Robot-Assisted Hospital Bed Transport

Robot-Assisted Hospital Bed Transport

Sahit Erdis

Te hnology

at Örebro University

Sahit Erdis

Robot-Assisted Hospital Bed Transport

Supervisor: Prof.HansSkoog

Examiners: Prof.IvanKalaykov

The ontrollingofmobilerobotshasbeenandstillisinthefo usofresear hers.

Fuzzyrule-based ontrollersareextensivelyusedto ontrolrobots.Path

plan-nerswere reatedusingdierentsear hmethodsndingtheshortesttraje tory

betweentwopointsandtherebyavoidingre ordedobsta les.Thelowdegree

ofautomationinhospitalspromiseshugepotentialforin reasinglogisti al

ef-fe ts by the use of mobile robots. Espe ially the automated transport of a

hospital bed, whi h manually requires twopersons, would releasetime from

transportationa tivities.Theusageofamobilerobotjoinedtoahospitalbed

makes ontrolling onsiderablyharder.Thisdo umentdes ribesaproje t

a - omplishedbymein ooperationwithRobCabAB.Duringtheproje t,apath

plannerwas reatedand ontrollingstrategiestomoveamobilerobotjoinedto

ahospitalbedbetweentwolo ationswasimplemented.The ontrolling

strate-giesarenotonlybasedonsensorreadingsfromalasermountedonthemobile

robotandalistofwaypointsprovidedbyapathplannerbutin orporatesalso

theposition ofthebedin theenvironment.Therobot adaptsits behaviorto

ensureasafemovement onsideringthepositionofthebedwhi h isnotonly

determined by thekinemati s of the robot-bed model but also by an

exter-nalfor eintheformofapersonfollowingthetransport(humanintelligen e).

Developmentwasdone on the Stage simulator and is intended to be nally

transferred toarealrobotplatform. Tests doneinthesimulatorshowedthat

theimplementedmethods areappli ableto bringthebedto thedesiredgoal

I would like to give spe ial thanks to my supervisor Prof. Hans Skoog for

allowing me to arry out this proje t. He is the head of RobCab AB and

introdu ed me to the proje t. In addition, I thank Karol Nie hwiadow who

is aPhDstudent atRobCab AB forhelping me withproblems. Dr. Dimitar

Dimitrovisapost-do toralresear herattheAASSresear h enteratÖrebro

University. I thank him for his help on the kinemati model. Last but not

least I thankMarianne Eri ssonwho isanurseat the hospitalofEskilstuna

(Mälarsjukhuset-Viktoriaenheten,Eskilstuna)foranextensiveinterviewabout

1 Introdu tion 13

1.1 Motivation . . . 15

1.2 Limitations . . . 16

1.3 MainContribution . . . 16

1.4 Stru tureof theThesis. . . 17

2 DevelopmentEnvironmentandSimulationSetup 19 2.1 StageSimulator . . . 19

2.2 SimulationofthePersonFollowingtheTransport . . . 20

2.3 HostComputer . . . 20

2.4 Des riptionoftheSimulatedEnvironment . . . 21

2.5 Kinemati Model . . . 21

2.5.1 Robot-Trailer . . . 22

2.5.2 Robot-Bed . . . 23

3 APrioriKnowledge,HumanBehaviorandTheoreti alModels 25 3.1 CommonManualBedTransportation . . . 25

3.2 RobotAssistedBedTransport . . . 26

3.2.1 PassiveRobot Rea tion . . . 26

3.2.2 A tiveRobotRea tion. . . 26

3.3 PremisesandHumanBehavior . . . 28

3.4 Ex essiveWidthofaTrailer. . . 32

3.5 Rea tionDemandingSituations . . . 33

4 Basi sandSimilarCon epts 37 4.1 PathPlanning . . . 37

4.1.1 RobotPathPlanning . . . 37

4.1.2 TheA*Sear hAlgorithm . . . 38

4.2 FuzzyRule-BasedControl . . . 39

4.3 Clearan eMap . . . 40

4.4.1 GeneralizedVoronoiDiagramin Roboti s . . . 43

4.5 Context-DependentBlending . . . 44

5 Designand Implementation 47 5.1 ComputingaGlobalClearan eMap . . . 47

5.1.1 Appli ation-Spe i Choi eofDistan eValues . . . 49

5.2 PathPlanner . . . 51

5.2.1 Method forFollowingaPath . . . 52

5.2.2 TransformingBetweenMapandRobot Coordinates . . 53

5.3 Controller . . . 54

5.3.1 GoToBehavior. . . 54

5.3.2 Obsta leAvoidan eBehavior . . . 55

5.3.3 SafeBedBehavior . . . 55

5.3.4 Arbitration . . . 57

5.3.5 ConvertingFuzzySetsto ControlValues. . . 57

5.3.6 CornerDete tion . . . 58

5.4 Lo al Map. . . 60

6 Experiments 61 6.1 Simulation1"ExpertPerson" . . . 62

6.2 Simulation2"LazyPerson" . . . 62

6.3 Simulation3"UnknownObsta le" . . . 65

6.4 Simulation4"RemoveRegisteredObsta le" . . . 66

6.5 Simulation5"MarkerPoles" . . . 67

6.6 Experimental AnalysisofthePathPlanner . . . 68

7 Con lusion 71 7.1 Summary . . . 71

7.2 FutureWork . . . 71

7.2.1 Pro essthePlannedPath . . . 71

7.2.2 ModiedClearan eMap. . . 72

Introdu tion

Hospitaltransportsofgoodsandpatientsbetweendierenthospitalunitsare

a time- onsuming and laborious task. Mobile robots an be used to

trans-portgoodsautonomouslyforexampleinsidehospitals,o esorfa toriesand

therebydisburdenthestafromtime onsumingtransportations.Anyonewho

wasin ahospitalhasprobablyseenatransport of abed, with abedfast

pa-tientonit,betweentwohospitalunits.It takestwopersons tomaneuverthe

bed from onelo ation to another. An automationof su h atime- onsuming

bedtransportwouldgivea onsiderablerelieftothesta.RobCab AB[42℄is

anewlyestablishedresear hand development ompanyin theeld ofmobile

robotte hnologywithheado einVästerås/Sweden.Theba kgroundofthis

proje tisthat RobCabABwouldliketodevelopmethods toautomate

om-monmanualhospitalbedtransports.Thisproje tisa omplishedforRobCab

ABforthatpurposeandseeksmethodstosubstituteonepersonina ommon

manualbedtransportbyarobotwhosemajortaskis topullthebed, andin

this waydisburdenthehospitalstabyoneperson.Theintentionisthatthe

remainingperson,followingthetransport,assiststhetransportat therearof

the bed. In addition, this robot-bed transport shall be donewithout having

any sensor devi es mounted on an ordinary hospital bed. There is a reason

why webelieve that this kindof anautomated bed transport with ahuman

helperismorerealizablethanafullyautomatedtransport.A ommonmanual

bed transport is a omplished by two persons, be ause the umbersomeness

of ahospitalbed makesatransportby onlyoneperson notfeasible without

assistan e(bytru ket .).Webelievethatabedtransporta omplishedbya

robotalone,wouldbequitedi ult,nottosayimpossible,evenusingthestate

oftheartroboti smethods.Havinginmindthepossibilityoffailureduringa

transportbyonlyonerobot, webelievethat the ombinationof arobotand

apersongivesadvantages.Su harobotbedtransporthas ertainsimilarities

withatransporta omplishedbyatrailertypemobilerobot, i.e.atransport

donebyamobilerobotatta hedto atrailerthroughajoin.Althoughseveral

mo-Figure1.1:Robot-assistedhospitalbedtransport.

bilerobots[25,26,27,19,29,39,32,55,57,30,40,66,13,47,35,63℄noone

has applied it to the problem of bed transport. The main hallenge of su h

arobot bed transport isto buildarobust ontrol programthat reliably

per-forms omplexmovementsinspiteofenvironmentalun ertainties,andtaking

into a ount the safety of the bed by onsidering its position inuen ed by

the person followingthetransport. Theinterplay betweentherobot andthe

remainingpersonasks forthedevelopmentofmethodsthat bothin planning

andexe utiontakeintoa ountthesafetyofthebedaswellas hangesinthe

orientationofthebed donemanuallyduringthetransport. Thisrequirement

laimsadenitionofintelligentbehaviorindierentsituationswhi h anthen

be onsideredduringthetransport.Itispartofthisproje ttogivedenitions

forbehaviorsduringatransport,i.e.howshouldtherobotandhowshouldthe

person behavein dierent situations toensurea safetransport. Thisproje t

is based on simulations. At the beginning of the proje t, the intention was

to evaluate the methods found in this proje ton areal robot platform like

theone urrentlydevelopedatRobCab AB.This ouldunfortunatelynotbe

a hieved,be ausethedevelopmentofthe methods des ribedheretook more

time than we expe ted. For this reason, all laboratory work has been done

onStagewhi his arobot simulator.As aresultof themethodsgivenin this

proje t,theauthor re ommendsan extensionof this proje twhere the

te h-niquesfoundhereareexploredonarealrobotplatformliketheone urrently

developed at RobCab AB. In order to rea h the above des ribed robot-bed

transport,a ontrolprogramwasdevelopedimplementingalgorithmstoplan,

navigateand ontrol themotion ofa mobile robot onne tedthrough ajoin

to abed.The programtakesinto a ountassistan e,in theform of sidewise

1.1 Motivation

The main task of a hospital is to are for si k people and that is why the

are-relatedpro essesarethemostimportantones.Thereareseveraldierent

support pro essesin theform of, among other things, logisti s.Fordo tors,

in general,tobeabletooperaterequiresthepatientstobetransferredtothe

operatingroom.Throughinterviewsandobservationsinawardofthehospital

ofEskilstuna(Mälarsjukhuset,Eskilstuna)weweretoldthatthehospitalsta

feel manualbedtransports inee tive,tiring, time- onsumingand altogether

as something they would like to beable to handle in a better way. A

om-mon manual bed transport, where twopersons are employed, takes at least

5-10minutesfor a"singletrip".Duringtheinterview, wegottheimpression

that bedtransports needto be ome moree ientin order tohelp to redu e

osts, waiting times andimprovethe apa ityand theuse ofresour es.This

impressionledusto look loseratthesituation oftheapparentlowdegreeof

automation in hospitalsand to what extentautomation ould ontribute

re-lievingthehospitalstafromtransporta tivities.DanielGåsvaerandPatri k

Phuainvestigateandevaluateina asestudy[12℄thepotentialoflogisti s

au-tomationinhealth areasameansofin reasingtheinterlogisti ale ien y.

The study shows that only 30%of the working time of the hospital sta is

spenddire tlyonpatient-relatedtasksandthatthereistremendouspotential

to releaseresour esby ndingvarious automationoptionsinthe hospital

lo-gisti s. As a partof their study they investigated twodierent wards and a

unitfortransportandservi efromthehospitalofEskilstuna(Mälarsjukhuset,

Eskilstuna)inordertogetinsightatthepresenttimeataSwedishward.One

of thehospital wardsinvestigated in [12℄ wasthe "Viktoriaenheten",award

where we ouldinterview aleading person aboutpatient transports aswell.

Theunitfortransportandservi eofdis ussisanexternunitthatmanagesthe

transportationandservi eissues.Thefa tthattheunitisexternalimpliesthat

the hospitalbuys servi esfrom that unit.A ording[12℄ atthe urrenttime

this unit perform about15000patient transportsperyear, whi h represents

about 87% of the total patient transports. The hospital sta also performs

many of these transportsthemselvesbe ausethe transport department does

notmanageto a omplishthelargenumberofpatienttransportsorbe ause

thetransportsarearrangedattooshortanoti e.Ofalltransportsdoneabout

55%are bedtransportswhile 45%are wheel- hairtransports. As aresultof

thela kof availability oftransportand servi ethestahaslesstimeforthe

patients.Manyhospitals are oftenverylarge, whi h means longjourneys in

the orridorsandelevators,whi hindi atestheextentofhospitallogisti s,as

wellasitspotentialbyworkinge iently.GåsvaerandPhua ometothe

on- lusionthathealth areisanindustrythatisingreatneedofe ientlogisti s

solutionsinwhi he onomi pressuredemandsmoree ien yin health are.

than the other way around. We want to release the hospital sta as mu h

as possible but leave the last de ision about the ontrol of the transport to

theperson.Arobotleadingthetransport atthefrontof thebedwould take

overthestrenuousworkofdrawingthebedandsteeringthefrontofthebed.

Furthermore,thepersonat therearhasabetteroverviewoverthetransport,

and is able for instan e to interrupt the transport qui kly when dangerous

situations arise.

1.2 Limitations

ˆ Patients may in the future, to someextent, be ome transported

auto-mati ally when their medi al ondition permitsthis, whi h will save a

lot of resour es. This question has also an ethi al and amoral aspe t

besidete hnology,and thereforedependsonhowopen theso iety isto

newte hnologies.Thisproblemisnotaddressedin thisproje t.

ˆ Thelo alizationproblemisnotaddressedinthisproje t.Lo alizationis

alreadysolvedontherealrobotplatform urrentlydevelopedatRobCab

AB. Ina nutshell, lo alization is there done by odometry, additionally

orre tedbyalaserrangenderwhi hs anstheenvironmentand

om-paresthes an withanenvironmentalmap.

1.3 Main Contribution

Thespe i ontributionsofthisthesisare:

ˆ Intelligentbehavior- denitionsare givenforhowrobotsand how

per-sonsshould behaveduring anautomatedhospitalbedtransport.

ˆ Pathplanner-theA*sear halgorithmwasfurtherdevelopedtoapath

planningalgorithm sear hingfor apathholding maximum learan eto

obsta les.

ˆ Clearan emap(CM)-amethodwasdevelopedtoe iently omputea

globalCM.

ˆ Fuzzyrule-based ontroller-afuzzy ontrollerwasdevelopedtakinginto

a ount, beside "obsta le avoidan e" and "go to the next way point"

behavior,thebehaviorofthepersonfollowingthetransport.

ˆ Cornerdete tion-amethodwasdevelopedto dete t,duringthe

trans-portofthebed, onvex ornersby omputingdistan esbetweenthebed

andobsta les.

ˆ Path following method - amorerobust method for path following was

developedusinglook-ahead.

ˆ Extendeddefuzzi ationmethod -topreventtoolowspeedsbeingsent

totherobotanextendeddefuzzi ation methodwasdeveloped.

1.4 Stru ture of the Thesis

Thisthesisisorganizedasfollows:

Chapter 2 Des ribesallthe omponentsinvolvedinthesetupusedtosimulate

a robot-bed transport, su h as the software and hardware interfa es,

thesimulatedenvironmentandthekinemati modelused tosimulate a

robot-bedtransport.

Chapter 3 This hapter mirrorsapartof thede isionmakingpro ess ofthe

proje t.First,itgivesanoverviewofthepriorknowledge atthe

begin-ningoftheproje t,i.e.whatkindofproblemswehaveseenandthe

pos-siblesolutionswedis ussed.Then,thegatheredinformationofavisitat

thehospitalofEskilstuna(Mälarsjukhuset-Viktoriaenheten,Eskilstuna)

is presented leading to a denition for "intelligent" behavior during a

hospitalbed transport. Finally, somedeveloped ideasare proposed

re-gardinghowtheproblemsemergingduringarobot-bedtransport anbe

solved.

Chapter 4 Presentsa olle tionofbasi sfromliteraturewhi h anbebrought

in onne tion with this proje t. An introdu tion to some well known

basi on eptsinroboti s ontrolisgiven.Knowledgeaboutthesetopi s

isneeded to understand the on epts des ribedin subsequent hapters

ofthisdo ument.

Chapter 5 Dis usses how the methods proposed in Chapter 3 were

imple-mented.

Chapter 6 Veriesthefoundsolutionsonsomesimulatedruns,andalso

om-paresthedevelopedpathplannerwithanexisting one.

Development Environment and

Simulation Setup

This hapterdes ribesallthe omponentsandingredientsinvolvedinthesetup

used to simulate a robot-bed transport. Firstly, the software-and the

hard-ware interfa esare des ribed. Se ondly, a short des ription of the simulated

environment is given. In the last part of this hapter, the kinemati model

usedto simulatearobot-bedtransportisdes ribed.

2.1 Stage Simulator

Stageisarobotsimulator.ItispartofthePlayerProje t[16,17,62,46℄whi h

is aproje tto reate software forresear h into roboti s and sensor systems.

There areplentyofexamplesofwhere theStagesimulatorhasbeenusedfor

resear h(e.g.[59,31,48,33,10,38,9,18,5,41,1,44,34℄).AllPlayersour e

ode is distributed under the terms of the GNU General Publi Li ense v2

("GPL"), i.e. the sour e ode is free software and the user hasthe freedom

to run, opy, distribute, study, hange and improve the software. Stage is a

multi-robotsimulatorthatprovidesfa ilitiesfor reatingyourownbitmapped

environments for experimenting with robots. Various sensors and a tuators

are provided, in luding sonar, s anninglaser range nder, olor-blob vision,

odometry,grippers, bumpers/whiskersand mobile robot bases.One anuse

Stage in three dierent ways; one,and probably themost spreadmethod to

useStage,isto ontroltheStagedevi esthroughPlayerwhi hisanetworked

robotserver.These ond is to use the ompiled "Stage"program that loads

arobot ontrolprogramfrom alibrary. Finallyone anwrite one'sown

sim-ulator byusingthe"libstage"C++libraryandtherebyrunand ustomizea

Stage simulationfrom inside programs. Unfortunately, the do umentationof

Stageprimarilydes ribeshowtousethesimulatorin onjun tionwithPlayer.

Apartfrom that,there areexample ontrollersin<stagesr >/examples/ trl

presentsanexample ontrollerin [61℄appli ablefor beginners.Regardlessof

inwhatwayoneusesStage,onealwaysneedsades riptionoftheworldtobe

simulatedbyStageintheformofaso alledworldle.Stageloads theworld

le on start-upand reatesentities as indi ated in the le. Depending on in

whi hwayoneusesStagetheworldleisgivenasthelast ommandline

ar-gumentwheninvokingStageorhisownwrittensimulatorprogram.Appendix

Apresentsasimpleworldle,indi atingthreeentitiesusing

type(

...

)

entries. Theworldle reatesaStagewindowwithasizeof700x700pixels entered

at position (10,7)ofthes reen.Thiswindowshowsaoorplanwiththeset

size in m and itsorigin at (10,7.5). The oorplan is stored in the bitmap

le

hospital

1_200

x

200

X

.

ppm

.Thelastentry reatesapositiondevi enamed "r0"with alaser atta hed to it. This position devi e is amobile robot with

theinitialposition(1.750,1.000)andorientationof0.000indegree.Alsonote

that sometime onstantsareset inthebeginningoftheworldle.

2.2 Simulation of the Person Following the Transport

In order to simulate the person ontrollingthe rear of thebed thegamepad

shown in gure 2.1 was set up, used for simulating a sidewise movement,

ontrollingthespeedet .

Figure2.1: Gamepadsimulatingtheperson ontrollingtherearofthebed.

2.3 Host Computer

The host omputerwasanA er Aspire 5920G,with a 2.2GHz IntelCore 2

Duopro essorand2GBRAM,withaNVIDIAGeFor e8600MGTgraphi s

2.4 Des ription of the Simulated Environment

During this proje ttwoposition models simulatingmobile robot bases were

used, one to simulate the robot pulling the bed and the other to simulate

the bed itself. Thesimulatedrobot is set to dierentiallike aPioneer robot

where speed and turn rate are ontrolled. A simulated s anninglaser range

nder su hastheSICKLMS200wasatta hedtothesimulatedrobot.There

werenodevi esatta hedtothepositionmodelsimulatingthebed.Moreover,

hospitalbedsareusuallyomni-dire tionally ontrollable,andforthispurpose

the model of the simulated bed was set to omnidire tional. The oor plan

reatedin this proje tmirrors orridorsand premisesin ahospitalwhere an

attemptwasmadetoholdarealisti ratiobetweenthebedandthe orridors.

Figure2.2showsthesimulatedenvironmentusedfordevelopmentduringthis

proje t,with the simulated robot at the oordinate (10, 2.5).The square at

the oordinate(13,2) isanunre ordedobsta le.

Figure2.2:SimulatedEnvironmentwiththerobotat the oordinate(10,2.5)

andanunre ordedobsta leatthe oordinate(13,2).

2.5 Kinemati Model

Inthe ontextof this work,amodel is a onstru tthat representsasystem,

in ontrast to a dynami model without onsideration of the ir umstan es

leadingtothemotion.

2.5.1 Robot-Trailer

Duringthis proje takinemati modelof anonholonomi mobile robot with

atrailerbasedonS.K.Agrawalet al.[25℄wasapplied. Figure2.3showsthe

s hemati ofthe system andits onguration.The trailer is atta hedat the

enter

O

ofthemobilerobotthroughasimulatedrotationaljoint.Thesystem's ongurationsqareshowninequation2.1:

q

=

x

1

y

1

θ

1

θ

0



T

(2.1)

Asindi atedingure2.3,

C

isthemidpointoftherearaxisofthetrailer and

θ

1 and

θ

0

aretheheadinganglesofthetrailerandtherobot.Thedistan e

betweenthemidpointoftherobotandmidpointoftherearaxisofthetrailer

is

L

. Observing the geometri relationshipsof themodel, the position ofthe trailerisgivenbyequations2.2.

x

1

= x

0

− Lcosθ

1

y

1

= y

0

− Lsinθ

1

(2.2)

Equation 2.3 shows the kinemati model of the system where

S(

q

)

is a matrixspanningthenullspa eof

C(

q

)

, i.e.the ongurationofthepoint

C

.

.

q

= S(

q

)

v

(t)

(2.3)

Velo ityisinthemodelrepresentedastheheadingspeed

v

andtheturning speed .

θ

0 of therobot. v

(t) =

h

v

.

θ

0

i

T

(2.4)

From2.4itispossibletondS(q)writtenas:

S(

q

) =









cos(θ

0

− θ

1

)cos(θ

1

)

0

cos(θ

0

− θ

1

)sin(θ

1

)

0

sin(θ

0

− θ

1

)/L

0 0 1









(2.5)

Figure2.3:Thekinemati modelofatrailertypemobilerobot.

2.5.2 Robot-Bed

Inordertosimulate asidewisemovementofapersonassistingthebed

trans-portthe setupgamepad, shown ingure2.1, ontrolstherearof thebedas

indi atedingure2.4.Thesignalssentbythegamepadwereset additionally

after velo ity is set for the bed. Angle

α

is measured and depending onthe gamepad signalanewpositionfor thebedis omputedandset a ordingto

Figure2.4:Thekinemati modelofthesidewisemovementofthebed.

x

1

= x

0

+ L ∗ cos(α + gamepad

_

signal)

y

1

= y

0

+ L ∗ sin(α + gamepad

_

signal)

θ

1

= α + gamepad

_

signal

(2.6)

A Priori Knowledge, Human

Behavior and Theoreti al Models

This hapter des ribes parts of the de ision making pro ess of the proje t.

First, it gives an overview of the prior knowledge at the beginning of this

proje t, i.e. what kind of problems we have seen and the possible solutions

we dis ussed. Then, the impressions and gathered information of a visit at

the hospital of Eskilstuna (Mälarsjukhuset-Viktoriaenheten, Eskilstuna) are

summarized and presented, leading to a denition for "intelligent" behavior

during a hospitalbed transport. At theend of this hapter,somedeveloped

ideasin form of theoreti alsolutionsare proposed whi hwebelieve ould, if

rightimplemented, ontributeto solveproblemsemergingduringarobot-bed

transport. It is intended to des ribethese approa hesand methods but this

doesnotmeanthatthemethodsshownhereareimplementedone-to-one.The

implementationisdes ribedin Chapter5.

3.1 Common Manual Bed Transportation

Nowadays,a ommonmanualbedtransportis arriedoutbytwopersons,one

in frontof thebed ontrollingthe frontofthe bed andthe otherat therear

ofthebed ontrollingtherearofthebed.Wereferheretosu hamanualbed

transport asahuman-humanbedtransport. Theperson ontrollingthefront

ofthebeddoesthisbypullingin thefrontforwardand sidewise.Theperson

followingthetransportattherearofthebed ontrolsthisbypushingthebed

andpullinginitsrearsidewise.

3.2 Robot Assisted Bed Transport

Substituting thepersonin front ofthe bed by arobot would imply thatthe

robothastotakeoverthetasksofthepersondes ribedabove.Theremaining

intherearofthebed.Apersonfollowingarobot-humanbedtransportatthe

rearwould havetoholdthebedina ertaindistan eto thenearestobsta les

prettysimilar towhentwopersonswould arryoutthetransport.Therobot

shall of ourse adapt its behavior (in a ertain margin) to the amount of

adjustmentdonebytheperson ontrollingtherearofthebed uptostopthe

transport. A perfe t path for su h a robot-bed transport would not be the

shortestpossibleaswouldbethe aseforarobot overingthedistan ealone.

Havingthis behaviorof keepinga ertain distan e betweenthe bed andthe

nearestobsta lein mind, therea tionof therobot to deviationof this ould

roughlybedividedintotwo ases:passiveanda tiverobotrea tion.

3.2.1 PassiveRobot Rea tion

Imaginefortherst asethattherobotplansapaththatholdsa ertain

dis-tan eto thenearestobsta les bothin straightahead orridorsandin urves.

Therobot ouldrea tinamorepassivewaywherethevelo ityofthe

trans-port isredu ed upto stopthetransport when thedistan e betweenthe bed

and an obsta lefalls belowa ertain threshold. This would bea way to

sig-nal the following person to rea tmore a urately and bring the rear of the

bedin abetterposition.Sin etherobotwouldstopwhen thebed toomu h

approa hesobsta les,thissolutionwouldprovideahigherse uritylevel.This

wayof ontrollingthevelo ityis furthermoreeasierto implementbe auseit

onlyneeds agradualredu tionof thevelo ity in proportionto falseposition

ofthebed.Themajordrawba kofthisapproa hisitspassivity,i.e.therobot

would not modify its own traje tory asa rea tion to adjustments (sidewise

movement)donebytheperson.

3.2.2 A tive RobotRea tion

A se ond way of robot behavior ould be more a tive. The robot ould try

to rea t by modifying its own traje tory to the amount of the adjustment

(side-wisemovement)donebytheperson.Consideringthisse ondapproa h,

pathplanningand ontrollingdependshighlyontheexpe tedbehaviorofthe

personfollowingtherobot-bedtransport.Therobot ouldthentrytorea tto

deviationfromthisassumptionanddepartfromitsplannedpath.Letushere

again a ton theassumption that the optimaldistan e betweenthe bedand

obsta les is a ertain distan e. The behaviorof theperson ould bedivided

into two asesaswell:anlazyandana tiveperson.

One ouldexpe tinpathplanningthatthepersonwillfollowthetransport

at therearof thebed,but willbehavesomewhatslowand,mostofthetime,

will not move the rear of the bed sidewise. Let us here all su h a person

for a"lazyperson".Not maneuveringthe rearof thebed at allwouldmean

atraje tory that tries,when exe uted,to hold, in everysinglesituation,the

desireddistan ebetweenthebedandthenearestobsta les.Inotherwords,the

safety(holdinga ertaindistan etoobsta les) ofthebedwouldlieprimarily

intheresponsibilityofthepathplanner,whi hwouldtrytondapathwhi h

ould be exe utedwithouthelp of theperson.Inthose situations duringthe

transport where the person intera ts by sidewise movement the robot ould

modifyitstraje toryandshort utitsownpathwhenadvantagesshowup.This

wouldsavetimeandshortenitswaytothegoal.Leavingthesafetyofthebed

to thepathplanner would releasethefeedba k ontrol loop(f l)mostofthe

time from rea ting to movements done by the person. The f l ould mostly

ontrol the "go to next way point" behavior and the "obsta le avoidan e"

behavior.Ontheotherhanditwouldbequitedi ulttondapathplanning

algorithm that is able to plan a traje tory under the assumption that the

personfollowingthetransportdoesnotrea tatall.Su hanalgorithmwould

haveto onsiderall onstraintsofatrailertypemobilerobot.Forexample,it

wouldhavetoplanforveeringtoavoidhangingon orners.Havingthenarrow

orridorsofhospitalsinmind,thepathplannerwouldpossiblynotalwaysnd

a feasiblepath to the goal.In narrow orridorsveeringmight notalwaysbe

possibleandinsu h asesthealgorithmwouldhavetoplanforapathmoving

the robot straight ahead before turning. This is indi ated in gure 3.1. For

obviousreasonsapprovedleast- ost pathmethods for pathplanninglikethe

A* sear h algorithm would not work here. A path, returned from the path

planner, had probably to be reworked after path planning. When avoiding

unre ordedobsta lethef lwouldhaveto,besidethebasi obsta leavoidan e,

takeovertheveeringpro essasdes ribedabove.

(a) (b) ( )

Figure3.1:(a)Veeringneeded.Thereisspa eforsu hamaneuver.(b)Angle

betweenrobotandbedheadingdire tionislargeandatthesametimeobsta le

aside. Safethe bed byturning to theoppositeside. ( ) Turning,but veering

notpossible.Goaheaduntilthebedisatthesameheightasthe orner.

Anotherassumptionaboutthebehaviorofthepersonfollowingthe

trans-portmayassumein pathplanningthat thepersonmorea tivelyparti ipates

in the transport. We dene heresu h aperson asan "expert person". One

Thealgorithmforpathplanning ouldthenbesimplerlikee.g.plana

traje -torythatkeepstherobotbothinstraight-ahead-passagesandin urvesinthe

middle of the orridor, i.e. the robot would most of the time hold the same

distan etothenearestobsta lessurroundingit.Thepathofthebedwouldin

turn movementsdeviate fromthat of therobot and thisshould be orre ted

bythepersonbysidewisemovement.Therobotwould havetorea ttothose

few aseswherethepersondoesnotrea tadequately.Therobot oulddepart

fromitsplannedpathwhenthedistan eofthebedtoobsta lesdeviatesfrom

theoptimal distan eand trytobring thebedba kto that optimalposition.

It oulde.g.whenthebeddeviatestotheleftsideifpossibleturnmoretothe

rightside and in su h away bringthe bed ba kon tra k.The safety ofthe

bedisin thisapproa hmoreinthedutyofthe ontrollerwhi hisresponsible

to he k where the bed is and orre t the false position of this. This would

of ourse burden the f l and would resultin a slowerloop. It also makesit

ne essaryin every ontrol loop to know theexa t position ofthe bed whi h

mightbedi ultbe auseofthea umulatingerrorof ommonposition

esti-mationmethods.Ontheotherhandwithsomemodi ationon ommonpath

sear hing algorithms it would be easier to reate a path planner that leads

the robot all thetime in the middle of the orridors. Ifweexpe t to havea

grid map des ribingthe environmentone ouldfor everysingle ell whi h is

free,i.e.notanobsta le ell, omputethedistan etothenearestobsta le ell.

Thisknowledge ouldbeusedintwoaspe ts.Firstit ouldbeappliedinpath

planning to get a path whi h fullls the requirement of a ertain learan e

to obsta les.Se ond,thef l ouldusethis knowledgeand,ifnotdonebythe

personfollowingthetransport,maneuverthebedinthedire tionofthose ells

withthehighestdistan evaluestothenearestobsta le.Aspe ial asewould

bewhenunre ordedobsta lehadtobeavoidedduringthetransport.Su h

o - asionswouldmakeitimpossibleto determinethemiddleofthepassageway

from thegridmap.Insu h asestherobot sensors ouldbeusedto ompute

distan es to obsta lesandderivefrom this data theoptimalposition forthe

bed.

3.3 Premises and Human Behavior

Inorderto getanimpressionofhowa ommonbedtransportationis arried

outandhowhumansbehaveduring this, aleadingperson fromthesta ofa

ward(Viktoriaenheten) of thehospital of Eskilstuna (Mälarsjukhuset,

Eskil-stuna)wasextensivelyinterviewed.Elevators,doors, orridors,bedset .were

measured,and pi turesweretakento getafeeling ofhowlargetheroomfor

maneuveringis.Moreover,amoviewasre orded,showinga ompletehospital

bedtransportfromthestationtotheradiologydepartment.

Figure 3.2showsa ommon hospitalbed that wasused during the

simultaneously. Common doors passed during a bed transport havea width

of 105 m. The smallestelevator whi h hasto be used during the transport

betweenthestationandtheradiologydepartmenthasadoorwidthof110 m

andis183x260 mlarge.Thenarrowest orridorhasawidthof250 m.Figure

3.3 showsthepremises in thehospitalofEskilstuna. Notethelongdistan es

(frame3.3d)whi hhaveto be overedduringatransport.

Figure3.2:Hospitalbed.

Themoviewasanalyzedtodenegeneralbehaviorpatternsandmaneuvers

duringabedtransport.Spe ialattentionhasbeenpaidtohowthe

transporta-tion sta maneuver the bed in straight-ahead-driving, in turn movements,

when entering and exiting elevators as well as when passing through doors.

Figure 3.4showsa oupleofs reenshotstakenfromthemovie.Frame3.4a

-3.4 showthebehaviorofthetransportationstawhendrivingstraightahead.

It anbeseenthat both persons tryto keepthe bed asfaraspossibleaway

fromthewalls,i.e.holdthebedinthemiddleofthe orridor.Frame3.4d-3.4f

showturnmovementsatdierentpla esofthehospitalduringthetransport.

Again,it anbeseenthat theattempt ismadetoholdthebedasfaras

pos-sibleawayfromobsta les.Frame3.4g-3.4i showhowthebedismaneuvered

whenpassingthroughdoors(3.4gisthedoorofanelevator).Hereit analso

beseenthat thetransportationsta triesto keepthebedin themiddle, i.e.

asfaraspossibleawayfromobsta les.Frame3.4jshowstheneedtointerrupt

thetransportpro essbe auseoflo keddoors whi hhavetobeunlo kedand

opened manually. The analysis showed that, both in straight-ahead-driving

andin turnmovements,personstrytokeepthebed inthemiddleofthe

(a) (b) ( )

(d) (e) (f)

Figure3.3:PremisesinthehospitalofEskilstuna.

Poli y"applies,i.e.persons arryingoutthetransportalwaystryto keepthe

bedasfaraspossibleawayfromobsta lesinordertoexe utenavigationtasks

(a) (b)

( ) (d)

(e) (f)

(g) (h)

(i) (j)

Figure3.4: Generalbehaviorpatternsduring amanualbedtrasport.

3.4a-3.4 behaviorwhendriving straightahead. 3.4d-3.4fbehaviorin turn

A typi al maneuverbefore entering an elevator is to bring the bed in a

position parallel to the long side of the elevator and then pushing the bed

inside it. Furthermore,itwasobservedthat whenleavinganelevator,aturn

movementisrststartedwhenthebedforthemostparthaspassedthrough

thedooroftheelevatortoavoidgettingstu ksidewise.Thesemaneuversare

shownin3.5.

Figure3.5: Typi almovements.

3.4 Ex essive Width of a Trailer

One hara teristi ofarobot-bed onstru tionasproposedhere,isthatthebed

isusuallywiderthantherobot.Thefa tthatthebeditselfdoesnothaveany

sensorswouldprobably ausetherobotto turnintotoonarrowpaths,where

thereisenoughspa efortherobot,butthebedwouldgetstu k.Markerpoles

areusedby arsortru ks.Theyarexedorretra tablesti ksusedas

driving-and parkingassistan e for ollisionavoidan e, mostlymountedonthefender

orners.Forexample,tru kswithmountingwiderthanthetowingvehi le,use

marker poles as indi ator for the width of the mounting. Two su h marker

poles are labeledby arrowsin gure3.6. Having su h arti ial markerpoles

on the robot would prevent it from moving into too narrowpaths. This, of

ourse,makesitne essarythatthedistan ebetweenthemarkerpolesandthe

nearestobsta leis known,whi h ouldbeprovidedbyalaserrangender or

Figure 3.6:Tru kwith markerpoles.

3.5 Rea tion Demanding Situations

The hara teristi sof the robot-bed kinemati model makes it ne essary to

dene situationswhere area tioneitherbytherobot orthepersonfollowing

thetransportisneeded.Asarststep,adistin tionismadebetweendierent

typesof ornersdepending ontheanglebetweenthewallsmetat the orner.

Figure3.7showstwokindsof ornerswherea ornerwithaninteriorangleof

90

o

is denedas" onvex orner"anda ornerwith aninteriorangle of270

o

asa" on ave orner"[43℄.

Figure3.7:Convexand on ave orners.

showstwosu h situations.Having thekinemati model from Chapter 2.5 in

mind andthefa tthat theplanned pathwill holdtherobot inthemiddleof

the orridor,thereisusuallynorea tionneededinthese situationsex eptfor

therobothavingtoavoidunknownobsta les.Now,imagineasituationwhere

thebedwill approa ha onvex orner.Su h a onvex orner ouldbelongto

a known orunknown obsta le.Figure 3.9 showstwo su h situations. In this

ase,rea tionisneededbe ausethekinemati s would notimply a orre tion

ofthebedpositionautomati allywithoutgettingstu konanobsta le(inthis

asethe onvex orner).

(a) (b)

(a)

(b)

Figure3.9:Bedoutoftra k.Rea tionneeded.

Thenextquestion,in this ontext, ishowtodete t su h a onvex orner

when it is lose to thebed, in order to rea ton it.If onenow omparesthe

dierentsituationsingure3.8and3.9andtriestondtheshortestdistan e

betweenapointalonganedgeofthebedandanobsta le,one anseeingure

3.8 that the shortestdistan e is alwaysbetween a orner of the bed and an

obsta lewhi h indi atesthat no onvex orneris losetothebed.Theother

situations in gure3.9 are dierent. The shortest distan e between the bed

andanobsta leisinthis aseagainbetweenapointalongtheedgeofthebed

andanobsta lebutnotbetweenanyofthe ornersofthebedandanobsta le.

Thisfa tindi atesa onvex orner losetothebed.Theremightbesituations

where this does not hold even though the bed approa hes a onvex orner.

Supposeasituationwherethebedispositionedattheendofa orridorinside

a urvea rossthe ourseof the orridor.Figure 3.10showssu h asituation.

Note, that the distan e between orner A and the nearest obsta le to A is

Figure3.10:Extended onvex ornerdete tionmethod.

aboveisusedtodete tsu ha orner.Observenow,pointCwhi histhepoint

alongthisleftedgewhi h isfarthestawayfromanobsta le.If,inarststep,

thelo ationofpointCis foundthenthe distan ebetweenCandits nearest

obsta le oldbeused to solvethis situation. First,we ould examinepoints

along these tion of theedge whi h liesbetween A and C.Forea h of these

points,we ouldndthedistan ebetweenthesepointsandthenearestobsta le

to these points. We ould omparethese distan es withthe distan eof A to

thenearestobsta letoAandthedistan eofCtothenearestobsta letoC.If

nolargerdistan eisfoundthanthedistan eofAandCtorespe tivenearest

obsta le,no onvex orneris loseto thisse tion oftheedge. We ouldthen

dothesamethingwithpointsalongthese tionoftheedgewhi hliesbetween

BandCandtrytondadistan ewhi hisshorterthanthedistan eofBand

Ctorespe tivenearestobsta le.Ifalsothisse ondtestfails,no onvex orner

is losetothewholeleftedge.Ingure3.10pointDhasashorterdistan eto

Basi s and Similar Con epts

This hapterpresentsa olle tionbasi sand on eptsfromliteraturewhi hare

relatedto thisproje t.Ashort introdu tionisgiven tosome,from literature

andresear h,wellknownbasi on eptsinroboti s ontrol.Knowledgeabout

these topi s is needed to understand the on epts des ribed in subsequent

haptersofthisdo ument.Formoreprofoundexplanationsofthese on epts

thereaderisreferredto relevantliteratureand tothereferen eslistedatthe

endof thisdo ument.

4.1 Path Planning

Pathplanningis a ommontermdes ribingmethods used to nda

ontinu-oussequen e(path)of onditions(states)betweenaninitial ondition(start)

and anal ondition(goal), whilerespe ting ertain restri tions.Path

plan-ningproblemsariseforexampleinoperationsresear h(mathemati alpro ess

optimization),s heduling(taskoptimization)androboti s.

4.1.1 RobotPath Planning

Path Planning in roboti sis used to determine aroute from one oordinate

lo ationtoanother oordinatealongasetofwaypointswhi his ollision-free,

feasiblegiventherobot'skinemati sanddynami sand,ifgiven,satisessome

extra onstraints (like e.g. be optimal with respe t to distan e orholding a

ertain distan e to obsta les). In roboti s the environment where the robot

movesinisoften alledworkspa e.Theworkspa eisusuallydividedintoaset

ofstatesrepresentedbyagridmap.Agridmapisagridde ompositionofthe

ontinuousstatespa ewith numbersin thegridnet.Thisredu es thesear h

areatoasimpletwodimensionalarray.Ea h ellinthearrayhasastatusof

either "walkable"(the ellisfree)or"unwalkable"(the elliso upiedbyan

obsta le). Supposethesear hstartsat thegoal ell

G

. Anumberin ell

C

i

,

j

representsthe ostoftravelingfromthegoal ell

G

to

C

i

,

j

toasapositioninwhi htherobot anbe, ommonlydes ribedbya oordinate

tuple like (

i

,

j

) or (

i

,

j

,

k

)depending onin whi h environmenttherobota ts (

R

2

or

R

3

). To hangefrom onestatetoanother, i.e.torea hfromonerobot

positiontoanother,astatetransformationisapplied.Theproblem ofnding

a ompletepathfromoneinitialstatetoagoalstate,i.e.fromonepositionin

anenvironmenttoanother,isformulatedasasear hinthestatespa e,i.e.as

asear hinallpossiblepositionsoftherobot.Sear hisdonebystartingatthe

start orthegoal elland he kingtheadja ent ellsand generallysear hing

outward until nding the start/goal. The order in whi h ells are explored

are referredto as sear h strategies. Various sear h algorithms are applied in

pathplanningandsomeoftheeasiestnon-heuristi onesarebreadth-rstand

depth-rst [50℄. Su h blind sear h methods usually tend to explore a huge

numberofstatesorneedlu kinsele tingagooddire tioninwhi htosear h.

Heuristi sear hmethodsuseinformationaboutthesear hspa eandaremore

ee tive.Examplesofheuristi sear hmethodsaretheso alledGreedySear h

andtheA*sear halgorithm[50℄.

4.1.2 The A* Sear h Algorithm

The A* (pronoun ed"A star")sear h algorithm is a best-rst graph sear h

algorithm that ndstheleast- ostpathfrom agiveninitial nodeto one goal

node.Thealgorithmwasrstdes ribedin1968byPeterHart,NilsNilsson,and

BertramRaphaelin[21℄.It onsidersboththe osttogoalandthe osttostart

whende idingwhi h elltoexpandnextinthesear h.Thepathisgenerated

by repeatedly hoosing the ell with the least total ost from a number of

andidate ells.Ifimplementedright,itisverye ientandguaranteestond

theshortestpathbetweengoalandstart.Thefun tionfor al ulatingthe ost

foragiven ell

C

anbewrittenas,

f(C) = g(C) + h(C)

(4.1)

where

g(C)

denotesthe ostfromtheinitial ellto

C

and

h(C)

isaheuristi estimate of the ost from

C

to thegoal. The

g(C)

fun tion is easy to al u-late; just fet h the valuelo ated in

C

. The

h(C)

fun tion is tri kier. It an beshown that the A*algorithm gives anoptimal path if

h

is an admissible heuristi (thismeansthat

h

should neveroverestimate the ost to thegoal). Having a

h

fun tion that underestimates the ost mu h, or in the extreme ase, is always0,will ripple theperforman e ofthe A*sear h. Therefore

h

should always al ulate the minimal possible ost. Constru ting the

heuris-ti fun tion for out8- onne tivity sear h is notsodi ult; let

di

and

dj

be the dieren ebetween

C

and thegoal in the

i

and

j

dire tions, respe tively. One realizes that the number of steps required to take diagonally to rea h

is

(Max(di

,

dj) − Min(di

,

dj))

. Ifthe ostofadiagonalstepisdened tobe

sc

d

,andthe ostofverti alorhorizontaltobe

sc

vh

, theadmissible heuristi fun tion is al ulatedby,

Min(di

,

dj) ∗ sc

d

+ (Max(di

,

dj) − Min(di

,

dj)) ∗ sc

vh

(4.2)

4.2 Fuzzy Rule-Based Control

The pathplanner returnsalist onsisting ofa olle tionof map oordinates

that des ribesthe shortest path from start to goal.This listwill be handed

overtoafuzzyrule-based ontroller.Afuzzyrule-based ontrollerisa ontrol

system based on fuzzy logi and is a way of des ribing behaviors by using

a olle tion of rules, rather than using some omplex mathemati al model.

The ontrolleranalyzes rispinputvalues,gotfromatobe ontrolledsystem,

translates them into fuzzy variables, whi h are logi al variable that take on

ontinuousvaluesbetween0and1,andprovides,a ordingtothosefuzzy

vari-ables, ontrolparameterforthesystem.Fuzzyvariablesareoftenreferredtoas

"fuzzypredi ates"be ausetheymirrorthetruthofafa t.Inea h ontrolstep

a fuzzy rule-based ontroller performs three sub-steps: the fuzzi ation,the

fuzzy-inferen eandattheendthedefuzzi ation.Fuzzi ationisthepro ess

of generating values for sets of fuzzy predi ates using membership fun tions

giventheinputofasystemtothefuzzy ontroller.Fuzzy-inferen eisthe

pro- essof reasoningwhere on lusionsfromasetofIF-THAN rulesarederived.

Thesesetsofrulesare ommonlyreferredtoasa"ruleset"or,be ause anbe

seenasabehavior,asa"behaviorprodu ingmodule"andrepresentsa

knowl-edge base telling the system how to behave in dierent situations from the

view pointof a parti ularbehavior.The fuzzy predi atesset in fuzzi ation

arein thefuzzy-inferen estepusedintheIF-partsofthebehaviorprodu ing

module(s)tosetotherfuzzysets, ontainingfuzzypredi atesdedi atedtothe

ontrolparameterofthesystem,intheTHEN-parts.IF-partandTHEN-part

ofarulearealso alledthe"stimulus-part"andthe"response-part".Afuzzy

ontroller anuseoneormorebehaviorprodu ingmodules.In aseofmultiple

behaviorprodu ing modules, an arbitration poli y determines whi h

behav-ior(s) should inuen e the operationof the robot at ea h moment and thus

ultimatelydeterminesthetaska tuallyperformedbytherobot.Thisis done

in the simplestform by sele tingonebehaviorfor exe utionand ignoring all

other orin moreadvan ed form bys aling the output ofea h behavior

pro-du ingmoduleandde ideinthiswayhowmu hitinuen esfuzzypredi ates

dedi ated to the ontrol parameterof thesystemto be ontrolled.Afterthe

stepof fuzzy-inferen eabaseisgiven,in formoftheintheresponse-partset

the response partof fuzzy-inferen eset fuzzy predi atesare in the

defuzzi- ationstep onvertedinto risp ontrolvalues.Dierentmethods anbeused

for defuzzi ation.Oneof themostoftenused methods is Center ofGravity

(CoG).Abigadvantageofusingarule-based ontrolleristhattheyare

pow-erfuland versatile;e.g.implementinga ompletelynewbehaviorisrelatively

simple(justgureoutthefuzzypredi atestouse,and onstru ttherules).

Example

Ea hindividualbehaviorprodu ingmodulefullyimplementsa ontrolpoli y

for asingleobje tive,likefollowingapathoravoidingobsta les.Inasimple

formafuzzy ontrollerletstherobotmovetoa ertain oordinateandthereby

avoidingobsta lesbyusingforea hobje tiveonebehaviorprodu ingmodule

and ombiningtheiroutputinsomeway.Arule ouldbe:

IF obsta le to right AND NOT(obsta le to left) THEN turn left

Thestimulus-partoftheruleabove ouldbelongtoafuzzysetavoidobsta les

and oulde.g. ontainobsta le to right,obsta le to leftandobsta le

ahead.Theresponse-partoftheruleabovewouldinthisexamplebelongtoa

fuzzysetrotate,whi h ould onsistof turn left,no turnandturn right.

Therulewouldbelongtoabehaviorprodu ingmoduleusedtoobtainobsta le

avoidan e.Infuzzy logi ,unlike onventionallogi , thestatementsobsta le

to rightandobsta le to left an be partiallytrue (or false);0.0means

absolutelyfalse,and1.0absolutelytrue.Whenarulehasbeenevaluated,the

truth of its response anbe fet hed and stored. Theresponse aboveis turn

left.Ase ondfuzzysetusedintheresponse-part ouldbe alledvelo ityand

ould onsist of ba k,none, slowand fast.After thefuzzy sets rotate and

velo ityhasbeen al ulated,respe tivesetis onvertedintoasingleresponse.

E.g.ifbothturn leftandno turnis1.0(absolutelytrue) andturn right

is0.0, theresultingresponse shouldbesomethingin betweenturn leftand

no turn.

4.3 Clearan e Map

Inordertoa hievetheinChapter3.3des ribed"MaximumClearan ePoli y"

itisne essarytohavesomeformofdistan esbetweenadmissiblepositionsand

obsta lesintheenvironment.Clearan emaps(CM)areusedingame

develop-mentandtheroboti seldtoprovidethedistan etothenearestobsta lefor

anypointoftheworld[56℄.Examples anbefoundin[45,20,4℄.On esu ha

maphasbeen omputed,it anbeusedtondpathsthatpass,withmaximum

learan e,aroundobsta lesoruseitinafeedba k ontrollooptomaintainthe

positions of obje ts. Figure4.1 shows asmall map of20 x60 pixels andthe

are not lo ated. Note, in this CM the distan e for a diagonal step (

sc

d

) is dened tobe

SQRT (

2

)

andthedistan eforverti alorhorizontalsteps(

sc

vh

) is dened to be 1.Depending on in whi h appli ation and to whi h purpose

theCM is used,form andlook ofit mayvary by hangedvaluesfor

sc

d

and

sc

vh

.Alsothea ura yofthedistan evaluesmaybeadjusted depending on need.

Figure4.1:20x60pixelmapandits orrespondedCM.

4.4 Voronoi Diagram

A Voronoidiagram isade omposition of spa einto regions hara terized by

a predetermined amountof obje ts (e.g. points), alled sites. Ea h region is

dened byonesite and oversall pointsin spa ewhi h are, with respe t to

a ertain metri (oftenEu lidean distan e), loser to that site of theregion

thanatanyothersite.Su hregionsarealsoknownasVoronoi ells.Thereare

pointsinspa ewhi hhavemorethanonenearestsite,i.e.formtheboundaries

betweentworegionsandaVoronoidiagramisformedbyallthesepoints.The

Voronoivertexesornodesarethepointsequidistantto three(ormore)sides.

MoreformulaexpressedaVoronoidiagramintheplaneisexpressedasfollows:

if

P = {p

1

,

p

2

,...,

p

n

}

isa set of sites (points) in the plane,then the Voronoi diagramisthesub-divisionoftheplaneinto

n

distin t ells,oneforea hsite.

Forea h ell appliesthat apoint

q

orrespondsto asite

p

i

i dist

(q

,

p

i

) <

dist(q

,

p

j

)

for ea h

p

j

∈ P

with

j 6= i

. Figure 4.2 shows asimple ase of a Voronoi diagram

1

given a set of points in the plane. A deeper introdu tion

to Voronoi diagrams is e.g. given in [60℄. Some examples of appli ations for

Voronoidiagramsare,nearestneighborqueriesfordatastru tureproblemsin

omputationalgeometryandbusinessappli ationssu hasdeterminingwhere

to lo ateastoresoit isno losertoanyexisting storeof itskind.A further

appli ation forVoronoi diagramsis inroboti pathplanning,where theyare

usedintwodimensionalspa eusingasear halgorithmsear hingtheVoronoi

edges for a maximum learan e paths. Examples of appli ations in roboti s

using Voronoidiagrams anbefound in [6,54, 36, 15,58℄. Often someform

ofgeneralizationoftheVoronoidiagramisne essarytofulll theneedsofan

appli ation.Thereare multiple methodsto onstru taVoronoidiagramand

oneofthesimplestistondtheperpendi ularbise tionbetweenasite

p

and asite

q

. This separatesthe planeinto twohalfplanes, onewithpoints loser to

p

and one with points loser to

q

. A Voronoi ell determined by

p

i

an foundbyinterse tingallthehalfplanesthatseparateasite

p

i

fromtheother sites

p

j

. Doing thisfor allthe points reates theVoronoidiagram.Although the pro edure aboveis easyto understand, it is, in termsof time, ine ient

and moree ient methods are usually usedto omputeaVoronoi diagram.

StevenFortunedes ribesin[14℄aplanesweepalgorithm alledthe"Fortune's

algorithm". His algorithm uses a sweep line and a bea h line to generate a

Voronoidiagrams.Thesweeplinepassestheentireplaneand omputesthereby

a ompleteVoronoidiagram.Thisalgorithmisverye ientand on eptually

easytounderstand.

1

Figure 4.2: Voronoi Diagram generated using the Matlab fun tion

VORONOI(X,Y).

4.4.1 Generalized Voronoi Diagram inRoboti s

GeneralizedVoronoidiagramsusedinroboti s anbeseenasvariantsofCMs,

oftenonlyreferredto as learan emaps. Theyhave ommonpropertieswith

CMs des ribedin4.3,butalsoa oupleofdieren es.Bothprovidedistan es

toaspe ieddis retesetofobje tsinthespa e.CMsdothisforanypointof

themap, whereasdistan eshastobe omputedfrom Voronoi diagramsfora

ertainlo ation. Asaforementioned,aVoronoidiagram anbeveryusefulin

robotpathplanning.Restri tingarobotto traversetheedgesofVoronoi

dia-gramwillinsurethatitisasfaraspossibleawayfromthenearestsurrounding

obsta les.Forthat purposeitisne essarytorepresentsidesasobsta lesand

thatiswhygeneralizationsofVoronoidiagramsinroboti s on erntheshape

ofthesiteswhereVoronoidiagramsare onstru tedfortheboundariesof

sim-plepolygons.TheedgesoftheVoronoidiagram arethenequidistantbetween

thetwonearestobsta lesandthese edgesare idealforamobile robot'spath

whenmaximum learan eisdesired.PaulBlaerhasdevelopedanalgorithmfor

omputing safe paths for mobile robots using generalizedVoronoi diagrams.

The algorithm is rst des ribed and used in [6℄ and is also des ribed in [7℄.

Moreover,Blaerpresentsin[7℄aJavaappletthatdemonstratesthepath

plan-ning algorithm in a tion.Givena map with avarietyof polygonalobsta les

thataretobeavoided,Blaer'salgorithmdeterminesmaximum learan epaths

byusing anapproa hbasedonthegeneralizedVoronoidiagram foraplanar

Voronoiverti esforapath,withmaximum learan e,aroundobsta lesusing

Dijkstra's algorithm.Tond thegeneralizedVoronoi diagramfor the

olle -tionofpolygonsstoredinthemap,Blaerusesanapproximationbasedonthe

problem of omputingthe Voronoidiagram foraset of dis rete sites(points

along the edges of the polygons). First, he approximates the boundaries of

thepolygonalobsta leswithanumberofpointsthat resultfrom subdividing

ea hsideoftheoriginalpolygonsintosegments.ThentheVoronoidiagramfor

this olle tionofapproximatingpointsis omputed.Hetheneliminatesthose

Voronoi edges whi h haveoneor both endpoints lying inside any of the

ob-sta lestonallygetanapproximationofthegeneralizedVoronoidiagramfor

theoriginal obsta lesin themapformed bytheremainingVoronoiedges.To

usethediagraminpathplanning,onemust onne ttherobot'sstartandgoal

pointsto the diagram.Blaerhas developed twopossible ways to a omplish

this. The rstmethod involvesadding twosmallobsta les at the lo ationof

thestartandthegoalandinthiswayfor ethealgorithmtoin ludethestart

andgoalautomati allyinthediagram.Thismethodhasthedrawba kthatit

requires theVoronoidiagramtobere omputedea htimenewstartandgoal

points are entered. The se ond method (used in the applet) adds the start

and thegoalof therobotto thenearestVoronoiverti esby straightlines.In

ase anobsta le liesbetween thestart orthe goaland the nearest vertex, a

vertex is sear hed where this is notthe ase (next nearest vertex et .). The

foundpath,whi hisisasubsetoftheVoronoidiagram,remainsforthemost

partequidistantbetweentheobsta les losesttotherobot.Figure4.3showsa

Voronoidiagram onstru tedforamapof apartof theMorningsideHeights

ampusofColumbiaUniversityusingBlaer'smethod.

4.5 Context-Dependent Blending

Usually,thea tivityofmultiplebehaviorprodu ingmoduleshavetobe

oordi-nated.Thesimplestwayoffusingthe ommandsfromdierentbehaviorsbya

swit hings heme,wheretheoutputfromonebehaviorissele tedforexe ution,

and alltheothersareignored,isofteninadequateinsituations whereseveral

riteria should be simultaneously taken into a ount. Saotti [49℄ dened,

a general ombination pattern, alled Context-Dependent Blending (CDB).

CDB usesbothfuzzy meta-rules toobtainthea tivationof dierent

on ur-rentbehaviormodules and fuzzy ombination to fuse the output from these

modulesin asewhenmultiplebehaviorsarepartiallya tivated.Saotti alls

these methods behaviorarbitration and ommandofusion, respe tively. The

arbitrationofbehaviorsaredeterminedbyfuzzymetarulesoftheform

IF A THEN a tivate behavior_B (4.3)

Figure 4.3: AVoronoidiagram onstru tedfor amap of apartof the

Morn-ingsideHeights ampusofColumbiaUniversity.

be added together before the nal defuzzi ation step. Saotti proposes in

[49℄ fuzzy meta-rules to assign behaviors the strength of their a tivation by

omputing weights onstituting therelevan e of ea h behaviorat everytime

instant.Theinuen eofabehaviorona tionsissituationdependentandthe

behaviorweightis al ulateddynami allytakingintoa ountthesituationthe

mobile robotisin.Equation4.4showsthemathemati al on eptofbehavior

weighting.CDBhasbeenusedbyseveralresear hersinautonomousroboti s

to build omplexrobot behaviors(e.g. [11, 65, 64, 52, 53,8, 22,3,37, 2,28,

Figure 4.4: Stru tureof afuzzy ontroller using CDB. Figure from [6℄, used withpermission.

b =

P

n

A

n

b

n

P

n

A

n

(4.4)

Design and Implementation

5.1 Computing a Global Clearan e Map

The hallenge in omputing aglobal learan e map from agrid map,

estab-lishedbyobsta le ellsandunknown ells,istondforagivenunknown ellin

thisgridmapthedistan etothenearestobsta le ell.Themethoddeveloped

in this proje t al ulatesnotonly theManhattandistan e betweentwo ells

but the diagonal distan e if the shortest distan e between an unknown ell

anditsnearestobsta le ellisso.On e itisdetermined whi hobsta le ellis

thenearestoneforanunknown ell,itiseasyto omputethedistan etothis

byusing 4.2.The CMis omputedforanewenvironmentmapon e atstart

upandsaved,i.e.it anbeloadedin ase ondrun fromaleandthereis no

needto omputeitagainex ept whentheenvironmentmap is hanged.The

pro edure sear hes throughthe whole grid map and omputes, for ea h

un-known ell,thedistan etothenearestobsta le ellandassignthisvaluetothe

unknown ell.Givenanunknown ell,rsttheneighbor ellswiththenearest

distan e, a ordingto 4.2, are he ked for its status. Then the next nearest

ellsare he kedandsoonuntilanobsta le ellismet.Themethodis

demon-stratedherewithanexample.Toformulatethemethodmoreunderstandable,

forthisexamplethedistan evaluesfordiagonal,horizontalandverti alsteps

denedinthe ommonintrodu tionofCMsin4.3aretakenover.Thatis,

sc

d

is dened to be

SQRT (

2

)

and

sc

vh

is dened to be 1. Figure 5.1 showsthe dierentstepsofthealgorithmonthebasisofasmallgridmapof11x11grids

whi hissu ientsmalltobeusedto explainthealgorithm.First in5.1athe

mapasawholeisshown.Obsta le ellsaremarkedatbottom-leftinthemap.

Themarked ellsforminga rossin themiddlehaveaspe ial fun tioninthe

sear halgorithmandareherenamed rossdistan es.Thisisfurtherexplained

below. Supposed, the algorithm has to ompute and assign adistan e value

to the ellin themiddle of themap. Letus, for simpli ity, allit ell 0(the

distan e from ell0to ell0is0). Inarststep,thealgorithmexaminesthe

(a) (b) ( )

(d) (e) (f)

Figure5.1: Determinethenearestobsta le ellfortheunknown ell0.

rst the ellsfor whi h thedistan eis 1to ell0are he kedand thenthose

for whi h the distan e is1.41. If noobsta le ellis met in this rststepthe

ellsalong a5x5arrayonestepfurther areexamined asshown in 5.1 .This

pro edure ontinuesuntilanobsta le ellismetasindi atedintheframe5.1e.

The ellmarkedwithastarisa andidateforthenearestobsta le ellfor ell

0,but observeit ispossibleto meetobsta le ellswithlowerdistan e values

to ell 0if the sear h ontinues. Would e.g. any of the ellsholding a ross

distan einframe5.1fbeanobsta le ell,thenoneofthemwouldhavealower

distan e to ell0.One an besurethat thefound ellisthenearestobsta le

ell rstif thevalue of thehighest ross distan e ex eedsthe distan e value

of the found andidate ell. Finally, the distan e valueof thefound obsta le

5.1.1 Appli ation-Spe i Choi eof Distan e Values

Ithasalreadybeenmentionedin4.3thatthe hoi eofdierentvaluesfor

sc

d

and

sc

vh

ae t ertain hara teristi softheCM.Dierentvaluesfor

sc

vh

do s alethedistan e valuefor ellsbutdonot hangethepositionof maximum

learan e. E.g. in straight ahead orridorsthe CM will indi ate theposition

farthestawayfromobsta le(i.e.fromthewalls)inthemiddleofthe orridor,

independently from the valueof

sc

vh

. This looks dierent for various values of

sc

d

,be auseitinuen esthepositionofmaximum learan ein urvesand is worthtolook loserinto. To larifythis,aCM was omputedforthemap

showningure2.2twi e,usingdierentvaluesfor

sc

d

.Tostartwith,rst

sc

d

and

sc

vh

are set to the valuesused in theexample shown in 5.1. Figure 5.2 showsapartoftheCM omputedforthemapingure2.2.Theextra tshows

the urve down to the right. Cellsframed by a solidline arethose withthe

highest distan e to obsta les,i.e. the position of maximum learan e would

be indi ated there by the CM. As an be seen, the traje tory of maximum

learan e is more round inside the urve. Figure 5.3 shows another part of

thisCM.Thistime,theextra tshowstheupperhorizontal orridorinheight

oftheexitleadingtotheinner orridor.Thegureindi atesthat thepathof

maximum learan eisslightlydrawntowardtheexitattheheightofit.Asthe

CMwouldbeusedinapathplannertoplanapathwithmaximum learan e,

avalueof

SQRT (

2

)

for

sc

d

mightsometimesbeadrawba k.Ifapathplanner would plan astraight ahead pathpassingthe exit,thepass would bedrawn

towardtheexitattheheightofthethis.Thiswouldhappenbe ausethepath

plannerwouldfavorapaththroughtheframed ells.

Figure 5.3: CM with

sc

d

dened to be

SQRT (

2

)

and

sc

vh

dened to be 1. Extra t shows the upper horizontal orridor in height of the exit leading to

theinner orridor.

These ond time

sc

d

wasdened to be1instead of

SQRT (

2

)

.Figure 5.4 showsthesamepartoftheCMasshowningure5.2 omputedwiththenew

valueof

sc

d

.Followingthetraje toryofmaximum learan e,thistimeitmakes asharp90

o

turnattheheightofthe orner.Dependingontheappli ationthe

Figure 5.4: CM with both

sc

d

and

sc

vh

dened to be 1. Extra t showsthe urvedowntotheright.

5.2 Path Planner

On etheCMhasbeen onstru tedone anuseittondrobotpathsthatpass

withmaximal learan eobsta les.Thismeansthattherequirementofnding

theshortestpathbetweentwolo ationsisreleasedinfavoroftherequirement

of nding apaththat holdsthe robot bothin straightahead driving and in

urvesinthemiddleofthe orridor.Thedevelopedmethodhereisinspiredby

methods usedingameprogrammingwhereterrainis reatedthat iswalkable

but atahighermovement ost.Duringarun oftheA*sear halgorithm ells

near an obsta leare penalized su h as the path in the middle of a orridor

be omesmoreattra tive.Forthispurposethe lassi alrepresentationofthe

A* sear h algorithm des ribed in 4.1.2 was modied and gives in the path

sear h ellsnear obsta les ahigher movement ost

g

. Given aCM, rstthe highest value in it is determined, i.e. the ell farthest away from obsta les.

Re all from 4.1 that for aparti ular ell

C

the value of

g(C)

gives the ost of movementfrom theinitial ellto

C

. Thisvalueispenalized byanamount depending on the distan e of

C

to its nearest obsta le ell. When a ell is expanded and

g

is omputed for a neighbor ell

C

then

g(C)

onsists not only of the

g

value of the expanded ellplus 1 or

SQRT (

1

)

, i.e. the ost of

(a) (b)

Figure5.5:Pathbetweentwolo ationswithmaximum learan eusing(a)the

rstCM and(b)these ondCM des ribedin 5.1.1.

ostofmovementforonestepto ell

ij

is al ulateda ordingtoformula5.1 where

max

CM

, as already indi ated, is the highest value stored in the CM and

dist

ij

is thedistan e tothe nearestobsta leforthea tual ell

ij

.

s

is a s alefa torwhi h anbeused tosteerhowhardapaththroughaparti ular

ell,withitslowerdistan etothenearestobsta le,ispanelized.

sc

isthestep ost. Sin e we dened the step ost for a diagonal step to be

SQRT (

2

)

and thestep ostof verti alorhorizontalstepsto be1,

sc

maytakeoneofthese values,respe tively(donot onfuse

sc

d

and

sc

vh

withthisvariable.

sc

isused in5.1whereasthelastmentionedvariablesareusedin4.2).Figure5.5ashows

a path between two lo ations generated by this method. Here,the rst CM

omputedin 5.1.1is usedandasshownthepathholdsamaximum learan e

tothewallsa ordingthedenedmeasurements.Figure5.5ashowsapathfor

thesamestartandgoalpointusingthese ondCMdes ribedin5.1.1.As an

beseenthepathiswiderinside urvesandmakesasharp90

o

turnthere.For

the purpose of this proje twe believethat the se ond CM usedto ompute

thepathingure5.5aismoreappropriate.

cost

ij

= (max

CM

− dist

ij

) ∗ s + sc

(5.1)

5.2.1 Methodfor Following aPath

ahead. Intheimplementationwedonotdoanypro essingofthelist ofmap

oordinates;theyareused dire tlyasgivenfrom theplanner.

To sele t whi h oordinate the robot is to move to we do the following:

(1)The urrentpositionoftherobot

(x

,

y)

is onvertedintomap oordinates

(i

,

j)

.(2)The losest oordinate

N

onthepathis al ulatedby omparingea h oordinate with the robot oordinate. The oordinate with least hessboard

distan etotherobot oordinateissele tedas

N

.(3)The oordinatetherobot is to move to is simply sele tedas the 5th next oordinate in a list of map

oordinates.The oordinatetherobotistomovetodependsonthesizeofthe

robotandthesize oftheenvironment.It anbe hangedeasily.

Itshouldbementionedthatwewrotethe odesothat

N

annotbemoved ba k,only losertothegoal.Whentestingonthe Stagesimulator,wefound

thisapproa htowork prettywell.

5.2.2 TransformingBetween Map and RobotCoordinates

The originof theglobal oordinate systemis dened in thebottom left

or-ner of the grid map and thegrid map itself denes its origin in the topleft

orner.Figure5.6 showsthisinasimplemap of3by3 ells.That makesthe

implementationofsometransformationfun tions ne essary.

Figure5.6:Themapandrobot oordinatesystems.

Lethbetheheightofthegridmap.Then,theequationstotransformfrom

amap oordinate

(i

,

j)

toarobot oordinate

(x

,

y)

iswrittenasin 5.2:

x = j ∗ cellWidth/

10.0

y = (h − i) ∗ cellHeight/

10.0

(5.2)

Getting the equations for al ulating

(x

,

y)

to

(i

,

j)

is just a matter of reworking 5.2. Division by 10 is ne essary be ause the measurements in the

maparedoneinmm.Itshouldbementionedthatsin emap oordinatesmust

beintegers,weperformrounding(trun ation)when onverting

(x

,

y)

to

(i

,

j)

.

5.3 Controller

The nature of a robot-bed transport asks for multiple behavior produ ing

modules.Threedierentbehaviorsareusedinthisproje tallworkingonthe

samefuzzysetsintheirresponse-part.Thesethreebehaviorprodu ingmodules

aregoto nextwaypoint,obsta leavoidan eandsafebed.Thefuzzysetsset

intheresponse-partofthedierentbehaviorsarerotateandvelo ity.Velo ity

onsistsofthefuzzyresponsesba k,none,slowandfastandrotate onsists

of the fuzzy responses turn left, no turn and turn right. Having gure

4.4 in mind, the amount of ontribution from the dierent behaviorsto the

overallrobotbehaviorisde idedbyCDB.Pra ti ally,ea hbehaviorprodu ing

moduleworksonitsownlo alversionsofrotateandvelo itywhi hnallyare

fusedin CDB.Forea h ofthisbehaviorprodu ingmodulesfuzzy metarules

al ulatestheirarbitration.HowCDBisusedandwhi hfuzzysetsareusedin

thestimulus-parts oftherespe tivebehaviorprodu ingmodules isexplained

in followingsubse tions. Note, that some of the fuzzy predi ates mentioned

inthefollowingsubse tionsarebothusedin thestimulus-partoftheobsta le

avoidan ebehaviorandofthesafebedbehavior.Forthatpurposewede ided

not to give names to the dierent fuzzy sets used in the stimulus-parts of

therespe tivebehaviorsandinsteadlistthefuzzypredi atesused.Espe ially

worthto mentionisthefuzzypredi ateDanger.Thispredi atebe omestrue

ea h time the bed approa hes an obsta le so mu h that it would get stu k

imminently,i.e.someformofrea tionbythepersonfollowingisinevitable.A

truefuzzypredi ateDanger ausesanemergen ystopuntilthebedismoved

inabetterposition,i.e.awayfromtheobsta le.Further,abitmoreadvan ed

two-stepdefuzzi ationmethod weredeveloped.

5.3.1 GoTo Behavior

Fuzzypredi atesusedinthestimulus-partofthegotobehaviorarePos_Left,

Pos_Ahead,Pos_RightandPos_Here.Thedegreeoftruthofthesepredi ates

is based on the urrent posture of the robot and the goal oordinate. For

example, Pos_Lefttellsif thegoalis lo atedto the leftof the robot, andit

is absolutely trueifthe angleto the goalis largerthana ertain value.It is

absolutely false if the angle is so small that the robot heads in dire tion of

itswaypoint. Fuzzyinferen eforthego tobehaviorisdonebythebehavior