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STP: Skills, tactics and plays for multi-robot control in adversarial environments BrettBrowning,JamesBruce,MichaelBowling,andManuelaVeloso {brettb,jbruce,mhb,mmv}@cs.cmu.edu CarnegieMellonUniversity,5000ForbesAvenue,PittsburghPA15213,USA November22,2004 Abstract Inanadversarialmulti-robottask,suchasplayingrobotsoccer,decisionsforteamandsinglerobot behaviormustbemadequicklytotakeadvantageofshort-termfortuitouseventswhentheyoccur.When nosuchopportunitiesexist,theteammustexecutesequencesofcoordinatedactionacrossteammembers that increases the likelihood of future opportunities. We have developed a hierarchical architecture, called STP, to control an autonomous team of robots operating in an adversarial environment. STP consistsofSkillsforexecutingthelow-levelactionsthatmakeuprobotbehavior,Tacticsfordetermining what skills to execute, and Plays for coordinating synchronized activity amongst team members. Our STP architecture combines each of these components to achieve autonomous team control. Moreover, theSTPhierarchyallowsforfastteamresponseinadversarialenvironmentswhilecarryingoutactions withlongergoals. Inthisarticle,wepresentourSTParchitectureforcontrollinganautonomousrobot team in a dynamic adversarial task that allows for coordinated team activity towards long-term goals, with the ability to respond rapidly to dynamic events. Secondly, we present the sub-component of skillsandtacticsasageneralized,single-robotcontrolhierarchyforhierarchicalproblemdecomposition withflexiblecontrolpolicyimplementationandreuse. Thirdly, wecontributeourplaytechniquesasa generalizedmethodforencodingandsynchronizingteambehavior,providingmultiplecompetingteam responses,andforsupportingeffectivestrategyadaptationagainstopponentteams. STPhasbeenfully implemented on a robot platform and thoroughly tested against a variety of unknown opponent teams under in a number of RoboCup robot soccer competitions. We present these competition results as a mechanismtoanalyzetheperformanceofSTPinarealsetting. Keywords: Multi-robotcoordination,autonomousrobots,adaptivecoordination,adversarialtask 1 Introduction To achieve high performance, autonomous multi-robot teams operating in dynamic, adversarial environ- mentsmustaddressanumberofkeychallenges. Theteammustbeabletocoordinatetheactivitiesofeach team member towards long-term goals, but also be able to respond in real-time to unexpected situations. Here, real-time means responding at least as fast as the opponent. Moreover, the team needs to be able to adaptitsresponsetotheactionsoftheopponent. Atanindividuallevel,therobotsmustbeabletoexecute sequencesofcomplexactionsleadingtowardslong-termgoals,butalsorespondinreal-timetounexpected situations. Secondly,eachrobotmusthaveasufficientlydiversebehaviorreportoireandbeabletoexecute thesebehaviorsrobustlyeveninthepresenceofadversariessoastomakeagoodteamstrategyviable. Al- though these contrasting demands are present in multi-robot [30, 17] and single-robot problems [9, 2, 32], the presence of adversaries compounds the problem significantly. If these challenges are not addressed for a robot team operating in a dynamic environment, the team performance will be degraded. For adversarial environments,whereateam’sweaknessesareactivelyexploitedbygoodopponents,theteamperformance willdegradesignificantly. The sheer complexity of multi-robot teams in adversarial tasks, where the complexity is essentially exponential in the number of robots, creates another significant challenge to the developer. Thus, control policy reuse across similar sub-problems, as well as hierarchical problem decomposition, are necessary to makeeffecientlyuseofdevelopertimeandresources. Addressing all of these challenges in a coherent, seamless control architecture is an unsolved problem, to date. In this paper, we present a novel architecture, called STP, for controlling a team of autonomous robotsoperatinginatask-drivenadversarialenvironment. STPconsistsofthreemaincomponents–Skills, Tactics, and Plays – built within a larger framework providing real-time perception and action generation mechanisms. Skills encode low-level single-robot control algorithms for executing a complex behavior to achieveashort-term,focusedobjective. Tacticsencapsulatewhattherobotshoulddo,intermsofexecuting skills, to achieve a specific long-term goal. Plays encode how the team of robots should coordinate their execution of tactics in order to achieve the team’s overall goals. We beleive that STP addresses many of the challenges to multi-robot control in adversarial environments. Concretely, STP provides three key contributions. Firstly, it is a flexible architecture for controlling a team of robots in a dynamic, adversarial task that allows for both coordinated actions towards long-term goals, and fast response to unexpected events. Secondly, the skills and tactics component can be decoupled from plays, and supports hierarchical controlforindividualrobotsoperatingwithinadynamicteamtask,potentiallywithadversaries. Lastly,the play-based team strategy provides a generalized mechanism for synchronizing team actions and providing foradiversityofteambehavior. Additionally,playscanbeeffectivelyusedtoallowforstrategyadaptation against opponent teams. STP has been fully implemented and extensively validated within the domain of RoboCuprobotsoccer[23]. Inthispaper,wedetailthedevelopmentofSTPwithinthedomainofRoboCup robot soccer, provide evidence of its performance in real competitions with other teams, and discuss how ourtechniquesapplytomoregeneraladversarialmulti-robotproblems. Thisarticleisstructuredasfollows. Inthefollowingsection,webeginbydescribingtheproblemdomain ofRoboCuprobotsoccerwithinwhichSTPhasbeendeveloped. Section3presentsanoverviewoftheSTP architecture and its key modules leading to a detailed description of the single robot components of skills and tactics in section 4 and team components of plays in section 5. Section 6 describes the peformance of STPinRoboCupcompetitionsagainstavarietyofunknownopponentteams,anddiscusseshowSTPcanbe improvedandappliedtootheradversarialproblemdomains. Finally, section7presentsrelatedapproaches toSTP,andsection8concludesthepaper. 2 The Robot Soccer Problem TheSTParchitectureisapplicabletoanautonomousrobotteamperformingataskinanadversarial,dynamic domain. Toconcretelyexplorethisproblem,wechoseRoboCuprobotsoccerasthetest-beddomain. More specifically,wehavechosentheSmall-SizeLeague(SSL),adivisionwithintheRoboCupinitiative. Inthis section,theSSLrobotsoccerproblemisconcretelydefinedalongwiththechallengesitposes. Thissection alsodetailsthespecifictest-bed,theCMDragonssystem,usedtovalidatetheSTParchitecturetoprovidea backdropfortheensuingsections. 2 2.1 Small-sizeRoboCupRobotSoccerLeague RoboCuprobotsoccerisaworld-wideinitiativedesignedtoadvancethestate-of-the-artinrobotintelligence through friendly competition, with the eventual goal of achieving human-level playing performance by 2050 [23]. RoboCup consists primarily of teams of autonomous robots competing against one another in games of soccer, along with an associated symposium for research discussion. There are a number of different leagues within RoboCup, which are designed to focus on different parts of the overall problem: developingintelligentrobotteams. ThisarticleisprimarilyfocusedontheSmall-SizeLeague(SSL). A SSL game consists of two teams of five robots play soccer on a 2.8m x 2.3m field with an orange golfball[3]. Eachteammustbecompletelyautonomousforthedurationofthegame,whichtypicallylasts fortwo10-minutehalves. Here,autonomymeansthattherearenohumansinvolvedinthedecisionmaking cyclewhilethegameisinprogress. TheteamsmustobeyFIFA-likerulesasdictatedbyahumanreferee. An assistant referee translates referee commands into a computer-usable format, which is transmitted to each team via RS-232 using a standardized protocol, via a computer running the RefBox program [3]. Figure 1 showsthegeneralsetupasusedbymanyteamsintheSSL.TheSSLisdesignedtofocusonteamautonomy. Therefore, global vision via overhead cameras and off-field computers, which can communicate with the robotsviawirelessradio,areallowedtobeused. Figure1: AnoverviewoftheCMDragonssmall-sizerobotsoccerteam. SSLrobotsoccerinvolvesmanyresearchissues. Examplesofsomeoftheresearchchallengesinclude: • Buildingcomplete,autonomouscontrolsystemsforadynamictaskwithhigh-performance; • Teamcontrolinadynamicenvironment,andresponsetoanunknownopponentteam; • Behaviorgenerationgivenrealsensorlimitationsofocclusion,uncertainty,andlatency; • Fastnavigationandballmanipulationinadynamicenvironmentarereal-worldsensors; • Fast,robust,low-latencyvision,witheasytousecalibrationroutines; • Robust,highperformancerobotswithspecializedmechanismsforballmanipulation. A typical SSL game is highly dynamic, where ball speeds of 3 to 4m.s−1 and robots speeds of 1 to 2m.s−1 are common. With such speeds in a small environment, it becomes critical for information to be translated into action quickly in order for the team to be responsive to sudden events in the world. For example, ifa robotkicks aball at 3.5m.s−1, alatency of 100ms meansthat theball willhave movedover 3 35cmbeforetherobotscouldpossiblyrespondtotheobservationthattheballhadbeenkicked. Highspeed ofmotionandlatencyimpactoncontrolinthefollowingways: • Vision, tracking, and modeling algorithms must compromise between the need to filter noise and detectunexpectedeventsinminimumtime; • Predictionmechanismsarerequiredtocompensateforlatencyforeffectivecontrol; • Teamandsinglerobotcontrolmustadaptquicklytodynamicchanges. The last point means that all control decisions need to be recalculated as often as possible to allow the system to react quickly to unexpected events. As a rough guide, the CMDragons system [12] recalculates everything for each frame, at a rate of 30Hz. Typically, high-level decisions change at a slower rate than low-leveldecisions. Foranapproximateguide,aplaytypicallylasts5-30s,whileatacticmayoperateover a time frame of 1-30s, and a skill may operate over a 300ms-5s time frame. However, any decision at any level can be switched in the minimum time of one frame period (33ms) to respond to any large scale dynamicchange. 2.2 TheCMDragons Figure2showsthemajorcomponentsofthecontrolsystemdevelopedforourCMDragonsSSLteam. This architectureistheresultofalongseriesofdevelopmentssinceRoboCup1997[37,36,35,10,12]. Figure3 shows the robot team members. As shown, the architecture consists of a number of modules beginning withvisionandtracking, theSTParchitecture,navigationandmotioncontrol,andfinallytherobotcontrol software and hardware. We briefly describe each of the non-STP components in the following paragraphs toprovidethecontextforlaterdiscussions. Information passes through the entire system synchronized with incoming camera frames at 30Hz. Thus a new frame arrives, vision and tracking are run on the processed frame, the resulting information is fed into the world model. The STP architecture is executed, followed by navigation and motion control. The resulting motion command is sent to the robot and the robot executes the command with local control routines. 2.2.1 Perception Vision is the primary means of perception for the CMDragons team. Everything in the SSL is color coded (seeFigure3),makingcolorvisionprocessingalgorithmsanaturalchoice. Theballisorangeandthefield isgreencarpetwithwhitelinesandwhiteangledwalls. Eachrobotispredominantlyblackwithayellowor bluecircularmarkerinitscenter. Dependinguponwhowinsthetossofthecoinbeforethegame,oneteam usesyellowmarkerswhiletheotherusesblue. Eachrobottypicallyhasanothersetofmarkersarrangedin some geometric pattern that uniquely identifies the robot and its orientation. Knowledge of an opponents additionalmarkersisusuallynotavailablebeforeagame. In the CMDragons team, images from the camera arrive at a frame rate of 30Hz into an off-field com- puter. Forreferencepurposes,mostofthesystemdescribedhererunsona2.1GHzAMDAthlonXP2700+ system, although a 1.3GHz processor was used previously without any difficulties. Using our fast color visionlibrary,CMVision[11],coloredblobsareextractedfromeachimage. Thecolorsareidentifiedbased onpriorcalibrationtoproduceathresholdmappingfrompixelvaluestosymboliccolor. Withknowledgeof eachrobotsuniquemarkerlayout,high-levelvisionfindseachrobotintheimageanddeterminesitsposition and orientation. The position of the ball and each opponent robot is also found. Orientation for opponents 4 Figure2: OverviewoftheCMDragonsteamarchitecture. cannot be found owing to the lack of advance knowledge on their marker layout. The world position of each object is then determined via a parametric camera model learned during game setup. Full details on thevisionalgorithmscanbefoundin[14]. FilteredpositionandvelocityinformationisderivedusingasetofindependentExtendedKalman-Bucy Filters (EKBF) for each object (see [12]). As velocity information cannot be derived from each camera imagealone,andthereistoomuchnoiseforframedifferentialstobeeffective,theEKBF’sareusedtoboth nullifytheeffectsofnoiseandintermittency(missingdata). Additionally,theEKBF’sprovideaprediction mechanism through forwardmodeling which is useful forovercoming latency. Insummary, the fullvision andtrackingmoduleprovidesestimatesofeachrobotlocationandorientation,eachopponentlocation,and balllocation,withvelocitiesforallelevenobjects. Takentogether,theseestimatesprovidetherobot’sbelief stateaboutthestateoftheworld. 2.2.2 WorldModelBeliefState Allbeliefsaboutthestateoftheworld,wheretherobotsareetc.,areencapsulatedinaworldbeliefmodel. In short, the world model acts as a centralized storage mechanism for beliefs for all layers of the control architecturetouse. Thebeliefmodelcontains: • Allperceptualinformationobtainedfromthetracker(e.g.,robotpositionsandvelocities); 5 Figure 3: The CMDragons robots. The robot on the left is an OmniBot, while the robots on the right are DiffBots. Eachrobotfitswithinan18cmdiametercylinderthatis15cmtall. Figure4: TheCMDragonscontrolarchitectureisbasedonway-pointprimitives. • Gamestateinformationderivedfromthereceivedrefereecommands; • Opponentmodelinginformationderivedfromstatisticalmodelsofobservedopponentbehavior; • High-levelpredicatesderivedfromtheperceivedstate,suchaswhichteamhaspossessionoftheball, isinattack,isinaparticularroleetc. Each high-level predicate, is a boolean function of the the tracker and/or game state belief. To account fornoise,eachbooleanfunctionincorporatesempiricallydeterminedhysteresistopreventundueoscillation at the decision boundary. These predicates, due to their boolean nature, provide a symbolic representation that is often more useful for making decisions than the raw belief models. For example, deciding whether torunanattackingplayoradefensiveplay. 2.2.3 NavigationandMotionControlActionInterface TheSTParchitectureconsistsofteamcontrolandindividualrobotcontrol. Followingthecommontechnique of hybrid hierarchical control [19, 33], we have developed lower modules for obstacle-free navigation and motioncontrol. Essentially,thesemodulesprovideresourcestotherobotforgeneratingactionsintheworld. The resources provide are obstacle-free navigation, motion control, and direct robot commands. Figure 4 showsthecontrolhierarchy. Thenavigationmodulegeneratesanear-optimal,obstaclefreepathtothegoallocationusingthebeliefs storedintheworldmodel. Basedonthispath,themotioncontrolmodulecalculatesatrajectorytoachievea 6 short-termtargetway-pointonthepaththatdoesnotcollidewithobstacles. Usingthistrajectory,avelocity commandisissuedtotherobothardwaretoexecute. Due to the dynamic nature of robot soccer, both navigation and motion control are recalculated each frame,foreachrobot. Thisplacesstrictcomputationallimitationsoneachofthesemodules. Wehavedevel- opedandimplementedafast,randomizedpathplanner[13]basedontheRapidly-exploringRandomTrees (RRT’s) algorithm [24]. Similarly, we have developed a trapezoidal-based, near-optimal motion control algorithmforquicklygeneratingrobotmotioncommands[12]. 2.2.4 RobotHardware Each robot is an omni-directional platform capable of spinning while driving in any direction. Each robot is equipped with a ball manipulation device that includes a solenoid actuated ’kicker’ and a motorized ’dribbler’. The kicker moves an aluminium plate to contact with the ball, propelling it at speeds of around 3.5−4m.s−1. Thedribblerisarubbercoatedbarthatismountedhorizontallyatballheightandconnectedto amotor. Asthebarspinsagainstaball,itcausestheballtospinbackwardsagainsttherobottherebyallowing the robot to move around effectively with the ball. Each robot has an on-board processor, and runs local velocity-based servo loops using integrated encoder feedback and standard PID control techniques [29]. Additionally,therobotisequippedwithanFMradioreceiverwhichitusestoreceivemovementcommands fromtheexternalcomputer. 3 The STP Architecture ThissectionoverviewstheSTParchitectureleadingintoadetaileddiscussionofskills,tactics,andplays. 3.1 Goals The presence of an opponent has many, sometimes subtle, effects on all levels and aspects of control. Generating robust behavior that responds to the actions of the opponent is a significant challenge. The challengesforteamcontrolare: 1. Execute a temporally extended sequence of coordinated activities amongst team members towards somelongertermgoalwhilesimultaneouslyrespondingasateamtounexpectedeventsbothfortuitous anddisastrousones. 2. Theabilitytorespondasateamtothecapabilities,tactics,andstrategiesoftheopponent. 3. Executerobustbehaviordespitesensorlimitationsandworlddynamics. 4. Provideamodular,compactarchitecturewithfacilitiesforeasilyconfiguringteamplay,andforana- lyzingtheperformanceofthedecisionmakingprocess. Thefirstandsecondgoalsaredirectimpactsfromcontrollingateamofrobotsinanadversarialenviron- ment. Wedesiretheteamcontrolarchitecturetogeneraterobustbehaviorthatincreasesthechanceoffuture opportunities against the opponent. Whenever such opportunities arise, whatever the cause, the team must takeadvantageofthisopportunityimmediately. Conversely,ifanopportunityarisesfortheopponentteam, our team must respond quickly and intelligently to minimize the damage the opponent can cause. Such responsive behavior must occur throughout the architecture. Building responsive team while overcoming the usual limitations of real world sensors, such as latency, noise, and uncertainty, is the major goal of the STPframework. 7 In robot soccer, robust development is a significant issue. Many teams have gone through bad experi- encescausedbypoordevelopmentproceduresorfacilities. Thus,agoodarchitectureisonethatiscompact and modular such that changes in one module have a minimal impact on the operation of another mod- ule. Giventhenumberofparametersinacomplexteamarchitecture,theabilitytoeasilyreconfigurethose parametersandtoanalyzetheperformanceofdifferentparametersettingsisextremelyusefultothedevel- opmentcycle. 3.2 Skills,TacticsandPlays Toachievethegoalsofresponsive, adversarialteamcontrol, wehavedevelopedtheSTParchitecture. The key component of STP is the division between single robot behavior and team behavior. In short, team behavior results from executing a coordinated sequence of single robot behaviors for each team member. Wenowdefineplays,tactics,andskills,andhowtheyinteractforateamofN robots. Aplay,P,isafixedteamplanwhichconsistsofasetofapplicabilityconditions,terminationconditions, and N roles, one for each team member. Each role defines a sequence of tactics T1,T2... and associated parameters to be performed by that role in the ordered sequence. Assignment of roles to team members is performed dynamically at run time. Upon role assignment, each robot i is assigned its tactic T to execute i from the current step of the sequence for that role. Tactics, therefore, form the action primitives for plays to influence the world. The full set of tactics can be partitioned into active tactics and non-active tactics. Active tactics are those involved with ball manipulation. There is only one active tactic amongst the roles perstepinthesequence. Thesuccessfulcompletionoftheactivetacticisusedtotriggerthetransitiontothe nextstepinthesequenceforallrolesintheplay. Playsarediscussedingreaterdetailinsection5. A tactic, T, encapsulates a single robot behavior. Each robot i executes its own tactic as created by the current play P. A tactic T determines the skill state machine SSM to be executed by the robot i. If i i the tactic is an active one, it also contains evaluation routines to determine if the tactic has completed. If the skill state machine differs from that executed previously, then execution begins at the first skill in the state machine i.e. S . If the skill state machine did not change, then execution continues at the last skill i transitioned to. The tactic T also sets parameters SParams to be used by the executing skill S . Thus, i i i skillsformtheactionprimitivesfortactics. A skill, S, is a focused control policy for performing some complex action. Each skill is a member of one, or more, skill state machines SSM ,SSM ,.... Each skill S determines what skill it transitions 1 2 to S0 based upon the world state, the time skill S has been executing for, and the executing tactic for that robot. The executing tactics may reset, or change and reset, the executing skill state machine. Each skill can command the robot to perform actions either directly, through motion control, or through navigation. If commanded through navigation, navigation will generate an intermediate, obstacle free way-point for motioncontrolwhichwillthengenerateacommandtosendtotherobot. Bothskillsandtacticsmustevaluatetheworldstate,insometimescomplexways,tomakeusefuldeci- sions. Forexample,sometacticsdeterminethebestpositiontomovetoinordertoreceiveapass. Alterna- tively,somedefensivetacticsevaluatewhichopponentrobotmightmovetoreceiveapassandwheretogo topreventtheopponentachievingthisgoal. Topreventunnecessaryduplication,andtogreatermodularize thearchitecture,weextracttheseevaluationsintoanevaluationmodulewhichisusablebybothtacticsand skills. Tactics,skills,evaluationsaredetailedinsection4. Plays, tactics, and skills, form a hierarchy for team control. Plays control the team behavior through tactics, while tactics encapsulate individual robot behavior and instantiate actions through sequences of skills. Skillsimplementthefocusedcontrolpolicyforactuallygeneratingusefulactions. Table1showsthe 8 main execution algorithm for the STP architecture. The clear hierarchical arrangement of plays for team control,tacticsforsinglerobotbehavior,andskillsforfocusedcontrolareshown. ProcessSTPExecution 1. CaptureSensors() 2. RunPerception() 3. UpdateWorldModel() 4. P ←ExecutePlayEngine() 5. foreachroboti∈{1,...,N} 6. (T ,TParams )←GetTactic(P,i) i i 7. (SSM ,SParams )←ExecuteTactic(T ,TParams ) i i i i 8. ifNewTactic(T )then i 9. S ←SSM (0) i i 10. (command ,S0)←ExecuteStateMachine(SSM ,S ,SParams ) i i i i i 11. robot command ←ExecuteRobotControl(command ) i i 12. SendCommand(i,robot command ) i Table1: ThemainSTPexecutionalgorithm. 4 Tactics and Skills for Single Robot Control Single robot control in the STP architecture consists of tactics and skills. Tactics provide the interface for teamcontrolviaplays,whileskillsprovidethemechanismsforgeneratingbehaviorinacompact,reusable way. Webeginbydescribingtacticsingreaterdepth,followedbyskills,andfinallytheevaluationmodule. 4.1 Tactics Tacticsarethetopmostlevelofsinglerobotcontrol. Eachtacticencapsulatesasinglerobotbehavior. Each tacticisparameterizedallowingformoregeneraltacticstobecreatedwhichareapplicabletoawiderrange ofworldstates. Throughparameterizationawiderrangeofbehaviorcanbeexhibitedthroughasmallerset of tactics, making play design easier. Table 2 provides the list of tactics we have implemented for robot soccer. Themeaningofeachtacticshouldbereasonablyobviousfromthetacticname. During execution, one tactic is instantiated per robot. A tactic, as determined by the executing play, is created with the parameters defined for the play. That tactic then continues to execute until the play transitionstothenexttacticinthesequence. Asdescribedabove,eachtacticinstantiatesactionthroughthe skilllayer. Inshort,thetacticsdeterminewhichskillstatemachinewillbeused,andsetstheparametersfor executingthoseskills. Exampleparametersincludetargetway-points,targetpointstoshootat,opponentsto mark,andsoon. Differenttasksmayusemanyofthesameskills,butprovidedifferentparameterstoachieve the different goals of the tactic. The shooting and passing tactics are good examples. The skills executed by the two are very similar, but the resulting behavior can be quite different due to the different parameter assignments. Finally,eachtacticmaystoreanylocalstateinformationitrequirestoexecuteappropriately. Table3showsthealgorithmfortheshoottacticusedtokicktheballatthegoalortowardsteammates forone-shotdeflectionsongoal. Notshownaretheconditioningofthetacticdecisiontreeontheparameters specifiedbytheactiveplay. Inthiscase, theplaycanonlydisabledeflectiondecisions. Thetacticconsists of evaluating the options of shooting directly on goal, or shooting to a teammate to deflect or kick on goal inaso-calledone-shotpass. Eachoptionisassignedascorewhich,loosely,definesalikelihoodofsuccess. 9 Active Tactics shoot (Aim | Noaim | Deflect hrolei) steal [hcoordinatei] clear active def [hcoordinatei] pass hrolei dribble to shoot hregioni dribble to region hregioni spin to region hregioni receive pass receive deflection dribble to position hcoordinatei hthetai position for start hcoordinatei hthetai position for kick position for penalty charge ball Non-Active Tactics position for loose ball hregioni position for rebound hregioni position for pass hregioni position for deflection hregioni defend line hcoordinate-1i hcoordinate-2i hmin-disti hmax-disti defend point hcoordinate-1i hmin-disti hmax-disti defend lane hcoordinate-1i hcoordinate-2i block hmin-disti hmax-disti hside-prefi mark horolei (ball | our goal | their goal | shot) goalie stop velocity hvxi hvyi hvthetai position hcoordinatei hthetai Table2: Listoftacticswiththeiracceptedparameters. Much of the operation of determining the angles to shoot at and generating the score is pushed into the evaluationmodule,describedinsection4.3. The tactic, indeed nearly all tactics, make use of additive hysteresis in the decision making process. Hysteresis is a necessary mechanism to prevent debilitating oscillations in the selected choice from frame toframe. Eachactionintheshoottactic,aswithanyothertactic,takesanon-negligibleperiodoftimeto performthatissubstantiallygreaterthanasingledecisioncycleat30Hz. Withthedynamicsoftheenviron- mentfurthercomplicatedbyocclusion,noise,anduncertainty,itsisoftenthecasethattwoormorechoices willoscillateovertimeintermsofitsscore. Withouthysteresis,therewillbecorrespondingoscillationsin theactionchosen. Theendresultisoftenthattherobotwilloscillatebetweendistinctlydifferentactionsand effectively be rendered immobile. The physical manifestation of this behavior, ironically, is that the robot appearsto’twitch’andbe’indecisive’. Inmostrobotdomains,suchoscillationswilldegradeperformance. Inadversarialdomainslikerobotsoccer,whereitisimportanttocarryoutanactionbeforetheopponentcan respond,suchoscillatescompletelydestroy. Hysteresisprovidesausable,easilyunderstandable,mechanism forpreventingsuchoscillationsandisusedpervasivelythroughouttheSTParchitecture. 10

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what skills to execute, and Plays for coordinating synchronized activity amongst team members. under in a number of RoboCup robot soccer competitions. requirements find quasi-static, near-optimal locations. The rest of the play specification are execution details, which amount to providing
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