Design, Modeling and Control of a Biped Line-walking Robot

8/3/2019 Design, Modeling and Control of a Biped Line-walking Robot

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InternationalJournalofAdvancedRoboticSystems,Vol.7,No.4(2010) 39ISSN17298806,pp.3947

Design, Modeling and Control

of a Biped Line-Walking Robot

Ludan Wang1, Fei Liu1, Shaoqiang Xu1, Zhen Wang1, Sheng Cheng1 and Jianwei Zhang1,21LaboratoryofIntelligentRobotEngineering,KunshanInstituteofIndustryResearch,Kunshan,China2TAMS,DepartmentofInformatics,UniversityofHamburg,Hamburg,Germany

[email protected]

Abstract:Thesubjectofthispaperisthedesignandanalysisofabipedlinewalkingrobotforinspectionofpower

transmissionlines.Withanovelmechanismthecentroidoftherobotcanbeconcentratedontheaxisofhipjoint

tominimizethedrivetorqueofthehipjoint.Themechanicalstructureoftherobotisdiscussed,aswellasforward

kinematics.Dynamicmodel isestablished in thispaper toanalyze the inversekinematicsformotionplanning.

Thelinewalkingcycleofthelinewalkingrobotiscomposedofasinglesupportphaseandadoublesupportphase.

Locomotion of the linewalking robot is discussed in details and the obstaclenavigation process is planed

accordingto

the

structure

of

power

transmission

line.

To

fulfill

the

demands

of

line

walking,

acontrol

system

and

trajectoriesgenerationmethod are designedfor theprototype of the linewalking robot.Thefeasibility of this

conceptisthenconfirmedbyperformingexperimentswithasimulatedlineenvironment.

Keywords:Bipedlinewalkingrobot,Singlesupportphase,Doublesupportphase,Obstaclenavigation1.IntroductionThepurposeofpowertransmissionlineinspectiontaskis

tocheck therunningstateandfind thedamagesofhigh

voltagepowertransmissionlinesequipments.Uptonow,

power transmission lines equipments are mainly

inspectedmanuallybyworkerswith a telescope on the

ground.Theseworkingmodeshavemanydisadvantages,

such as long inspection cycle, high working intensity,

hugeexpenseandhighdanger.Performingtheinspection

by helicopters, as another method, is more efficient

comparedtomanuallyoperation,butitismoreexpensive

and climatedependent. Since the early 1990s, many

researchers have investigated in the development of

inspectionrobotstoassistpeopleortoreplacepeopleon

powertransmissionlinesite.

As illustrated in figure1, despite the tension conductor

therearesomeaffiliatedpowerfittings,suchasdamper

weights, suspension clamps, installed on the power

transmission line system. Thus, although the best

approachto

locomotion,

considering

power

consumption

andspeeddisplacement,isrollingontheconductor,high

degreeofmobility shouldbe added to the linewalking

robottoovercome thosepowerfittingsasobstacles.One

commonapproachtolinewalkingrobotforfulfillpower

transmissionlineinspectiontaskusesaconventionalrail

wheeled vehiclewith the addition of a device that can

overcome obstacles on the line. A wheeled trolley

(Sawada,J.et.al.,1991)thatcarriesanarcshapedrailwas

developedby Sawada and his group. By extending the

rail toeither sideof the tower thebodyof robot canbe

carried to theother sideofobstacles.LineScout (Pouliot

andMontambault,

2008),

aline

walking

robot

developed

at HydroQuebecs research institute (IREQ), is a

platformcancrossobstaclesbydeployinga twogripper

auxiliaryframeunder thecableandsecuringagraspon

bothsidesoftheobstacle.Thetractionwheelscanthenbe

releasedfromtheconductor,flippeddown,andmovedto

theothersideoftheobstacle.

Fig.1.Structureofpowertransmissionline

Generally, robots with structure mentioned above are

relativelyheavy since thewheeled systemandobstacle

navigation device are developed separately.Articulated

legwheel systems,with compact configuration, help to

provide enhanced locomotion capabilities on uneven

terrain, thus legged structureswith twoormorewheels

are

predominant

in

the

development

of

power

transmission line inspection robot nowadays. The

principalreasonforarticulationsistoenabletherobotto

accommodate and overcome most obstacles by

permitting the correspond wheel to rise up when it

collides with the obstacle. Tribrachiation mobile robots

(Tang, L.; et. al., 2004), (Liang, Z.; et. al., 2005),

(Nayyerloo, M.; et. al., 2008), with multidegreeof

freedom structure, allow a minimum of two traction

wheelstobesecuredtothecable.Technically,morethan

two legsprovide redundant support and often increase

theloadcapacityandsafety.However,thesebenefitsare

achieved at the cost of increased complexity, size, and

weight.As

aresult,

the

biped

is

the

most

common

congiguration of power transmission line inspection

tower

power transmission line clampdamper-weight


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InternationalJournalofAdvancedRoboticSystems,Vol.7,No.4(2010)

40

robotstudiednowadayssinceitrequiresminimumjoints

andactuators toprovide locomotion.Thechallenge is to

provide adaptability to such robots so that they may

surmountavarietyofobstaclesusinglimitedresources.

Due to the unpredictable environment of power

transmission grids, the linewalking robot is unable to

movereliably

at

fast

speed,

thus

the

gravity

force

plays

a

dominantrole inrobotdynamicswhen therobotmoves

on the power transmission line. During the obstacle

navigation process, likebiped robot for groundmotion

(Shih,C.&Gruver,W.1992),walkingof line inspection

robot isaperiodicphenomena, the locomotionofbiped

robot can be divided into singlesupported phase and

doublesupported phase respectively (Wang, L.; et. al.,

2009).Inordertoassistandobtainastablemotioninthe

singlesupported phase it is important to either anchor

thesupportingarm to the linewithgripper toresist the

gravity or control the total center of gravity position

beneaththe

supporting

arm.

Dual

arm

robots

(Wang,

L.;

et. al., 2006), (Cai, L.; et. al., 2008) with weight central

adjustment system were designed, and the

counterweights,whichgenerallycontainingelectricaland

electronic components, can be shifted forward or

backwardtocenterthemassoneitherofthetwoarms,by

which the robot ishanging to keep thehorizonposeof

thebodyandprotectthelineagainstthegrippingforces.

Due to additional counterweight system, obstacle

navigationprocessof those robots is complexand time

consuming.Expliner(Debenest,P.;et.al.,2008)isanother

type twoarm vehicle for power transmission line

inspection,

by

transferring

a

fair

amount

of

its

weight

beneath thesupportingarm theotherarmcanbe raised

andpivotedtotheothersideoftheobstacles.Thisrobot

haspotentialtoovercomeobstacleswithincomparatively

fewer steps since the rising locomotion of arm canbe

realized by adjusting center gravity position properly

alone. But inherently requires a large space for the

locomotion of counterweight,which results in the less

compactconfiguration.

Thelinewalkingrobotpresentedisintendedtoprovidea

novelmechanismforpower transmission line inspection

purpose. It featuresabiped structureand is supported

bytwofeet.Eachlegoftherobothasaprismaticjointto

adjustthelengthofthelegandthecentroidofthelegcanbe adjusted to the axis of the hip joint to reduce the

energy consumption related to gravity.The structureof

this paper is as follows. Section 2 describes the

mechanismof thebipedrobotand itskinematicsmodel;

section3describesthekinematicsanddynamicsmodelof

therobot.Locomotionstridesoftherobotareproposedin

section 4. Robot control and trajectories generation are

presented in section 5 for subsequent evaluation of the

linewalkingmechanism.Theexperiment ispresentedin

detail in section 6; finally section 7 presents the

conclusion.

2.MechanicalSystem2.1.Mechanismoflinewalkingrobot

Thelinewalkingrobotisdesignedasabipedrobotandit

is supported by two feet which can hold the power

transmission lines.Bothof the feetcanbeputonorput

offline

by

the

multi

articular

movement

of

the

robot

and

with thealternativefootmovement therobotcanrealize

linewalking locomotion. The mechanism of the line

walking robot is showed in Figure 2. The robot is

composed of three segments: leg,waist andbody.Each

legof theLWR is composedofonepitchjoint,one roll

joint and one prismaticjoint. Pitchjoint and rolljoint

providesteeringcapabilityofthefeetrelativetoleg,and

byadjustinganglesof thejoints therobotcanadapt the

feet totheorientationofline.Theprismaticjointsenable

therobottoexpendorcontractitslegs.Theslideblocksof

the two legs are connectedby a rotationjointthe hip

articulationand

the

angle

of

this

joint

together

with

the

lengthofthetwolegsdeterminethegaitoftherobot.

Fig.2.3DModelofthebipedlinewalkingrobot

2.2.KinematicsModel

Basedonthemorphologyofthebipedrobot,atleastone

foot must remain in contact with the line all the time.

Hence,robotkinematicsmodeling isestablished relative

tothe

supporting

foot.

Since

the

robot

features

a

symmetry structure, there is no difference between

attaching coordinate frame to the left foot or the right

foot.Herethestartfootcoordinateframeisattachedto

theleftfoot,whichisanchoredontheline.Therightfoot

can move freely and is described as the end foot

coordinate frame. Figure.3 illustrates coordinate frame

assignment. DenavitHartenberg notation is used to

define the link parameters that are indicated in Table.1

whenleftfootanchoresontheline.

Left yaw

Left pitch

Left prismatic

Hip rotation

Power transmission line

Feet

Right yaw

Right pitch

Right prismatic

Screws


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LudanWang,FeiLiu,ShaoqiangXu,ZhenWang,ShengChengandJianweiZhang:Design,ModelingandControlofaBipedLineWalkingRobot

41

Motionjoint 1ia 1i id i

Leftpitch 0 0 0 1

Leftyaw 0 2 0 2

Leftprismatic 0 0 d3 0

Hiprotation

0

2 04

Rightprismatic 0 2 d5 0

Rightyaw 0 0 0 6

Rightpitch 0 2 0 7

Table1.LinkDHParameters

Fig.3.Coordinateframesoflinewalkingrobot

Parameters1

,2

, 3d , 4 , 5d , 6 , 7 are controlled

variablesandnotethat 1

where isaconstant

which represent the title angle of the line and is

variableofleftpitchjoint.

Inthe

single

support

phase,

the

mechanism

of

the

line

walking robot formsanopenkinematicschain.And the

final robot transformation matrix can be written as

follows:

1000

1000

0

7

zzzz

yyyy

xxxx

pasn

pasn

pasn

pasnT (1)

The forward kinematics of the robot is derived in the

equationsetsasfollows:

542

62642

742762642

742762642

31541421

621641421

7621641421741421

7621641421741421

31541421

621641421

7621641421741421

7414217621641421

dssp

ccscsa

csssscccss

ssscscccsn

dcdccscsp

csssscccsa

sssscscccscccscss

cssscscccssccscsn

dsdcssccp

cscsssccca

sssccsscccccssccs

scsscccssccsscccn

z

z

z

z

y

y

y

y

x

x

x

x

(2)

In thedoublesupportphase forward kinematics canbe

determinedsimilarly.

3.DynamicsandInversKinematics3.1.Dynamicsmodel

Inamatrix

form,

the

robot

dynamics

can

be

expressed

as

tqGtqtqhtqtqDtF ,

Where tq , tq , tq are 1n vectors of generalized

jointvariable,velocity,andacceleration,respectively.

Inpracticalsituation, the linewalkingrobot isunable to

move at fast speed. Therefore, the accelerationrelated

inertia matrix tqD and the velocityrelated Coriolis

and centrifugal force vector tqtqh , are neglectable.

Thegravitationeffectsofthelinksplayadominantrolein

robot

dynamics.

When

the

right

foot

of

line

walking

robotfixedonaline,wehavetheelementsofthegravity

term 7654321

,,,,,, gggggggqG are

0

0

7

6

414217655

41421557654

1765433

421576552

4142155765

13765431

g

g

scccsgmmmg

scccslmdmmmg

gcmmmmmg

ssgsdmmmhmg

csscclmdmmm

gsdmmmmhmg

(3)

Where:iic cos ; iis sin im is the mass of link i ,

lis the distancebetween yawjoint and the centroid of

prismaticjoint.

As shown in figure.4, the linewalking robot forms as a

plain fivelink close chainRPRPRmechanismwith two

freedomofdegreesinthedoublesupportedphasewhen

walkingonaline.Thetwoprismaticjointsareselectedto

determinethelocomotionofthedoublesupportedphase,

byusingLEmethodthedynamicmodeloftherobotcan

bederived

as

afunction

of

the

trajectories

of

the

two

prismaticjoints,andthegravitytermasfollows.

3513

2

5

2

3

22

5755

5375

2

3

2

5

22

3133

tan2

1

2tan2

1

tan2

1

2tan2

1

dldglm

dldldglmg

dldglm

dldldglmg

S

SS

S

SS

(4)

WhereSl isthestepsize.


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42

3.2.InverseKinematics

Inverse kinematics canbeused to obtainjoint variables

with a known configuration of start and end foot

placements. By applying standard algebraic and

trigonometric techniques to the forward kinematics, the

joint variable can be found as a function of end foot

coordinates.In

order

to

minimize

the

influence

of

gravity

andreducethedriventorqueduringthewalkingprocess,

jointsvariablesaredeterminedaccordingtotheelements

of thegravity term in thedynamicequation.By solving

equation 01g and 0

4g wehave:

76555

10

mmmhmd

(5)

Byplungingaboveeq5totheforwardkinematics

equation(2)jointvariablescanbefoundusing

42

1

7

4

1

6

76555

52

1

4

543

1

2

1

2sin

sin

sin

tan0

sssn

sa

mmmhmd

dsp

dcpd

pp

zz

y

z

y

xz

(6)

Whichareall functionsofdesired location.Similarjoint

variables solutions are obtained in the right foot

supported phase,but using the right foot as a ground

reference.

Fig.4.Closechainstructureindoublesupportphase

During the doublesupport phase, both feet have line

contact,thusformaplanarfivebarmechanismwithtwo

DOFs as shown in Figure .4.As shown in figure 5,by

solving the triangle form equationwe can get thejoint

displacementof 3d , 4 and 5d asfollows:

sin2

2arccos

sin2

15

22

55

53

22

5

2

34

3

22

33

kk

kk

dxlxldd

ddldd

xdxdd

(7)

Where

is

the

inclination

angle

of

the

line.

As

shown

in

Figure5(thesubscriptskandk+1representstartingstage

andendingstage respectively),with forwardkinematics

equation we can get other joints displacements as

follows:

2

62642

2

4

2

2

626422

7

4116

542

2

3545

2

4

2

2

42354

1

arcsin

sincossinarcsinarcsin

arcsin

scccsss

sscccsns

aadsp

ddcdsc

scpddcp

zz

yx

z

yx

(8)

dk

d kd k+1

d k+1

d

d

x

Fig.5.Closechainstructureindoublesupportphase

4.LocomotionAnalysisThewayinwhichwalkinglocomotionisimplementedin

linewalking robot isbased on so called staticwalking.

Basedonthemorphologyofthebipedlinewalkingrobot,

at leastone footmustremain incontactwith the lineall

the time, thus a walking cycle can be realized by

combining

single

supported

phase

and

double

supported

phasealternatively.Whilebothof the twofeetareon the

line in the doublesupported phase, only one foot is

stationary on the line in the singlesupportedphase. This

bipedrobotcanactuallypropelitselfusingseveraltypes

of locomotion strides. These are classifiedbased on the

type of swingfoot motion, the flipping stride and

crawling stride, which are derived from alternative

crossingand inchwormmotion,respectively.Bothof the

flipping stride and crawling stride are achieved by

anchoring one foot to the line and swinging the other

foot, the differencebetween the two strides is that the

swinging foot will stride over the fixed foot in the

flippingphase and the rear foot is changed to the front

foot, while in the crawling phase position of the

corresponding foot will be controlled to reduce or

increase the distance between the two feet like an

inchwormwhichmeans therear footalwaysbe therear

foot.

4.1.FlipperStride

Asmentionedabove,flippingstridecanbe dividedinto

singlesupportedphaseanddoublesupportedphaseshown in

Figure6.Assumingthattherobotisinitiallyinthedouble

supportedphaseandbothofthecentralgravitiesofthetwo

legslocate

at

the

right

leg.

During

the

single

supported

phase, the right leg keeps sticking on the line vertically


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43

and theswing foot is liftedand flippedfrom therear to

the front of the fixing foot. The following sequence of

motion canbe executed thatwould result in the robot

movingforward.

a. Contract rightprismaticjoint tomake sure that therightfootcouldcrosstherightfoot.

b. Rotatehipjointangletomove leftfootfromLF2toLF3, as determinedby eq.(6) and rotate left pitch

joint to angle which will provide correct left foot

orientation.

c. Expand rightprismaticjoint toplace the left footatLF4

With the completion of this section, the left foot of the

robot has moved forward distance in straight line. A

doublesupported phase then follows the singlesupported

phasetoadjustthecenterofgravityfromtherightfootto

theleftfootwhichisessentialtostartthefollowingsingle

supportedphase.Adjusting isachievedbyperforming the

followingsequence

and

is

illustrated

in

figure

6.

54

5

54

4

2-3

1-4

Fig.6.FlipperStride

d. Expand right prismatic joint and contract leftprismaticjointtoadjustthecenterofgravitiesofthe

two legs from the right leg to the left legandmake

sure the left leg is vertical, at the same time, three

joints:Ryawjoint,Lyawjointandhipjointshould

rotateat thesame time tokeep theorientationsand

positionofthetwofootfixed,asdeterminedbyeq6.

The robot is now again in the beginning of single

supportedphase.

4.2.CrawlingStride

The flipper model of locomotion requires considerable

space,makingitstraveldifficultinconfinedspace.Hence

a walking stride with crawling motion of the robot is

performedusingsignificantlylessspaceabovetherobot.

Thisstrideiscalledcrawlingstride.Thecrawlingstrideis

achieved primarilyby themotion of the swinging foot

along the line without crossing the sticking foot. The

followingsequenceofactionsprovidethecrawlingstride.

Assuming that the robot is initiallyat theendofdouble

supportedphase,

and

is

supported

at

RF

1,

the

robot

must

performthefollowingprocess.

a. Expand the right prismaticjoint and rotate the hipjointtomovetheleftfootalongthelinefromLF1to

LF2, at the same time the leftyawjoint shouldbe

rotatedtoprovidethecorrectorientationofleftfoot.

b. Expand right prismatic joint and contract leftprismaticjointtoadjustthecenterofgravitiesofthe

twolegs

from

the

right

leg

to

the

left

leg

and

make

sure the left leg is vertical, at the same time, three

joints:Ryawjoint,Lyawjointandhipjointshould


positionofthetwofootfixed.

c. Expand the left prismatic joint and rotate the hipjointtomovetherightfootalongthelinefromRF2

toRF3,atthesametimetheleftrightjointshouldbe

rotated to provide the correct orientation of right

foot.

d. Contract right prismatic joint and expand leftprismaticjointtoadjustthecenterofgravitiesofthe

twolegs

from

the

left

leg

to

the

right

leg

and

make

sure theright leg isvertical,at thesame time, three

joints:Lyawjoint,Ryawjointandhipjointshould


positionofthetwofootfixed.

e. Therobotisnowagainintheinitialmode.

Fig.7.CrawlingStride

Figure 7 conceptually describes how the proposed gait

patternworks.Withthecompletionofthissequence,the

rightand left feethavemoved forward indistance.The

robotcouldsimilarlyrepeatthestepinreverseorderand

move in reverse direction. Since the robot requires

significantly less vertical space, the crawling stride is

adaptedformoreconfinedenvironments,butataslower

paceowingtodecreasedsteplength.

4.3.CrossingBetweenCrossLine

Totraversebetweentwocrossedlinesinhorizontalplane,

rotationofthetwopitchjointsmustbeconsideredtoadapt

theorientationofthefeettothelines.Alsotheprocesscan

be realizedby thealternatingof thesinglesupportedphase

and doublesupported phase, and either the flipping or

crawling stridecanbeused.Thedifference is thatbefore

step c in the flipping and crawling stride, the rightpitch

jointshould

rotate

to

adjust

the

position

of

the

left

foot

to

the targetplace that isabove thecrossed lineand the left


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44

pitchand leftyawjoints rotate toprovidecorrected left

footorientation.Thefollowingstepsaresimilar.

4.4.ObstacleNavigation

Accordingtothestructureofthepowertransmissionline

system obstacles canbe divided into two types: lower

obstacleslike

counter

weight

and

higher

obstacles

like

clamps. For lower obstacles, obstaclenavigation canbe

realizedduringtheprocessofflipperstride,asshownin

figure1.4,andtheonlythingthatshouldbepayattention

to is to contract the prismaticjoint of the sticking leg

enoughinstep(a)tomakesurethattheleftfootcanpass

over the obstacle in step (b). While for the higher

obstaclessuchasclamps,theswingingfootcannotstride

overitthusbeforestep(c)intheflippingstride,theright

pitchjointshouldberotatetoavoidtheobstacleandafter

step (c) the right pitch joint should be rotated to the

inverse direction to set the foot on the line. Figure 9

illustratethe

difference

of

obstacle

navigation

process

whenencounteranhigherobstacle.

obstacle

Fig.8Obstaclenavigationprocessoflowerobstacles

obstacleobstacle

Fig.9Obstaclenavigationprocessofhigherobstacles

The walking steplength of the linewalking robot is

determinedby the geometry size of the robot and the

inclinationangleof theline that therobotiswalkingon.

Suppose the inclination angle is as shown in Figure

9.a, by applying standard algebraic and trigonometric

techniques the steplength of the robot can be found

using

sincos 22staticstaticswingUp

dddstep (9)

sincos 22sticstickswingDown

dddstep (10)

SinceUpDown

stepstep and the steplength is a constant

inthedoublesupportedphase,thesteplengthis

sincos 22sticsticswing

dddstep (11)

Tostick

d value equation (10) is a monotone decreasing

function andswing

d is a constant (determinedby eq. 5),

thusthesteplengthgetthemaximalvaluewhenstick

d is

theminimum.

sincosmin

2

min

2

max sticsticswingdddstep (12)

5.RobotControl5.1.RealizedDevices

Therobotconsistsoftwolegscoupledwitharotatejoint.

Each leghasaprismaticjointand two rotatejoints.The

combinationofDCservomotorandballscrewischosen

for the prismaticjoint. The dimension of the prototype

robot is approximately 800mm high and 100mm wide

whenallthejointsareinthezeroposition.Themaximum

lengthofthetowerobstaclesthattherobotcanovercome

is 300mm, and the minimum cross angle of the

suspensionangletoweris120degrees.

The biped linewalking robot is controlled by an

industrialPC.

The

driver

module

is

based

on

the

TMS320F2812digitalsignalprocessorchipfromTI.Each

DSPcontrollerhastwobuiltinquadratureencoderpulse

(QEP)circuitstoreadtheencoderoftheservomotor,thus

with each chip, twomotors canbe controlledwith the

encoder feedback.The total servomotornumber of the

linewalking robot is 7, which means at least 4 driver

modulesareneeded.ThecontrolprogramiswritteninC

languageandtheservofrequencyis1KHz.

Asthegravityeffectsaredeterminedbytheconfiguration

ofall the robot linksandplay adominant role in robot

dynamic model. In order to compensate for gravity

effects,

we

can

pre

compute

these

torque

values

based

on

thedesiredtrajectoryandfeedthecomputedtorquesinto

thecontrollertominimizetheeffects.

5.2.TrajectoriesGeneration

A quintic polynomial specifying the joint position, q ,

velocity, q , and acceleration, q , at thebeginning and

theendofthepathsegmentisusedtogenerateasmooth

trajectorywithoutjerk.A fifthorderpolynomial is thus

used

tatatatataatq 5

4

4

3

3

2

210

Where 0 ttt , and 0t is the start time of thetrajectory. Constraints on the polynomial are imposed


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45

using initial and final values of position, velocity, and

acceleration. As time to complete the joint motion

decreases, the velocity and acceleration required to

achieve the desired final position increases. Hence the

final time,ft , of a joint trajectory is limited by the

maximum torque that the corresponding motor can

sustain at a specified speed. Figure 10 shows thejoint

position trajectories in flipping stride with final times

requiredtocompleterespectivejointresponses.

It should be mentioned that in order to reduce the

complexities of the controller only the two prismatic

jointsareactivelycontrolledinthedoublesupportphase

and theangleofhipjoint is lockedasaconstant,which

means, according to the geometry technology, the hip

joint ismovedon thecircumcircleof RLO asshown in

figure11.Thus,asshowninfigure12,duringthedouble

supportphasethedisplacementofhipjointisaconstant

value, and only the two prismatic joints need to be

controledto

track

the

caculated

trajectories

as

the

two

yawjointscanbetreatedaspassivejoints.

0 5 10 15 20150

200

250

300

time/s

displacement/mm

right prismatic joint

left prismatic joint

0 5 10 15 20-60

-40

-20

0

20

40

60

80

time/s

displacement/deg

right yawleft yaw

hip joint

Fig.10.Tajectoriesofawalkingcycle(onesinglesupport

phaseandonedoublesupportphase)

4

5

Fig.11.Optimizeddoublesupportphaseadjustment

0 2 4 6 8 10 12 14 16 18 20150

200

250

300

time/s

displacement/mm

right prismatic joint

left prismatic joint

0 2 4 6 8 10 12 14 16 18 20-60

-40

-20

0

20

40

60

80

time/s

displacement/deg

right yaw

left yaw

hip joint

Fig.12.Tajectoriesofawalkingcycle(onesinglesupport

phaseandonedoublesupportphase,optimized)

6.ExperimentsExperimentswereconductedtoverifythemechanismof

thebipedlinewalkingrobotdevelopedinthisstudy.

(a) (b)

(c) (d)

Fig.13.Picturesoflinewalkingprocess

AsshowninFigure.13,thelinewalkingrobotwashung

from the simulation line, and the experiments were

executed in two steps: firstly, theCoMof the robotwas

locatedattheleftleg,withtheposeadjustmentindouble

supportphasetheCoMwasadjustedtotherightleg,and

theleft

leg

was

lifted

by

the

contraction

of

right

prismatic

joint, finallywith the rotation of hipjoint left leg was


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46

swung from rear to front to realize onewalking cycle.

Figure 14 shows the process of obstacle navigation of

relative lowobstacle (damperweight), and the stride is

notdifferentfromtheflipperstrideexceptthattheswung

legistherightleg.

(a) (b)

(c) (d)

Fig.14.Picturesofobstaclenavigation(damperweight)

Figure15showspartoftheobstaclenavigationprocessof

relative high obstacle (single clamp), during which the

right pitchjoint needs tobe rotated forth andback to

makesurethatthelegcankeepawayfromobstacles.

(a) (b)

Fig.15.Picturesofobstaclenavigation(singleclamp)

7.ConclusionAbipedmechanism,whichisappliedinthedesigningof

robots for the inspection ofpower transmission lines is

proposed in this paper. The novel mechanism design

enablesthe

centroid

of

the

robot

to

be

concentrated

on

the

hipjointtominimizethedrivetoqueofthehipjointand

keep the robot stable during the singlesupport phase.

The forward and inverse kinematics equations were

proposed for trajectory generation, anddynamicmodel

wasestablishedforlocomotionplanning.Aprototypeof

power transmission line inspectionrobotwasdeveloped

based on this mechanism and experiments showed its

validity. Future work should focus on inclusion line

detectingsensor,

on

board

control,

and

evaluation

of

the

robot in realpower transmission line environmentwith

obstacles.

8.ReferencesCai, L.; Liang, Z.; Hou, Z.G.& Tan,M. (2008). Fuzzy

controloftheinspectionrobotforobstaclenegotiation,

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Hirose,S.;

Tamara,

K.;

Kimura,

A.;

Kubokawa,

H.;

Iwama, N. & Shiga, F. (2008). ExplinerRobot for

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Liang, Z.; Li, E.; Tan, M.; Liu, G. & Rees, D. (2005)

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Documents

Design, Modeling and Control of a Biped Line-walking Robot