DTIC ADA438794: Real-Time Support for Mobile Robotics

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by  Defense Technical Information Center

Real-Time Support for Mobile Robotics (cid:0)
HuanLi,JohnSweeney,KrithiRamamritham,Roderic Grupen,andPrashantShenoy
Departmentof ComputerScience,
UniversityofMassachusetts,
Amherst,MA 01003
(cid:1) lihuan,sweeney,krithi,grupen,shenoy @cs.umass.edu
(cid:2)
Abstract createanetworktopreservequalityofservicebetweenthe
operatorandthesearchrobot.Theleadrobotcanthuspene-
Coordinated behavior of mobile robots is an important tratefurtherintotherubbleattheexpenseofcommunication
emerging application area. Different coordinated behav- latencies and distributed control overhead. One instantia-
iors can be achieved by assigning sets of control tasks, or tionofsuchastrategyconstructsaseries,kinematicchainof
strategies,torobotsinateam. Thesecontroltasksmustbe mobilerobotswhereeachofthemactivelypreservesLine-
scheduled either locally on the robot or distributed across Of-Sight (LOS) [27] and intra-network bandwidth. In the
theteam. Anapplicationmayhavemanycontrolstrategies simplestcase,pairwisecoordinatedcontrollersweredevel-
todynamicallychoosefrom,althoughsomemaynotbefea- opedforateamoftworobots. Onecontroller,denotedpull,
sible, given limited resource and time availability. Thus, allowsaleaderrobottosearchanareawhile“pulling”afol-
dynamic feasibilitycheckingbecomesimportant as theco- lowingrobotbehindit. Theothercontroller,push,allowsa
ordinationbetweenrobotsandthetasksthatneedtobeper- follower to specify the search area of the leader, in effect,
formedevolveswithtime. Thispaperpresentsanonlineal- “pushing” the leader along. The application constructs a
gorithmforfindinga feasiblestrategygivena functionally strategy by assigning push or pull controllers to the entire
equivalent set of strategies for achieving an application’s team. Thetaskmodelsforthesetwostrategies,namely,the
goals. pushandpullcontrollersthemselves,areshowninFigure1.
We present two heuristics for feasibility checking. Both Inthetwotaskgraphs,sensorandmotortasks , ,
(cid:4)(cid:6)(cid:5)(cid:8)(cid:7) (cid:9)(cid:11)(cid:10)(cid:8)(cid:12)(cid:13)(cid:7)
considercommunicationcostandutilizationboundtomake and are preassigned to specific execution sites, while
(cid:14) (cid:7)
allocation (of tasks to execution sites) and scheduling de- three control tasks , , and may reside on either
(cid:15)(cid:17)(cid:16) (cid:15)(cid:19)(cid:18) (cid:20)(cid:21)(cid:18)
cisions. Extensive experimental results show the effective- team member, if necessary, to optimize processor utiliza-
nessoftheapproaches,especiallyinresource-tightenviron- tionorcommunicationcosts.The and tasksareused
(cid:15) (cid:16) (cid:15) (cid:18)
ments.Wealsodemonstratetheapplicationofourapproach by the robots to determine current search and LOS areas,
toreal-worldscenariosinvolvingteamsofrobotsandshow respectively, while is used for coordinating the desired
(cid:20) (cid:18)
how feasibility analysis also allows the prediction of the movementsoftherobotssothatLOSismaintainedandthe
scalabilityofthesolutiontolargerobotteams. search can make progress. The functionality of the team
is not affected by changing the allocations of the control
Keywords: Distributed real-time systems, allocation, tasks. Thedifferencesbetweenpushandpullcanbeseenat
schedulability,precedenceconstraint thetaskgraphlevel.Forexample,withpush,thecommuni-
cation specifiestotheleaderwhichareasitmay
(cid:15) (cid:16)(cid:11)(cid:22) (cid:20) (cid:18)
search,whilewithpull, tellsthefollowerwhere
1 Introduction
(cid:20) (cid:18)(cid:11)(cid:22) (cid:14) (cid:16)
itmaymove.
Apromisingapplicationforateamofmobilerobotsisto A discussion of how applications generate possible
collaboratewitheachother toaccomplisha commongoal, strategiesisbeyondthescopeofthispaper. Usually,appli-
forexample,searchingaburningbuildingfortrappedpeo- cationsdeterminetherequiredtypeofcoordinatedbehavior
ple. Human operators may direct the search by teleopera- for a team of robots, and generate a set of functionally
tion,butwirelesscommunicationsinthesesituationscanbe equivalentstra(cid:23)tegies. Sinceeachstrategyisconstructedby
unreliable. Whenasearchrobotventuresoutsideareliable periodicreal-timetasks,astrategythatisvalidattheappli-
communication range, a second robot can autonomously cationlevelmaynotalwaysbefeasibleatthesystemlevel.
Howtofindfeasible,schedulable,strategiesfromaasetof
(cid:3) ThisresearchwassupportedinpartbyDARPASDRDABT63-99-1-
0022andMARSDABT63-99-1-0004 functionallyequivalentstrategies,givenbytheapplication,
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1. REPORT DATE 3. DATES COVERED
2005 2. REPORT TYPE -
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Real-Time Suport for Mobile Robotics
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14. ABSTRACT
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a. REPORT b. ABSTRACT c. THIS PAGE 9
unclassified unclassified unclassified
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
POS2 POS2 The rest of the paper is structured as follows. In Sec-
H2 L2 M2 H2 L2 M2 tion2,thesystemmodelandgoalaredescribed.Thedetails
IR2 IR2 oftheallocationandschedulingalgorithmsareprovidedin
Section 3. Resultsofevaluationsfromsimulationarepro-
POS1 POS1
videdinSection4. Section 5analyzesareal-wordrobotic
H1 M1 H1 M1
application. Section 6 discusses related work. Section 7
IR1 IR1
concludesthepaperbysummarizingtheimportantcharac-
strategy strategy
(cid:0)(cid:2)(cid:1)(cid:4)(cid:3)(cid:6)(cid:5) (cid:0)(cid:7)(cid:1)(cid:9)(cid:8)(cid:10)(cid:8)
teristicsofthealgorithmanddiscussesfuturework.
Figure1.TasksinaLeader/Followerteam
2 SystemModeland OurGoal
isonegoalofthiswork.
2.1 SystemandTaskModel
Theteamsizeisnotfixed,so,asrobotsenterorleavethe
team, the application must recompute the set of strategies
thatcanbeused. Astheteamsizechanges,theapplication A coordinated team consists of a set of sites (robots),
eachsitehavinganidenticalprocessor.Inthispaper,weuse
maydeterminethatthegoalofthebehaviormustchangeas
well, which, in turn, also changes the set of correct strate- siteandprocessorinterchangeably. Robotsinateamshare
gies that can be used. Figure 2 shows a sequence from a acommunicationmedium,whichallowsbroadcastcommu-
nicationbetweenrobots. Topreventcontention, communi-
simulationwithfiverobotsusingpushandpullcontrollers,
whererobot isthe leadersearchingfor thegoalwhichis cationisalsoprescheduled.
the square in(cid:11) the lower left of the map. Each time a robot Astrategy,whichisspecifiedattheapplicationlevel,is
joins the team and the set of possible strategies changes, denotedatthesystemlevelbyanacyclicTaskGraph(TG).
the application must run the on-line scheduling algorithm Toachieveacommongoalfortheteam,asetoffunctionally
equivalentstrategiesmayalsobesuppliedbyapplications.
todeterminewhichstrategiesarefeasible;otherwise,asys-
tem failure may occur. The control tasks that make up a In a TG, nodes represent tasks ( ), directed edges be-
(cid:14) (cid:7)
strategymay be distributedamong sites in a team, such as tweentasksrepresentprecedence(e.g.,producer/consumer)
relationships. Theamountofcommunicationisdenotedas
and inthepushandpullmodels. Agoalofour
w(cid:15) o(cid:16)(cid:13)r(cid:12)k(cid:15) is(cid:18) todet(cid:20)e(cid:18)rminetheassignmentoftaskstositesinorder a communication cost attached to the edges. All tasks in
tooptimizethecoordinatedbehaviorwhileminimizingthe ourmodelareperiodic. Eachtaskischaracterizedbyape-
communicationoverheadandworkloadateachsite,thereby riod , Worst CaseExecutionTime(WCET) , andrela-
(cid:9) (cid:7) (cid:15) (cid:7)
improvingoverallschedulability. tive deadline , here, . Periods can be different
(cid:16) (cid:7) (cid:16) (cid:7)(cid:18)(cid:17) (cid:9) (cid:7)
fordifferenttasks.Butiftheproducerandtheconsumerrun
Asshowninthetaskgraphsofpushandpull,communi-
witharbitraryperiods,taskexecutionsmaygetoutofphase,
cationbetweentasksisneededto achievecoordination. In
whichresultsinlargelatenciesincommunication[21].Har-
thispaper,weassumethateachrobotisequippedwithwire-
monicityconstraintscansimplifythereading/writinglogic
lessbroadcastcommunication. Becauseasharedmultiple-
andreducethoselatencies[20]. Harmonicperiodsmayalso
access medium is used in the system, contention for the
increase the feasible processor utilization bound [25]. To
communication medium can occur at run time. We avoid
thisend, weassumetheperiodoftheconsumerisamulti-
thiscontentionbyschedulingthecommunicationaswell.
pleofthatoftherelatedproducer.
Assigning tasks with precedence relationships in a dis-
tributedenvironmentisingeneralanNP-hardproblem[17],
2.2 OurGoal
andevensomeofthesimplestschedulingproblemsareNP-
hardinthestrongsense[7]. Systematicallyderivedheuris-
Given a set of sites and a set of functionally equivalent
ticallocationandschedulingalgorithmsare,therefore,pro-
strategies,ourgoalistofindafeasiblestrategy. Astrategy
posedandevaluatedinthispaper.
isfeasibleifandonlyif:
The contributions of this paper are as follows. We de-
velop an online algorithm for finding a feasible control withinthe (LeastCommonMultiple)oftaskpe-
(cid:19)
(cid:20)(cid:20)(cid:15) (cid:14)
strategy given a functionally equivalent set of strategies riodsinthatstrategy,eachinstanceofataskissched-
for achieving an application’s goals. Specifically, we pro- uled at its schedule start time and the completion of
pose two simple but efficient heuristics for allocating con- thisinstancewillnotbelaterthanitsrelativedeadline;
trol tasks to distributed processing entities, which aim to
allconstraints,suchasprecedence,aresatisfied.
improvethe overall schedulability by minimizing commu- (cid:19)
nication costs and utilization of processors. We have per- Basedonthenatureoftheapplication,sometasks,e.g,sen-
formedextensiveevaluationsofthealgorithmsandalsoex- sor and motor systems, are required to run on designated
ercised it using a case study of a real world example from sites, e.g., a specificrobot platform. Othertasks, however,
mobile roboticstoachieveasimple butefficientallocation can be assigned to any site in a team. To find a feasible
andcommunicationschemeforateamofrobots. strategy,thesystemneedsto:
(a) (b) (c)
Figure2.Asequenceofactiverobotsinarobotteam
1. assignunallocatedtaskstoappropriatesites; tasks should be assigned to the same processor, thereby
eliminating the communication cost. At each step, for all
2. determineascheduleforalltaskinstances.
allocated tasks and related unallocated successors, the al-
gorithm selects an unallocated task 21 that has the largest
3 Allocation andScheduling Algorithms 43*(cid:2)1 , where (cid:11)3 is located on si(cid:14)te 65 and (cid:11)3 (cid:11)1 .
(cid:15) (cid:15) (cid:5) (cid:14) (cid:12) (cid:14) (cid:22) (cid:14)
Thealgorithmthenattemptstoallocate 1 to 5 ,basedon
(cid:14) (cid:12)
Wenowgivethedetailsoftheallocationandscheduling whetherornottheutilizationof 5 becomeslargerthanthe
algorithms. Thenotationusedinthispaperisexplainedin threshold (cid:14) . If the utilization is(cid:12)not largerthan (cid:14) , 1 is as-
Table1,where (cid:1) isdefinedas: signed to 25 and (cid:14) needs not change; otherwise, t(cid:14)he algo-
(cid:15) (cid:15) (cid:5) (cid:7) rithm tries(cid:12) to find a site (cid:11)7 that currently has the least uti-
(cid:3)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:8)(cid:7)(cid:9)(cid:7) (cid:1) (cid:23)(cid:11)(cid:10) (cid:4)(cid:13)(cid:12)(cid:15)(cid:14) (cid:10) (cid:5) (cid:23) (cid:4)(cid:13)(cid:5) (cid:3)(cid:16)(cid:14)(cid:18)(cid:17) (cid:14)(cid:13)(cid:7) (cid:22) (cid:14) (cid:1)(cid:16)(cid:19) lization,andattemptstoa(cid:12)ssign(cid:14)21 to(cid:12)(cid:21)7. Inthiscase,(cid:14) may
(cid:15) (cid:15) (cid:5) (cid:7) (cid:17) (cid:21)(cid:20) (cid:1) needtobeupdated. Ifaproperprocessorcanbefound,the
(cid:15) (cid:7) (cid:15) algorithmcontinueswiththenextunallocatedtaskthathas
the largest among the remaining unallocated tasks,
(cid:15) (cid:15) (cid:5)
Notation Meaning using the new threshold. If there is no task left to be as-
(cid:22)(cid:24)(cid:23)
TaskID signed and the workload of every processor is less than 8 ,
(cid:25) (cid:23) (cid:22) (cid:23)
WorstCaseExecutionTime(WCET)oftask thealgorithmisdeemedsuccessful;ifthealgorithmchooses
(cid:26)(cid:28)(cid:23)(cid:27) (cid:22)(cid:24)(cid:23)
Deadlineofthe(cid:29)(cid:31)(cid:30)! instanceof atasktobeallocated,butnositecanbefound(becauseany
" (cid:23)(cid:27) (cid:22) (cid:23)
# (cid:23) Earlieststarttimeofthe(cid:29) (cid:30)! instanceof processor’sutilizationwillbelargerthan8 afterloadingthis
$ (cid:23) SiteID # (cid:23) task), thealgorithmfails. Thepseudo-codeforthe Greedy
Utilizationofthesite
$&%(cid:23) # (cid:23) (cid:22) allocationalgorithmisshowninTable3.
(cid:22) (cid:23)(’ (cid:22)*) Utilizationofthesite that %(cid:22)+i)son (cid:22) (cid:23) The basic idea of updating the threshold (cid:14) is to use an
(cid:25),(cid:25).- (cid:23)0/) Precedenceconstraintbetween(cid:22) (cid:23)(cid:21)’and(cid:22)*) increasing limit on utilization. Initially, (cid:14) is the maximum
CommunicationCostRatioof
valueof theutilizations ofallprocessors to whichpreallo-
catedtaskshavebeenassigned.Atthetimeswhenthealgo-
Table1.Notationusedinthispaper
rithmhastofindasite(cid:11)7 withtheleastutilization,soitcan
(cid:12)
assign 21 to (cid:21)7, several conditions need to be considered.
3.1 AllocationAlgorithm Suppos(cid:14)e (cid:14):9 is(cid:12)theutilizationif 21 isassignedto 65 , and (cid:1)(cid:21)79
is the utilization if (cid:11)1 is assig(cid:14)ned to (cid:11)7. First,(cid:12)if (cid:14):9<; 8 ,
cesOsoprtsimisalaanssinigtrnamcteanbtleofprreoabl-letimm.etTawskostroesdoiusrtrcieb-ubtoeudnpdreod- in thiscase, if site (cid:8)>(cid:14) @= ? and (cid:1)(cid:21)749 A 8 ,(cid:12)thenthetask canbe
iterative heuristics are proposed in this section. Based on assigned to 7 and th(cid:17)e threshold is updated to (cid:7)B(cid:12)DCE(cid:17)(cid:3)(cid:14) (cid:1)(cid:11)79 (cid:19) ;
(cid:12) (cid:12)
utilizationofeachprocessorandtheamountofcommunica- otherwise, no processor can be found for loading 1 since
tionbetweentasks,theheuristicsattempttominimizework- allutilizationswillbelargerthan 8 . Second,if(cid:14)F9 A(cid:14) 8 ,then
loadofeachprocessor,aswellasthetotalcommunication. 1 is assigned to 7, but (cid:14) is updatedto (cid:14):G since this is the
(cid:14) (cid:12)
Adynamicutilizationthresholdisusedateachstepinboth expectedlowestvaluesincethelasttime. Thepseudo-code
heuristics. The function of this threshold is to: 1) balance forthefunctionupdatingthethresholdisshowninTable4.
andminimizetheworkloadofeachprocessor;2)avoidthe The returned value is either the new threshold if it finds a
violationofutilizationboundforschedulabilitypurpose. location,or H(cid:28)8 ifitdoesnot.
3.1.1 GreedyHeuristic 3.1.2 AggressiveHeuristic
Thisheuristicconsiderstheamountofcommunicationand Toaddressthemotivationbehindthisheuristic,letususea
computation involved for each pair of producer and con- simple task graph depicted in Figure 3, for which WCETs
sumer tasks. A decision is made as to whether these two and periods are given in Table 2. Consider the commu-
Site(T1)=S1 Site(T2)=S1 Site(T3)=S2 GreedyAllocationAlgorithm
C1 = 2 C2 = 2 C3 = 1 Input:ataskgraph(*),+.- (cid:2)0/21;354,674 foreachtask894;
T1 T2 T3 communicationcosts;preallocatedtaskswithrelatedsites;thenumberofsites:
Output:anassignmenttoallunallocatedtaskssuchthatutilizationofeach
1 1 4 1 1 processorislessthan1
Va;riables:
:thesetoftasksthathavebeenallocated;
T4 T5 <= ::tthheesseettooffctaosmkmstuhnaitchaativoenncootsbteraetnioaslalocated
C4 = 2 C5 = 8 > :arrayofutilizations(workload)
:thresholdofutilization
Figure3.Asimpletaskgraphexample 626 = 4@?A :communicationcostratioof B"CEDFDHGJI 4BLK(cid:26)VM44LCEWI V B"AC0N"MPORQ 40S Q AUT
Algorithm3.1:
WPeCrTiEoaTdsk(((cid:15) (cid:7))) (cid:14)120(cid:16) 2(cid:14)20(cid:18) (cid:14)(cid:1)21(cid:0) 2(cid:14)(cid:3)20(cid:2) 4(cid:14)(cid:1)80(cid:4) 12/*..ZILne4iistti)t ahle)*iz(cid:15)teh:(cid:22)r>Aesih)YVa3oAA+gldX[Z9(cid:2)Z9f48o14UAcr(cid:2)\(cid:7)Z9wb )4or;ebk(cid:16)lod(cid:2)>a(cid:18)d_,(cid:2)(cid:26)c]R(cid:7)]Ro @]nf(cid:2)t+g:&r8olA^,,1ins)huitciah_lit4zhe;atthfoerthearecshhporldoc*e/s;sor_‘4:
Table2.Pa(cid:9)ra(cid:7) metersfortasksinFigure3 5463.... IWInfeih+tx (cid:8)iiialtlejiwz(ei<(cid:16)th=1o,idsu)YotnsooXUtl62eumti6opnt=(cid:1)y;)k d?lmo\8 k b ; (cid:2) 8nl b < ^ (cid:2) 8 kpo 89l ;
nications to task (cid:14)(cid:1)(cid:2) . (cid:14)(cid:3)(cid:2) is assigned to site (cid:12) (cid:18) in the 78.. FLientdZ s9quc),hta+gsZkqF8rl tVahallt1h;asthemaximumvalue6H6 = k ?l outof= ;
Ganrdeedy algo(cid:2)(cid:2)r.ithHmowbeecvaeur,sew(cid:15)e(cid:15)no(cid:5)(cid:5)ti(cid:0)(cid:6)c(cid:2)e(cid:2) itshelaargcceurmthualnate(cid:15) d(cid:15) c(cid:5)om(cid:16) (cid:2)(cid:2)- /9*._ I(cid:7)f @f+@+g+8 k) 1 )h_ q ,ca7wlcvu>7laxtev tihen+geZw9q u(cid:2)t5(cid:16)il(cid:2)iz89altio1@1(cid:8)n,y{if8mz|1l,idsoa;llocatedtosite5 */
mt(cid:17)e(cid:15)ru(cid:15)ntoi(cid:15)(cid:5)caa(cid:15)(cid:16)sts(cid:2)i(cid:2)(cid:5)oign(cid:20)(cid:18)nc(cid:15)os(cid:15) tto(cid:5)fr(cid:18)o(cid:2)m(cid:2) (cid:19)in(cid:12);s(cid:16)te(cid:15)iasd(cid:15) lo(cid:5)afr(cid:0)(cid:13)g(cid:2)e(cid:2) r..tShoa,ninthtuaittifvreolmy,i(cid:12)t(cid:18)is, bi.eet.-, 111021...(cid:130)UU8ppkddeaa xbttieet;sswee "i(cid:2)ttt!n8mh;=s[o(cid:129),,uf[s<tt(cid:26)bus!nco<shuluutct+ghih8oatntkph;=ao/t*);c @89afn=(cid:127))ln1o~;etd XUfi}62n+g89d6X[la8n=Folak^p?(cid:2)p89l(cid:128)<r^(cid:129)op1})r.iaX[t<,e6Hs6i~te=X[*8lJ/l?(cid:129)J^^;,
(cid:2)
(cid:14) (cid:12) (cid:16) (cid:12)(cid:13)(cid:18)
The second heuristic we propose takes into account the aWeusethesamenotation(cid:131) toexpressdifferentfunctionalitiesin
total communication from the same site to see which un- twoheuristicsalgorithms
allocated task has the largest accumulated , andthen
(cid:15) (cid:15) (cid:5)
selectsthistasktobeconsiderednext. Sincetheutilization Table3.Greedyallocationalgorithm
bound is still needed to be considered, oncethe task is se-
lected,theassignmentandthresholdupdatesarethesameas
intheGreedyheuristic. Tothisend,line5inTable3needs FunctionofAssignmentandThresholdUpdate
ti(cid:15)osc(cid:7)bh(cid:15)ean(cid:15)cgh(cid:5)eadn(cid:7) (cid:2)g1toe(cid:12) :d(cid:14) (cid:5)(cid:7)(cid:16)to(cid:9)(cid:18)(cid:17): (cid:17)I(cid:5)(cid:20)n(cid:12) i(cid:14)t(cid:19)i(cid:7)a(cid:6)l(cid:22)(cid:5)iz1e(cid:14)(cid:13)(cid:22)(cid:5)1(cid:21),S(cid:6)(cid:17)i(cid:5)(cid:24)te(cid:23)(cid:6)(cid:17) (cid:13)(cid:14)(cid:5) (cid:12)(cid:26)(cid:7)(cid:25)1(cid:8)3(cid:19) (cid:14)(cid:1)(cid:7)(cid:17)(cid:14) (cid:23)1(cid:10)(cid:12)(cid:9)(cid:27)(cid:9)(cid:12)3 (cid:11);a(cid:11)(cid:14)(cid:12)n(cid:14)(cid:11)d(cid:13)1 (cid:12)l(cid:5)(cid:22)in13e(cid:14)(cid:1)1(cid:17)(cid:23)2. /a(cid:132)*s7s1tui.giisn tiChnthegarts89ehesrlhe1s:toohldo59(cid:3)lUd*(cid:133)p;/d89al,tdea(onfldo/*aptro 9c9ei,ssislnoetsrs55t,hiTsaanssetklhee8cttlehd)re;s h9oilsdthe*/newworkloadif
aFcctosuoosrmhlirlgioepgnnwlheitceildnyargttsheoctadhh(cid:12)seae(cid:16)tldh,Agueaoglnragliedbrtaheitslsmhitsteyiuinvstiein(cid:14)(cid:1)lsiah(cid:4)zSloageiwtsociortnaiinlotmsh,nomaotar4,es(cid:11)(cid:29).(cid:14)(cid:1)s(cid:28)ei(cid:30)(cid:2)gf.fniesTechfidtiirvtssoetslws(cid:12)ieg(cid:16)ilth,ehtsclirtyneecdgmeaaor(cid:12)ndrde(cid:16)s 5234.... CaFAUsleeispnts2ddiZ:agtt9(cid:134)n he 9e)*t>apj{srkZwo c(cid:134) 8i,tehrldssottohoVare/p*ll7nrte o; hw9caeitusshstlioaalsrirzgl5aee;tariostthnauZntiqltihz)eattiho rn9e;sZ‘h(cid:134)(cid:135)ol)*d :*/(cid:7)# +.Z 4 1 (cid:2) Z 4(cid:8)b > ,
3.2 MakingSchedulingDecisions 678... CaIsfeA+277l.l1)(cid:136)o:ca 5(cid:137)t9e1 jtdas(cid:16)k+gZ,8d9(cid:134)lo(cid:133)t/o*(cid:16)pp1rr,oodcceoessssoorr75; cannotload89l */
9. Update> withthenewZm(cid:134)5)*Z 9(cid:134);
neeAdeftderfoarseuaccchesinsfsutalnacsesiogfnmtaesknst.isBfeofuonred,waesdcihsceudsuslethies 1101.. Els e)*ret:(cid:22)urni 3-1+ ;(cid:2) Z 9(cid:134) 1;
algorithm,first,letusdefinesometerminology. 1123.. Ca/A*sel+l7o2c.)2a:te5J t91(cid:139)as(cid:138)(cid:133)k8+g(cid:16)Z,l9(cid:134)dtooj p/*r(cid:16)o1Zc,e9(cid:134)csas(cid:133)nonr o79;tfi(cid:133)nd(cid:16)a*p/rocessortoload8 l */
(cid:19) Earliest start time The earliest start time of an in- 14. Update> withthenewZ (cid:134) )*Z 9(cid:134);
stance of a task is derived from the precedence con- 9
15. ) ;
straints. Let be the of task periods. If task 16. Retu rn ; /*newthreshold*/
(cid:20) (cid:20)(cid:20)(cid:15) (cid:14)
has no predecessors, the first instance is ready to
e(cid:14) x(cid:7) ecute at time , denoted as (cid:31) (cid:16) ; and for the Table4.Assignmentandthresholdupdates
(cid:1) "! instanceof th(cid:11) attask, (cid:31)$# (cid:17)(cid:7) (cid:17)H 8(cid:11)(cid:19)&% , where
(cid:23)8 A A (cid:11) (cid:11) (cid:16)’ . (cid:7)If(cid:17) h(cid:23)as predece(cid:9) s(cid:7)sors, its
firsti(cid:23)nstance(cid:7)b(cid:12) ec(cid:7)om(cid:17) es(cid:20) en(cid:9) a(cid:7)bled(cid:14)on(cid:7) lywhenallitsprede- (cid:25) ? 5(cid:140)(cid:9) (cid:5)(cid:141)m(cid:142)9(cid:143)(cid:135)(cid:142) (cid:4) (cid:142) (cid:3)(cid:13)(cid:3)(cid:16)(cid:5) (cid:141) (cid:3)+(cid:17) (cid:19) . Since we will model
(cid:12) (cid:14) (cid:9) (cid:14) (cid:7)
cessorshavecompletedexecution. Inordertoachieve communication as a task if the producer/consumer
this condition, the tasks in the original task graph are tasks are on different sites, and we have harmonicity
topologicallyordered.Whenatask isprocessed,the constraintsforallsuchpairs,initially,thelowerbound
lowerboundof(cid:31) (cid:16) issetto(cid:7)B(cid:12)DCE(cid:17) (cid:31) (cid:16)(cid:14) (cid:7)(cid:31) 5(cid:16) (cid:20) .5 (cid:19) ,where of(cid:31)e# isassignedto (cid:17) (cid:9)H 8 (cid:19)(cid:16)% (cid:20) (cid:31) (cid:16) .
(cid:7) (cid:7) (cid:12) (cid:15) (cid:7) (cid:23) (cid:9) (cid:7) (cid:7)
Communication task If the producer and consumer time units, respectively. Thecommunicationcost lies
(cid:19)
are allocated on the same site, the communication intherange (cid:17) % % 3 (cid:19) , where
costisavoided;otherwise,communicationneedstobe istheCommu(cid:15)ni(cid:5)catio(cid:15)n:R(cid:7)a#ti(cid:12)o(cid:15)u(cid:5)sedto(cid:15) a:(cid:22)sisigncommu(cid:15) n(cid:5)i-
scheduled. We model this as a communication task. cation costs. Experiments were conducted with
For (cid:1) , a communication task has fol- valuesbetween0.1and0.4. (cid:15) (cid:5)
lowi(cid:14)ng(cid:7) f(cid:22)eatu(cid:14) res. (cid:14)(cid:1)(cid:0) u :(cid:22):
To address harmonicity relationships, we set a period
(cid:19)
1. (cid:9) (cid:1)(cid:0) un:(cid:22)e:eds(cid:17) to(cid:9) p(cid:1) r.ocTehsissdisatbaesceanutsferoemach inosntalyncoencoef rwaintgheo,ut(cid:17)(cid:3)(cid:7)in(cid:10)c(cid:23)o(cid:9)(cid:4)m(cid:7)(cid:3)in(cid:12) (cid:7)Bg (cid:12)(cid:15)edC g(cid:9)(cid:5)e(cid:7)(cid:3)s)(cid:19) ,,faonrdea(cid:17)c8 h(cid:7)in(cid:12)(cid:15)pCutt(cid:1)as(cid:19)kf(cid:14)or(cid:7) (etaacskh
d(cid:14) uringoneperiodof (cid:1) ; (cid:14) (cid:7) output task (cid:1) (task without outg(cid:12)oing e(cid:9)(cid:5)d(cid:6)ges), where
2. l(cid:31)eow6# ue:(cid:22)r:bou(cid:17) nd(cid:17) (cid:23)beHcau8 s(cid:19)(cid:127)e(cid:14)% th(cid:9)e(cid:0) uin:(cid:16)s:tan(cid:20)ce(cid:31) s(cid:7)h(cid:16) .ouTldhibseigsina (cid:7) (cid:5)(cid:8)(cid:10)(cid:7)(cid:23) (cid:9)(cid:5)(cid:142)n(cid:141)(cid:7)(cid:3) (cid:17) (cid:20)8‘(cid:14)(cid:28)!(cid:5)(cid:8)8 (cid:7) a(cid:142)nn(cid:141)d% (cid:0)(cid:15) (cid:0)(cid:7) (cid:142)na(cid:141)nd (cid:7) (cid:30) (cid:12)(cid:15)(cid:28) C .(cid:9)(cid:4)(cid:7)T(cid:3) o(cid:17)(cid:10)en(cid:9)su(cid:0) r(cid:0)e(cid:142)nt(cid:141)ha% t (cid:15)(cid:21)th(cid:7)e,
(cid:20) (cid:17) (cid:9) (cid:17) (cid:11)
executionatleastafterthecompletionofthefirst periods ofoutputtasksarenoless thanthoseofinput
instanceof ; tasks,aparameter,(cid:7) (cid:1) (cid:8)(cid:3)(cid:14) (cid:11)(cid:21)(cid:12)(cid:15)(cid:4)(cid:13)(cid:14) (cid:5) (cid:141) isusedtosettheup-
(cid:14)(cid:13)(cid:7) perboundoftheperiodforoutputtask (cid:1) : (cid:7) (cid:12)(cid:15)C (cid:1)
3. b(cid:16)ho(cid:0)#uun:(cid:16)d: sin(cid:17) ce(cid:23) th%ec(cid:9) o(cid:0)mu :(cid:22)m: unHica(cid:15) ti(cid:1)o.nTshhiosuilsdafinniusphpietsr t(cid:7)as(cid:1)k(cid:8)(cid:3)s(cid:14) a(cid:11)(cid:21)n(cid:12)(cid:15)d(cid:4)(cid:13)(cid:7)(cid:14) (cid:5) (cid:141) (cid:3)(cid:14)% (cid:21)(cid:7)B(cid:12)(cid:15)(cid:4)(cid:13)(cid:12)D(cid:14) CE(cid:5) (cid:17) (cid:7)Bis(cid:12)(cid:15)rCa(cid:9)(cid:5)nd(cid:7)(cid:3)o(cid:19)m, lwyhcehro(cid:14)ese(cid:14)(cid:13)n(cid:7) baertew(cid:9)(cid:12)eine(cid:6) pnu(cid:17)1t
executionnolaterthanthelateststarttimeof (cid:1) . (cid:1) (cid:8) (cid:11) (cid:141)
(cid:14) and5.Inordertomakeperiodsharmonic,first,wepro-
cessinputtasksandmaketheirperiodsharmonic;then
Withinthe ,eachinstanceoftasksistreatedasan
(cid:20) (cid:15) (cid:14) we tailor the techniques from [20] to process output
individualentitytobescheduled. Wetakeintoaccountthe
tasks;finally,weusetheGCDtechniqueforintermedi-
deadline, laxity and earliest start time, which characterize
atetaskstoachieveharmonicityconstraints. Theidea
themostimportantpropertiesforreal-timetasksandprece-
ofcomputingGCDistodoabackwardperiodassign-
dence constraints, to activelydirect the searching to find a
feasibleschedule. Thepotentiallyheuristicfunctionsof ment: atask25 getsperiod 5 fromallitssuccessors
are: (1) Minimum deadline first: (cid:17) (cid:19) (cid:10) ; ((cid:15)2) so that (cid:9) 5 (cid:17)(cid:14)(cid:14) (cid:13) (cid:15) (cid:16) (cid:6) (cid:9)E7 (cid:7)(cid:9)67 (cid:9)(cid:9) (cid:3) (cid:1)(cid:21)(cid:4)(cid:13)(cid:4) (cid:17) (cid:14)25 (cid:19) (cid:13) . Because of
Minimum earliest-start-time first: (cid:15) (cid:17)(cid:14) (cid:19) (cid:17) (cid:14) (cid:10)(cid:23) (cid:16)(cid:31) ; (3) precedenceconstraints,periodsofoutputtaskscannot
Minimumlaxityfirst: (cid:17) (cid:19) (cid:10) (cid:15) (cid:14) (cid:7) (cid:17) (cid:10) (cid:14)(cid:17) +(cid:23) H (cid:17) (cid:31) (cid:20) beconsideredseparatelyfromthoseofinputtasks,so
w(cid:14)(cid:15) h(cid:7) (cid:19)F(cid:10)e(cid:23)(cid:19)r;e(cid:16)((cid:2)4)(cid:20) (cid:15)i(cid:2)st(cid:17)h(cid:14)% e(cid:14)(cid:19)w(cid:17)e(cid:10) (cid:23)ig(cid:14)h(cid:20) t(cid:15);(cid:10)f(cid:23)(a6c(cid:14))(cid:16)to(cid:15) r(cid:20)(cid:17)t(cid:17)o(cid:14) (cid:2)(cid:14)a(cid:19) d(cid:17)j%u(cid:23) s(cid:14)t(cid:14)(cid:20) th(cid:10) (cid:10)(cid:17)(cid:23)e(cid:23) e(cid:31)f(cid:31)f(cid:20)e;(cid:23)c(cid:2)(t5(cid:16)o)%f(cid:7)(cid:15)d(cid:14) if(cid:17)f(cid:14)(cid:10)e(cid:23) r(cid:19)e(cid:7)(cid:20)n(cid:17) t; rc(cid:9)(cid:12)(cid:9)(cid:12)iuo(cid:16)(cid:16)(cid:6)(cid:6)lda,st(cid:17)(cid:17)ewadrhe(cid:16)ui(cid:7)ccpho(cid:12)(cid:15)omnCis(cid:9)(cid:12)pttuh(cid:16)(cid:6)hteee’ dl(cid:9)(cid:5)laeu:(cid:19)r(cid:3)agps(cid:18)eotsn%ptep(cid:9)(cid:5)rei:o(cid:3)rid.toodOoaftochohfeuirietnpvopueuutthpttauatratsmkstkaoss,snkii(scs(cid:9)(cid:15)’itc:py(cid:3)a.el)--,
temporalcharacteristicsoftasks.
(cid:9) (cid:16)(cid:6)
Thesearchattemptstodetermineafeasibleschedulefor Parameter (cid:5) (cid:21)(cid:14) is used to set the precedence
a setoftasksinthefollowingway. It startswithanempty (cid:19) (cid:13)(cid:1) (cid:143)(cid:139)(cid:142)(cid:21)(cid:20) (cid:141)m(cid:142)9(cid:142)
relationships in terms of data processed by multiple
partial schedule as the root, and tries to extend the sched-
producers/consumers. For each task, except for out-
ulewithonemoretaskbymovingtooneoftheverticesat put tasks, the (cid:5) ((cid:14) is randomly chosen be-
the nextlevelin the searchtreeuntila feasible scheduleis (cid:13)(cid:1) (cid:143)(cid:139)(cid:142)(cid:22)(cid:20)(cid:139)(cid:141)m(cid:142)9(cid:142)
tween 1 and 3. The total number of tasks in a
trdaeesmrkivawiendiit.nhgTthhueensshmcehuaerldliesutslitecvdfautlaunsecktisisoanste(cid:15)leeaccitshedaleptvopeleilexodteftntohdeetahtcerehceuo.rfTrethhneet th(cid:14)a(cid:12)es(cid:3)rke? (cid:3)as(cid:142)ree(cid:14)t(cid:3) f(cid:10)(cid:24)ios(cid:23)(cid:135):r(cid:142) t(cid:11)(cid:21)a(cid:30)s(cid:12)(cid:15)k(cid:4)(cid:13)% (cid:14)s(cid:5)e(cid:14)(cid:141)t(cid:12)s(cid:3)A(cid:27)w? i(cid:3)t(cid:142)(cid:26)h(cid:14),(cid:3)fao(cid:10)(cid:24)(cid:23)(cid:135)nu(cid:142)dr i(cid:11)(cid:21)anl(cid:12)(cid:15)pl(cid:4)(cid:13)ut(cid:14)th(cid:5) ea(cid:141) n,rdewsfuholeutsrresohu(cid:25) otpwuAnt
partialschedule.Because(cid:14) (cid:10) (cid:23) (cid:31) considerstheprecedence tasks,thoughwehaveconductedexperimentswithdif-
constraints, it performs better than other simple heuristics
ferentnumbers.
in our experiments. The simulation studies also show that
(cid:17) (cid:14) (cid:10) (cid:23) (cid:16) (cid:20) (cid:2) % (cid:14) (cid:10) (cid:23) (cid:31) (cid:19) hassuperiorperformance. All the simulation results shown in this section are ob-
tained from the average value of 10 simulation runs. For
4 Simulated Results each run, we generate 100 test sets, each set satisfying
Tostudythefeaturesoftheproposedalgorithms,wecon- (cid:7)(cid:15) #(cid:7)i)s(cid:16) t(cid:17)h(cid:15) e(cid:7)0’n(cid:9)u(cid:7)m(cid:19) bAer (cid:7)of,pwrohceerseso(cid:23) rsi.s tFheornaumgbiveernoftatsaksksseta,nidf
ductedseveralexperimentstoevaluatetheallocationheuris- thisconditionis notheld, atleastoneprocessorutilization
ticswithregardstoschedulability. Howtouseitforanac- will be larger than 1. The scheme used here is to remove
tual robotics application is discussed in Section 5. Tasks the task sets that are definitely infeasible. Obviously, this
generated in a directed acyclic graph have the following doesnoteliminateallinfeasibletasksetsbecausethepres-
characteristics: enceofcommunicationcostsarenotconsidered. However,
since feasibilitydetermination is intractable, if oneheuris-
Thecomputationtime ofeachtask isuniformly tic scheme is able to determine a feasible schedule while
(cid:19)
(cid:15) (cid:7) (cid:14) (cid:7)
distributedbetween and 3 set to 10 and60 anothercannot,wecanconcludethattheformerissuperior.
(cid:15) : (cid:7)# (cid:15) :(cid:22)i
Therefore,theperformanceofthealgorithmsandparameter maintaining minimal utilization for each processor. Since
settingsarecomparedusingthe (cid:1)((cid:4)(cid:13)(cid:4) (cid:142) (cid:3)(cid:13)(cid:3) (cid:12)(cid:15)(cid:14) (cid:10) (cid:5) (cid:17) (cid:19) : Aggressivetakesintoaccounttheutilizationboundateach
(cid:12) (cid:5) (cid:12) (cid:5)
assignmentstep,andtriestoclusterasmanytasksaspossi-
(cid:11) t Z (cid:0)(cid:24)(cid:0) ble,soastoeliminatethetotalcommunicationcost,itisnot
(cid:12) (cid:5) (cid:17) (cid:11) surprisingthat itachievesbetterperformancethanGreedy,
whichconsidersonlytheindividualcommunicationcostfor
(cid:11) t Z (cid:0)(cid:24)(cid:0) is the total number of schedulable task sets found
agivensite.
by the algorithm, and is the total number of task sets
(cid:11)
The other observation is that the improvements in per-
tested. Here is100foreachsimulationrun,andforeach
(cid:11)
result po(cid:11) inttZ (cid:0)(cid:24)i(cid:0)n’(cid:15)t8he .graphs, (cid:12) (cid:5) (cid:17) (cid:17) (cid:15) (cid:7)(cid:16))z (cid:16) (cid:12) (cid:5) (cid:7) (cid:19) ’(cid:15)8(cid:6)(cid:11) , where tfhoarmnathneceimopfrGorveeemdeynotrwAigthgr(cid:15)es(cid:5)siv(cid:17)ew(cid:11)(cid:29)(cid:28)!i8th,e(cid:15)sp(cid:5) ec(cid:17)ial(cid:11)(cid:29)ly(cid:28)(cid:30) wishelanrgtheer
(cid:12) (cid:5) (cid:7) (cid:17) (cid:6)(cid:11) (cid:11) task set size is large, say, no less than . Table 5 shows
Thetestsinvolvedasystemwith2to12processorscon-
(cid:0) (cid:11)
thedifferenceinimprovementofGreedytotherandom;Ta-
nectedbyamultiple-accessnetwork. Resourcesotherthan
ble 6 is for the improvementof Aggressive to the random.
CPUsandthecommunicationnetworkwerenotconsidered.
Whereas we study the algorithm under various parameter Both are with (cid:2) (cid:12) (cid:3) ? and (cid:2) (cid:12) (cid:3) ? , respec-
(cid:14) (cid:17) (cid:0) (cid:11) (cid:14) (cid:17) (cid:25)(cid:4)(cid:0)
tively.Aswecansee,inmostcases,theimprovementswith
settings, due to space limitation, here we only show some
of the salient results and conclusions. Details that are not (cid:28)(cid:30) are much largerthan those with (cid:29)(cid:28)!8 for
(cid:15) (cid:5) (cid:17) (cid:11) (cid:15) (cid:5) (cid:17) (cid:11)
either the Greedy or the Aggressive heuristic. The reason
reportedherecanbefoundin[13].
is that when , the communication costs intro-
(cid:29)(cid:28)(cid:30)
(cid:15) (cid:5) (cid:17) (cid:11)
ducemoreworkloadintothesystem,andhenceincreasethe
4.1 ChoosingaSchedulingHeuristic
resource contention. So communication costs dictate the
In order to eliminate bias from the scheduling search schedulability much more than the case when (cid:15) (cid:5) (cid:17) (cid:11)(cid:29)(cid:28)!8 .
In contrast to random assignment, our approaches exploit
heuristics,wefirstexaminewhichheuristicfunctionissuit-
thisimportantpropertytodirecttheallocationassignment,
able to evaluate the allocation algorithms in terms of Suc-
hence,theyworkbetterinaresource-tightenvironment.
cessRatio(SR)ofschedulabilityforafixedtasksetsize.
Finally, we found that as the number of processors in-
ForbothGreedyandAggressive,wefound(cid:14) (cid:10) (cid:23) (cid:31) isthe creases, theimprovementsforbothGreedyandAggressive
bestsimpleheuristic. Thisisbecausetheearlieststarttime
become less for a given task set. This observation shows
ofeachinstanceofataskencodesthebasicprecedencein-
that the tightertheresourceconstraint, thebetterour algo-
formation.Forintegratedheuristics,(cid:14) (cid:10) (cid:23) (cid:16) (cid:20) (cid:2) (cid:0) (cid:14) (cid:10) (cid:23) (cid:31) rithmsperform.
has substantially better performance than other heuristics
including (cid:14) (cid:10) (cid:23) (cid:31) . The reason should be clear: besides Processor 4 6 8 10 12
precedenceconstraints, anotherimportantfactor, deadline,
CR=0.1 19.2 15.6 9.7 3.7 2.4
isalsotakenintoaccount.
CR=0.4 17.9 14.6 15.0 13.7 15
Since (cid:10) (cid:20) (cid:2) (cid:0) (cid:10) (cid:31) isaweightedcombination
(cid:14) (cid:23) (cid:16) (cid:14) (cid:23)
ofsimpleheuristics,weinvestigateitssensitivitytochanges
ofweight((cid:2) )values.When(cid:2) ,theheuristicbecomes (a)(cid:2) (cid:14) (cid:12) (cid:3) ? (cid:17) (cid:0) (cid:11)
(cid:17) (cid:11)
the simple heuristic (cid:10) , and does not perform well.
(cid:14) (cid:23) (cid:16) Processor 4 6 8 10 12
Whentheweightincreasesfrom to(cid:30) ,orfrom to8 when
(cid:2) (cid:5) (cid:4) ,weseeasignifican(cid:11)tperformance(cid:11)incr(cid:1)e(cid:0)asefor CR=0.1 4.7 13 7 2.9 0.3
(cid:5)(cid:141)
va(cid:9)rious(cid:2)(cid:17) (cid:0) (cid:5) (cid:4) values.Thealgorithmisrobustwithrespect CR=0.4 4.5 12.1 11.4 12.3 13.1
(cid:5)(cid:141)
(cid:9)
toheuristics,asperformanceisaffectedonlyslightlywhen
theweightvariesfrom(cid:30) to (or 8 to if (cid:2) (cid:5)(cid:141) (cid:5) (cid:4) ). (b) (cid:2) (cid:14) (cid:12) (cid:3) ? (cid:17) (cid:25)(cid:5)(cid:0)
(cid:25) (cid:11) (cid:1)(cid:0) (cid:25) (cid:11) (cid:9) (cid:17) (cid:0)
Sowewillchoose(cid:2) forfollowingexperiments.Here-
(cid:17) (cid:30) Table 5. Improvement of Greedy over random
after, we denote “The Number of Processors” as “#Proc”,
approach(Percentage)
and“TheNumberofTasksWithinaSet”as“#Task”.
4.2 PerformanceoftheAllocationAlgorithm 4.3 EffectofCommunication
Inthissection,weevaluatetheperformanceoftheallo- Duetospacelimit,weomitdetailsoftheeffectofcom-
cation algorithms, Greedy and Aggressive, compared with munication costs that may be found in [13]. Our results
anothermethod,randomallocation. Figure4illustratesthe show that when the number of processors is very limited,
resultsfortasksetsizeof 8 , and ,respectively,when e.g., 2 or 3, the performance is almost the same. This is
(cid:3)(cid:0) (cid:0) (cid:11) (cid:25)(cid:4)(cid:0)
(cid:29)(cid:28)!8 . Asshowninthegraphs,foreachinstance,the because in such a situation, it is hard to find a feasible
(cid:15) (cid:5) (cid:17) (cid:11)
performance of Aggressive is better than that of Greedy, schedule for both cases. But as the number of processors
which is in turn better than the random allocation. The increases,theperformancefor (cid:29)(cid:28)!8 isbetterthanthat
(cid:15) (cid:5) (cid:17) (cid:11)
gains come from the elimination of communication while for . Thisisbecauseeachcommunicationintro-
(cid:29)(cid:28)(cid:30)
(cid:15) (cid:5) (cid:17) (cid:11)
Figure4.Effectofallocationalgorithms(CR=0.1)
Processor 4 6 8 10 12 Task 8 (cid:17) (cid:19) (cid:5) (cid:3) 8 (cid:17) (cid:19) 8 (cid:17) (cid:19)
(cid:4)(cid:6)(cid:5) (cid:0) (cid:9) (cid:0) (cid:15) (cid:16) (cid:15) (cid:18) (cid:20) (cid:18) (cid:14) (cid:0)
CR=0.1 24.8 20.2 13.2 6.5 3.8 Push 20 120 35 25 5 20
CR=0.4 22.8 18.3 18.1 16.1 16.3 Pull 20 120 25 25 18 20
(cid:2) (cid:12) (cid:3) ? Table7.WCETs(ms)oftasksinFigure1
(cid:14) (cid:17) (cid:0) (cid:11)
Processor 4 6 8 10 12 (cid:6)
cation can use for a team of three robots: ,
(cid:1)(cid:9)(cid:8)(cid:10)(cid:8) (cid:1) (cid:8) (cid:8) (cid:13)
CR=0.1 7.1 14.3 7.7 4.0 0.3 (cid:6) (cid:6) (cid:6) (cid:9) (cid:12) (cid:9)
, , and . The
(cid:1) (cid:8) (cid:8) (cid:1) (cid:3)(cid:13)(cid:5) (cid:13) (cid:1) (cid:3)(cid:13)(cid:5) (cid:1) (cid:8) (cid:8) (cid:13) (cid:1)(cid:4)(cid:3)(cid:13)(cid:5) (cid:1) (cid:3)(cid:13)(cid:5) (cid:13)
CR=0.4 6.4 12.5 11.8 13.3 13.6 ta(cid:9)skgr(cid:12)a(cid:9)phsforthe(cid:9) sefou(cid:12)r(cid:9) strategiesare(cid:9) show(cid:12)n(cid:9) inFigures5.
First, let us use the Aggressive heuristic to analyze the
(cid:12)
(cid:2) (cid:3) ? tasks’ locationsin eachstrategy. Thedetails ofthe alloca-
(cid:14) (cid:17) (cid:25)(cid:4)(cid:0)
tionstepsareomittedhereduetospacelimitations. Inthis
Table 6. Improvement of Aggressive over ran-
example,sincetheaccumulatedcommunicationcostiscon-
domapproach(Percentage)
sidered, the allocation is the same for all strategies: is
(cid:15) (cid:16)
assignedto , to , to , to and to .
(cid:0) (cid:0) (cid:0)
ducesadditionalprecedence constraintsthat willaffectthe (cid:12) (cid:16) (cid:15) (cid:18) (cid:12) (cid:18) (cid:15) (cid:25) (cid:12) (cid:20) (cid:18) (cid:12)(cid:13)(cid:18) (cid:20) (cid:12)
Next,thealgorithmwillseewhichstrategiesareschedu-
earlieststarttimeofconsumers. Thecommunicationcosts
lableusingtheheuristic (cid:10) (cid:20) (cid:2) % (cid:10) (cid:31) . Tosim-
alsoaffecttheoverallsystemworkload,therefore,lowering (cid:14) (cid:23) (cid:16) (cid:14) (cid:23)
plifytheanalysis,here(cid:2) issetto 8 . Thecompletiontimes
communicationleadstoimprovedschedulability.
for tasksoneachsiteareshowninTable8. Thealgorithm
(cid:6) (cid:6)
finds that, except for , denoted as ,
(cid:1) (cid:3)(cid:13)(cid:5) (cid:1) (cid:8) (cid:8) (cid:13) (cid:0)(cid:9)(cid:5) (cid:0)(cid:9)(cid:8) (cid:13)
5 Application of Our Algorithms to Mobile all other strategies are f(cid:9)easibl(cid:12)e(cid:9), but with different com(cid:12) ple-
Robotics tion times (including communication delay). Since multi-
plestrategiesarefeasible,theapplicationcanusesomecri-
teria to rank the strategies. In this case, if the total laxity
In this section, we return to the robotic problem dis-
isusedasthecriterion,thentheapplicationwillchoosethe
cussed in Section 1, where two strategies, push and pull, (cid:6)
strategy,whichhasthemaximalvalue.
are givenfor a team oftwo robots. In Table 7, the WCET (cid:9) (cid:1) (cid:8) (cid:8) (cid:12) (cid:9) (cid:1) (cid:3)(cid:13)(cid:5) (cid:13)
The application can then use the feasible results when
oftasksaretakenfromanexperimentalimplementationon
computing newsets of strategies. For example, if at some
a StrongARM 206MHz CPU; in Table 9, communication
timeafourthrobotjoinstheteam,theapplicationimmedi-
costsarebasedonthebytestransmittedusing802.11bwire- (cid:6)
ately knows that any strategy that contains
less protocol with 11 Mbit/s transmission rate. Although (cid:9) (cid:1) (cid:3)(cid:13)(cid:5) (cid:12) (cid:9) (cid:1) (cid:8) (cid:8) (cid:13)
will not be feasible, since that strategy was already deter-
802.11b does not allow for real-time transmission guaran-
mined to be infeasible. Therefore, the application can use
tees,bypreschedulingcommunications,mediumcontention
is avoided. The periods are assigned with (cid:7) for all the feasibility analysis to prune infeasible strategies as the
(cid:0)(cid:4)(cid:0) (cid:11) (cid:3) team’ssizescales.
sensor tasks and motor drivers by the application. There-
fore,theperiodsofcontrollertasksarealsodesignedtobe (cid:6) (cid:6) (cid:6) (cid:6)
(cid:0)(cid:4)(cid:0) (cid:11) (cid:7) (cid:3) by the harmonic constraint. Though these figures stSriatteeg1y (cid:9) (cid:5)19(cid:12) 5(cid:9) (cid:5) (cid:13) 2(cid:9)05(cid:8) (cid:12).9(cid:9) 7(cid:8)9(cid:13) 2(cid:9)22(cid:5) .(cid:12)9(cid:9)79(cid:8) (cid:13) (cid:9) 1(cid:8) (cid:12)9(cid:9)5(cid:5) (cid:13)
aregivenbasedontasksinFigure1,theyarecompatibleto
Site2 202.979 208.958 220 205.979
tasks that occur with more robots; let us consider the sce-
Site3 210.958 203 230.958 203
nario when a third robot wants to join the team. Since the
pushandpullcontrollersarepairwise,therearefourstrate-
Table8.Thecompletiontimeforallstrategies
gies,composedofpushandpullcontrollers,thattheappli-
POS3 POS3 POS3 POS3
H3 L3 M3 H3 L3 M3 H3 L3 M3 H3 L3 M3
IR3 IR3 IR3 IR3
POS2 POS2 POS2 POS2
H2 L2 M2 H2 L2 M2 H2 L2 M2 H2 L2 M2
IR2 IR2 IR2 IR2
POS1 POS1 POS1 POS1
H1 M1 H1 M1 H1 M1 H1 M1
IR1 IR1 IR1 IR1
(cid:6) (cid:6) (cid:6) (cid:6)
(a) (b) (a) (b)
(cid:1)(cid:4)(cid:3)(cid:6)(cid:5) (cid:1)(cid:4)(cid:3)(cid:13)(cid:5) (cid:13) (cid:1) (cid:8) (cid:8) (cid:1) (cid:8) (cid:8) (cid:13) (cid:1)(cid:4)(cid:3)(cid:6)(cid:5) (cid:1) (cid:8) (cid:8) (cid:13) (cid:1) (cid:8) (cid:8) (cid:1)(cid:4)(cid:3)(cid:6)(cid:5) (cid:13)
(cid:9) (cid:12) (cid:9) (cid:9) (cid:12) (cid:9) (cid:9) (cid:12) (cid:9) (cid:9) (cid:12) (cid:9)
Figure5.Fourpossiblestrategiesforateamofthreerobotsusingthepushandpullcontrollers
Comm. (cid:5) (cid:5)
(cid:4) (cid:5) (cid:16) +(cid:18) 1 (cid:22) (cid:15) (cid:16) +(cid:18) 1 (cid:9) (cid:3) (cid:16) +(cid:18) 1 (cid:22) (cid:15) (cid:16) +(cid:18) 1 (cid:15) (cid:16) (cid:22) (cid:20) (cid:18) (cid:15) (cid:16) (cid:22) (cid:14) (cid:16) (cid:15) (cid:18) (cid:22) (cid:20) (cid:18) (cid:9) (cid:3) (cid:16) (cid:22) (cid:20) (cid:18) (cid:20) (cid:18) (cid:22) (cid:14) (cid:18) +(cid:16) 1
Push 0.02327 0.01236 2.979 2.979 2.979 0 2.979(0)
Pull 0.02327 0.01236 0 2.979 2.979 0.01236 2.979(2.979)
Table9.CommunicationcostsofFigure1
6 Related Work the optimal solution in the sense of minimizing maximum
normalized task response time is found to the problem of
Numerous research results have demonstrated the com- allocating communicating periodic tasks to heterogeneous
plexity of design for real-time system, especially with re- processing nodes. Though the heuristic guides the algo-
spect to temporalconstraints [9, 19, 20, 21, 22]. Alsothe rithm efficiently towardan optimal solution, the algorithm
schedulabilityanalysisfordistributedreal-timesystemsat- cannotbesimplyappliedandextendedtoourenvironment.
tractedalotofattentioninrecentyears [12,15,16,28].For The major differences are: 1) applications require that the
taskswithtemporalconstraints,researchershavefocusedon decisionbemadeon-line;2)weconsideranon-preemptive
generatingtask attributes,e.g., period,deadlineandphase. schedule which is NP-hard in the strong sense even with-
For example, Gerber et al. [9, 22] proposed the period outprecedenceconstraints[8],whilethealgorithm[3]used
calibration technique to derive periods and related dead- in their method is to find a preemptive schedule; 3) the
lines and release times from given end-to-end constraints. precedence constraints are predetermined among specific
Techniques for deriving system-level constraintsfrom per- instancesoftasksintheiralgorithm,whileinourapproach,
formancerequirementsareproposedbySetoetal. [23,24]. thisisaccomplishedbytheschedulingsubjecttotheprece-
Whenend-to-endconstraintsaretransformedintointerme- denceconstraints.In[1],aperiod-basedmethodisproposed
diate task constraints, most previous research results are totheproblemofloadpartitioningandassignmentforlarge
basedontheassumptionthattaskallocationhasbeendone distributedreal-timeapplications.Scalabilityisachievedby
apriori. However,schedulabilityisclearlyaffectedbyboth utilizingarecursivedivide-and-conquertechnique.[18]dis-
thetemporalcharacteristicsandtheallocationoftasks. cussedastaticalgorithmforallocatingandschedulingcom-
For a set of independent periodic tasks, Liu and Lay- ponentsofperiodictasksacrosssitesindistributedsystems.
land[14]firstdevelopedthefeasibleworkloadconditionfor Howtoallocatingreplicatesisamajorissuecountedinthe
schedulability analysis under uniprocessor environments. algorithm. Our task allocation and scheduling algorithm,
Much later, Baruahetal. [5] presentednecessaryandsuf- however,focusesontheimprovementofschedulabilityby:
ficient conditions, namely, ( is the number of 1) using a dynamic increasing threshold to bound the uti-
A
processors)basedonP-fairne(cid:9)sssche(cid:23)dul(cid:23)ingformultiproces- lization bound along each allocation step; 2) consider the
sors. Also, theupperboundsofworkloadspecifiedforthe precedence constraints as early as possible by setting the
given schedules, e.g., EDF and RMA, are derived for ho- earlieststarttimeintotheheuristicschedulingfunction.
mogeneous or heterogeneousmultiprocessor environments
[2,4,6,10,11,26].Allthesetechniquesareforpreemptive
7 ConclusionandFuture Direction
tasksandtask orjobmigrationsareassumedtobepermit-
tedwithoutanypenalty. Ifprecedenceandcommunication
constraintsexist,theseresultscannotbedirectlyused. Allocating and scheduling of real-time tasks in a dis-
Pengetal. [17],Abdelzaheretal. [1]andRamamritham tributedenvironmentisadifficultproblem. Thealgorithms
[18]studiedthetaskallocationandschedulingproblemina discussed in this paper providea frameworkfor allocating
distributedenvironment. Intheirmodels,subtasksormod- andschedulingperiodictaskswithprecedenceandcommu-
ulesofataskcanhaveprecedenceandcommunicationcon- nication constraints in a distributed dynamic environment,
straints. Fromthisperspective,theirworkcomesclosestto suchasmobileroboticsystem.
ours. Byusinga branch-and-boundsearchalgorithm[17], Ouralgorithmwasappliedtoarealworldexamplefrom
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