme, a set of more complete evaluaton metrcs s also under development for the robotc convoy systems presented n ths paper. [2] Balch, T., Taxonomes of Multrobot Task and Reward, Teams, Edted by Balch, T., and Parker L.E., A K Peters, 2002 [3] Hu, X., and Zegler, B. P., Model Contnuty to Support Software Development for Dstrbuted c Systems: a Team Formaton Example, Journal of Intellgent & c Systems, Theory & Applcaton, Specal Issue: Multple and Dstrbuted Cooperatng s, pp. 7-87, January, 2004 [4] Hu, X., and Zegler, B.P., A Smulaton-based Software Development Methodology for Cooperatve Real-tme Intellgent Systems, to appear n Annual of Complex Systems and Intellgence Scence, World Scentfc Publshng Co., 2004 [5] Zegler, B.P., Km, T.G., et al.. Theory of Modelng and Smulaton. New York, NY, Academc Press, [6] Komorya, K.; Tan, K., Utlzaton of the vrtual envronment system for autonomous control of moble robots, Intellgent Moton Control, 990. Proceedngs of the IEEE Internatonal Workshop on, Volume: 2, August 990 [7] Wang. J.: Methodology and desgn prncples for a generc smulaton platform for dstrbuted robotc system expermentaton and development. Systems, Man, and Cybernetcs, 997. Computatonal Cybernetcs and Smulaton., 997 IEEE Internatonal Conference on, Volume: 2, 997 Page(s): vol.2 [8] Dxon, K.; Dolan, J.; Wesley Huang; Pareds, C.; Khosla, P., RAVE: a real and vrtual envronment for multple moble robot systems, Intellgent s and Systems, 999. IROS '99. Proceedngs. 999 IEEE/RSJ Internatonal Conference on, Volume: 3, 7-2 Oct. 999 [9] Shaw, S. C., Real-tme Systems and Software, John Wley & Sons, 200 [0] Hu, X., A Smulaton-based Software Development Methodology for Dstrbuted Real-tme Systems, Dssertaton, Unversty of Arzona, 2003 [] Pepelman. J., N. Alvarez, K. Galnet, R. Olmos.: 498 A & B Techncal Report. Department of Electrcal and Computer Engneerng, Unversty of Arzona, 2002 [2] Brooks, R. A., "A Robust Layered Control System For A Moble ", IEEE Journal Of cs And Automaton, RA-2, Aprl. pp. 4-23, March ACKNOWLEDGEMENT Ths research was supported by NSF grant DMI , DEVS as a Formal Framework for Scalable Enterprse Systems. 6. REFERENCE [] Dudek, G., Jenkn, M., and Mlos, E., A Taxonomy of Multrobot Systems, Teams, Edted by Balch, T., and Parker L.E., A K Peters, 2002