Street, Cambridge, CB23EJ, UK Zoology, Cambridge, Downing of University of *Present address:Department University, OR97331,USA. Hall,Corvallis, 204Rogers Hatfield, Hertfordshire AL97TA,Hatfield, Hertfordshire UK. 3786 Received 15January 2014;Accepted25August2014 attributed. use, distribution andreproductioninany mediumprovided that isproperly theoriginalwork Attribution License(http://creativecommons.org/licenses/by/3.0), unrestricted permits which theCreative Commons of distributed undertheterms This isanOpenAccessarticle § ‡ 1 terrain environments(Alexanderetal.,1979;Birn-Jeffery and ostriches, movewithspeedandeconomythroughcomplexnatural million yearstotheropoddinosaurs.Groundbirds,suchasquail and equally beascribedtoaheritageofbipedalagilitytracingback 230 Modern birdsuccessiscommonlyattributedtoflight,but could avoidance, Trajectory optimisation KEY WORDS:Bipedalrunning,Gaitstability, Groundbirds,Injury achieved throughappropriatelytunedintrinsicdynamics. safety asthedirectimperativesofcontrol,withadequatestability ground birdstargetthecloselycoupledprioritiesofeconomyandleg key priorityonbothlevelanduneventerrain.We suggestthatrunning features ofavianbipedallocomotion,andsuggestseconomyasa conditions. We presentasimplestancelegmodelthatexplainskey dependent actuationtoaddorremoveenergydependingonlanding patterns, involvingasymmetricforce–lengthtrajectoriesandposture- times leglength.Allspeciesusedsimilarstanceactuation body weightsoflevelrunningforobstacleheightsfrom0.1to0.5 remained remarkablyconsistentacrossobstacleterrain,within0.35 multiple steps,notdirectlyprioritisingbodystability. Peaklegforces dynamics tominimisefluctuationsinlegpostureandloadingacross a consistentobstaclenegotiationstrategy, involvingunsteadybody priorities divergewithsize.We foundthatallmeasuredspeciesused body size,butitremainsunknownwhethernon-steadylocomotor a shifttowardsstraighterlegsandstiffer steadygaitwithincreasing overcome size-relatedchallenges.Weight-support demandsleadto safety withincreasingbodysize,reflectinguseofactivecontrolto hypothesis thatcontrolprioritiesshiftbetweenbodystabilityandleg force–length dynamics(foreconomyandlegsafety).We alsotestthe stability (attenuatingdeviationsinbodymotion)andconsistentleg negotiate single-stepobstaclesthatcreateaconflictbetweenbody task-level controlprioritiesofcursorialbirdsbyanalysinghowthey 500-fold massrangefromquailtoostrich.Hereweinvestigatethe Cursorial groundbirdsareparagonsofbipedalrunningthatspana and MonicaA.Daley Aleksandra V. Birn-Jeffery safety andeconomyonuneventerrain Don’t breakaleg:runningbirdsfromquailtoostrichprioritiseleg RESEARCH ARTICLE © 2014.PublishedbyTheCompanyofBiologistsLtd|JournalExperimentalBiology(2014)217,3786-3796doi:10.1242/jeb.102640 INTRODUCTION ABSTRACT Author ([email protected]) for correspondence contributedThese equally tothiswork authors andMotionLaboratory,Structure Royal Veterinary College, Hawkshead Lane, 1,§ 2 Dynamic Robotics Laboratory, OregonState 1, * ,‡ , ChristianM.Hubicki 2,‡ , Yvonne Blum achieve stability isalsochallenging,because significant interplay to threesteps(DaleyandBiewener, 2011; JindrichandFull,2002). recovering fromunexpectedperturbations withinapproximatelytwo suggests thatrunninganimals doexhibitstablebodymotion, height (Blumetal.,2011; Geyeretal., 2005).Empiricalevidence been usedtoobservethedeviations ofthebodyCoMstatesatapex 2005; Seyfarthetal.,2003).Forexample,Poincarésections have al., 2007;Blumet2011; DingwellandKang,2007;Geyeretal., returning thebodyCoMtonominalperiodicgait(Blickhan et stability) focusonwhethergaitperturbationsdiminishover time, Mathematical analysesofbodystability(localorcyclicalasymptotic the looserdefinitionofgeneralstabilityas‘avoidingfalls’. body centreofmass(CoM)motionfromsteadygait,asopposed to have thepotentialtobekeyanddistinctpriorities. proximate causesoffalls,sobodystabilityandleginjuryavoidance (Verheyen etal.,2006). Thus,bothinstabilityandinjurycanbethe by musculoskeletalinjuryfromrepetitivehigh-stressloading because fallsincreaseriskofpredation.Yet, fallscanbepreceded potential asanultimatelyrelevantandgeneraldefinitionofstability, understood andchallengingtomeasure.‘Avoiding falls’ has the keycontrolprioritiesofanimals,yetstabilityremainspoorly to survive. behaviours, becauseanimalsmustavoidcatastrophicfallsandinjury sometimes shiftawayfromeconomy, particularlyinnon-steady environments (Nishikawaetal.,2007).Therefore,prioritiesmight locomotion islikelyrareinthecomplextopographiesofnatural and Taylor, 1990;SrinivasanandRuina,2006).Yet, steady suggesting economyasakeypriority(Cavagnaetal.,1977;Kram locomotion emerge fromminimisingmuscleworkandenergy cost, excessive legforces(Biewener, 1989).Manyfeaturesofsteady Biewener, 2006;JindrichandFull,2002),avoidinginjuryfrom (Birn-Jeffery andDaley, 2012;Carrieretal.,2001;Daleyand and Usherwood,2010),maintainingdesiredspeeddirection and Ruina,2006),avoidingfalls(ClarkHigham,2011; Daley energy cost(Cavagnaetal.,1977;Roberts1998a;Srinivasan sometimes conflicting,task-leveldemandsincludingminimising Running animalsmustcontroltheirlegstobalancenumerous, and (2)howdotheseprioritiesvarywithterrainbodysize? (1) whatarethetask-levellegcontrolprioritiesofrunninganimals; et al.,1998a). (Gatesy andBiewener, 1991;HutchinsonandGarcia,2002;Roberts striding bipedalismandhowthesedemandschangewithbodysize a naturalanimalmodelforunderstandingthefunctionaldemandsof extant bipeds,over500-foldfromquailtoostrich.Birdsthusprovide 2004). Theseathletesspanthebroadestbodymassrangeamong Daley, 2012;Dial,2003;Jindrich etal.,2007;Rubenson Pinpointing theunderlyingmechanisms usedbyanimalsto Here weuse‘bodystability’ toreferattenuatingdeviationsin The ideasabovesuggestthatlocomotorstabilitymightbeamong Here, weasktwoquestionsfundamentaltolocomotorbehaviour: 1 , DanielRenjewski 2 , JonathanW. Hurst 2

The Journal of Experimental Biology of locomotion, because costdependsonmuscle force(Kramand loading havesignificantimplications forthemetabolicenergy cost Biewener, 2011; McMahon etal.,1987).Changesinlegpostureand posture andmusculoskeletalgearing (Biewener, 1989;Daleyand posture demandsincreasedmuscle forcesbecauseofchangesinleg also minimisesexternalmechanical work.However, crouched to minimisedeviationsinbody trajectoryfromsteadygait,which shorten thelegtoaccommodateobstacle,usingposturechange force–length dynamics(Fig. trajectory (Fig. extremes: ‘crouching’,whichminimisesfluctuationsin body manoeuvres tonegotiateanobstaclefallbetweentwohypothetical musculoskeletal loadsandthusbotheconomylegsafety. Active regulate legpostureandloading,whichinfluence deviations inbodytrajectory)intodirectconflictwithdemands to single-step obstacleputsdemandsforbodystability(attenuating strategy, fromwhichwecaninfertask-levelcontrolpriorities.The 1),whichallowsthebirdstoplantheir single-step obstacle(Fig. contexts. steady CoMtrajectoryoverawiderangeofspeciesandterrain terrain conditions;thus,itremainsunclearwhetheranimalsprioritise terrain locomotionhasbeenstudiedinrelativelyfewanimalsand locomotion (SrinivasanandRuina,2006).Nonetheless,uneven external mechanicalwork,whichfactorsintotheenergy costof fluctuations inbodyCoMtrajectoryhasthepotentialtominimise Moritz andFarley, 2006;Yen etal.,2009).Additionally, minimising (Chang etal.,2009;Ferris1999;MoritzandFarley, 2003; that steadybodyCoMtrajectoryisadirecttarget ofneuralcontrol 2009; Yen etal.,2009).Thesefindingshaveledtothesuggestion while minimisingvarianceinbodyCoMtrajectory(Changetal., animals havebeenobservedtoallowvarianceinjointdynamics Farley, 2003;MoritzandFarley, 2006;Moritzetal.,2004),and(3) et al.,1999;Ferris1998;Grimmer2008;Moritzand use activemechanismstodosounder‘expected’ conditions(Ferris humans target steadybodyCoMtrajectoryonvariableterrain,and and Full,2002;MoritzFarley, 2003),(2)hoppingandrunning Farley etal.,1998;Ferris1999;Grimmer2008;Jindrich and recoverquicklytosteadygait(DaleyBiewener, 2006; that animalsminimisedeviationsfromsteadybodyCoMdynamics terrain: (1)previousperturbationexperimentshavedemonstrated actively target bodystabilityasacontrolpriority, evenonuneven steady gaitonceperturbed. body trajectory, andreactive responsestoreturnthebodytoward manoeuvres tominimisetheinitialeffects ofaterrainchangeon active control.Activemechanismsmayincludeanticipatory anticipated terrainchanges,oralsotarget bodystabilitythrough animals relyheavilyonintrinsicstabilitymechanismsevenfor control intervention.Yet, itremainsunknownwhetherrunning 2006; JindrichandFull,2002).Thisminimisestheneedforactive rapid recoveryfromsurpriseperturbations(DaleyandBiewener, stability mechanismstominimisegaitdisturbancesandfacilitate Full etal.,2002;JindrichandFull,2002).Animalsemployintrinsic short timeperiodbeforefeedbackispossible(Daleyetal.,2009; unexpected perturbation,toobservetheimmediateresponsein mechanisms canberevealedbysubjectingananimaltoasudden, dynamics withoutneuralfeedbackcontrol.Intrinsicstability intrinsic-dynamic stability, properties conferredbytheinherent control priority, adirectobjective oftheappliedactivecontrol,and control. Here,weconceptuallydistinguishbetweenstabilityasa occurs betweenintrinsicmusculoskeletaldynamicsandactiveneural RESEARCH ARTICLE Here westudyrunningdynamicsofbirdsnegotiatingavisible, There areseverallinesofevidencetosuggestthatanimalsmight

1A), and‘vaulting’,whichmaintainsconsistentleg

1B). Ina‘crouching’ strategy, birds and gravitationalpotentialenergy( in theobstacledismount[ energy ( trajectory ontheobstaclestep,butrequiresworktoincreasemechanical (B) Vaulting ontotheobstaclecanmaintaintypicallegpostureandbody muscle forcerequiredtosupportbodyweight,duealteredgearing. centre ofmass(CoM)trajectoryandmechanicalenergy, butwouldincrease obstacle couldallowconstantbodymotion,minimisingdeviationsin hypothetical referencepoints.(A)Adoptingacrouchedlegpostureonthe control priorities.Schematicillustrationofidealisedstrategies,as Fig. (0.22 obstacle negotiationbehaviouramongbirdsfrombobwhite quail body stabilityandlegsafetywithincreasingsize,wecompare control. of bodyCoMtrajectoryisadirectpriorityactivelocomotor this terrainperturbationallowsustotestthehypothesisthatstability force–length dynamics,foreffective gearingandlegsafety. Thus, ‘vaulting’ reflects aprioritytomaintainconsistentmusculoskeletal stabilise bodyCoMtrajectoryandminimiseexternalwork,whereas suggest thatagreaterdegreeof‘crouching’ reflectsapriorityto in legpostureandloading(Birn-Jeffery andDaley, 2012).We gait toraisebodyheightontotheobstacleandminimisefluctuations anticipation oftheobstacle(Fig. Ruina, 2006).Ina‘vaulting’ strategy, the bird launchesupwardsin Taylor, 1990;McMahonetal.,1987)andwork(Srinivasan in legpostureor loading[groundreactionforces (GRFs),legtouch- large animalsfaceaninherentlyhighriskofinjurybecause changes stresses (Biewener, 1989;GatesyandBiewener, 1991). Nonetheless, animals runwithstraighterlegs tominimisemuscleandbone sectional area(Biewener, 1989).To ameliorate thisproblem,large but strengthsofmusculoskeletal structuresincreasewithcross- strength oftheirlegsbecausepeak loadsincreasewithbodymass, terrain relativetotheirleglength.Large animalsarelimitedbythe animals arelessinjuryprone(Vogel, 1981),butlivein‘rougher’ injury becauseofhighmusculoskeletalstresses,whereas small inherent challengesofbodysize:large animalsareathighriskof behaviours mayreflectuseofactivecontroltoovercome the hypothesis isbasedontheideathatnon-steadylocomotor also possibletouseacombinationofmultiplestrategies. without anticipatoryadjustmentsisexchangebetweenkineticenergy( landing conditionsintheobstaclestep[ To alsotestthehypothesis that controlprioritiesshiftbetween

.Obstaclenegotiationstrategiesasa‘window’ intotask-level 1. C B A kg) toostrich(117 L E leg tot Energy exchangestrategy Vaulting strategy Crouched posturestrategy ) instep− The JournalofExperimentalBiology(2014)doi:10.1242/jeb.102640 1. (C)Anadditionalpossiblestrategythatcanoccur E +ΔE p → kg), spanninga500-foldmassrange.This E tot k (Birn-Jeffery andDaley, 2012)]orboth.Itis E p

). Thiscanoccurbecauseofaltered 1B), activelydeviatingfromsteady Δ

E E

k k ΔE → –ΔL E p (Daley andBiewener, 2011)], leg

p

Δ E

–ΔE

p

tot

Δ E k E 3787 k )

The Journal of Experimental Biology on theobstacleaccountingfor44%ofheight0.1 a consistentbalanceof‘vaulting’ and‘crouching’,withcrouching obstacle usingan‘energy-exchange’ strategy (step+1).Birdsused qualitatively similar tothedynamicsofbirds negotiatingan E Table angle, similarpeakforceand exchangeof The step+1dynamics,andin particularthesteeperlegcontact 3788 RESEARCH ARTICLE statistics. Peak forcesremainwithin0.35bodyweights(BW)oflevelgait(B;greyshadingindicates±0.5BW).SeesupplementarymaterialTables heightacrossspecies. grounded runningtrialsexcludedfromtheaveragetrajectories).Instep0,crouchingaccountsfor39±7%(mean±s.d.)ofobstacle (C) Changeinpotentialenergyperstepduringobstaclenegotiation.A data(walkingand andBshowagrandmeanacrossspeciesfortheaerialrunning obstacle, where posture (supplementarymaterialTables on theobstacle(step0),butwithasignificantlymorecrouched onto theobstacleinstep 2A),performingananticipatoryvault obstacle overthreesteps(Fig. used adynamicallysimilarbehaviour. Thebirdsnegotiatedthe Surprisingly, wediscoveredthatallspecies,regardlessofbodysize, in legpostureandpeakforces. large animalstoprioritiseleginjuryavoidance,minimisingchanges gait deviationstoagreaterdegreethanlarger animals.We expected would prioritisebodystability, usingposturalchangestominimise consequences ofscaling.We thereforepredictedthatsmallanimals priorities andmorphologymayhaveco-evolvedtoovercomethe priorities, morphologyandterrainconditions.We reasonthatcontrol and legpostureasawindowintotherelationshipbetweencontrol 1990). Thus,weaimtousethespectrumofgroundbirdbodysize variation (DaleyandUsherwood,2010;McMahonCheng, which allowssmoothbodymotionwithrobustnesstoterrain (flexed) legposture(Biewener, 1989;GatesyandBiewener, 1991), safety factorlimits.Incontrast,smallanimalsrunwithcrouched down collisions]couldincreasemuscleandbonestressesbeyond consistent combinationofvaultingontotheobstacle(step Fig. during stance( infcnl cosseis(i.3;supplementarymaterialTable significantly acrossspecies(Fig. gravitational potentialenergy, with asteeperlegangle,avoiding highpeakforcesandconverting ‘step 0’).Intheobstacledismount (step+1;Fig. RESULTS k B A (step +1). (A) Dynamics illustrated by velocity vectors (arrows), CoM position (balls) and leg posture (stick figures). (B) Ground reaction force(GRF). (step +1).(A)Dynamicsillustratedbyvelocityvectors(arrows),CoMposition(balls)andlegposture(stickfigures).(B)Ground

.Observedobstaclenegotiationstrategy. 2. GRF (body weights) 0 1 2 3

S2, 0 0.1 0.2 0.3 0.4 0.5L H leg TD , levelversusstep0=–0.044),whichdidnotdiffer Step –1 Δ L E 0.5 leg p , is nominalleglength(supplementarymaterial Δ E k − ; supplementarymaterialTables 1, maintaininganearlysymmetricstance 1.0 E p 0 , toforwardkineticenergy, Fraction ofstance

S2, S5),anddismountingthe Step 0 Ground birdsfrombobwhitequailtoostrichusesimilardynamicsnegotiateobstacles,reflectinga 0.5 E p to forwardE 2A), birdslanded − 1), somecrouchingontheobstacle(step0)andenergyexchangeindismount,converting 1.0

S2, S5). 0 Δ k

L , is S3, E leg k , Step +1 0.5 ( Fig. body dynamics(Fig. postural changeduringobstaclenegotiationtominimisein Biewener, 1991).Yet, smallbirdsdidnotmakegreater useof gait (Fig. more ‘crouched’ posturesonaverageduringtheirnominalsteady Materials andmethodsforcalculation).Smallbirdsdidrunwith based onbodymass,gravityandisometricleglengthscaling(see similarly acrossspecies,oncenormalisedtodimensionlessquantities Daley andBiewener, 2006). unexpected potholeoravisibledownwardstep(Blumetal.,2014; trajectory. birds didnotmake greateruseofposturalchangesto stabilisebody a similarrangeofpostureinuneven terrain.Contrarytopredictions,small differences amongspeciesinlegpostureduringsteadygait, allspeciesused and Biewener, 1991),measuredatmid-stanceduringrunning.Despite the ratioofhipheighttosum hindlimbsegmentlengths(Gatesy L leg Deviations fromsteadygaitduringobstaclenegotiationscaled

) obstacleterrain. .Scaling oflegpostureinleveland0.1timesnominallength 3. Posture index (Lleg/ΣLsegs)

3), consistentwithpreviousfindings(Gatesyand 1.0 The JournalofExperimentalBiology(2014)doi:10.1242/jeb.102640

L C –0.2 ∆EP (J/mg leg) 0.4 0.6 0.8 0.2 0.4 0 Leg postureismeasuredasa‘posture index’ equalto

3). We observednosignificanttrendswith . . 0100 10 1.0 0.1 Quail 0 0.1 Ostrich Turkey Guinea fowl Pheasant Bobwhite quail Guinea Pheasant fowl Obstacle height/L Body mass(kg)

0.2 Level Turkey

0.3 tp– tp0Step+1 Step0 Step –1

S1–S6 fordetailed leg

0.4 Ostrich

0.5 Step –1 Step 0 Step +1 E p to

The Journal of Experimental Biology material Table (mean ±s.d.)ofobstacleheightacrossconditions(supplementary consistent withincreasingobstacleheight,accountingfor39±7% level controlpriority. and Usherwood,2010),thisdoesnotimplybodystabilityasatask- provide intrinsicstabilityagainstunexpecteddisturbances(Daley size. Thus,althoughthecrouchedpostureofsmallanimalsmay hypothesis thatactivecontrolprioritiesshiftsignificantlywithbody material Tables Tables quail andotherspecies(supplementary materialTables during thepre-obstaclestepdidnotsignificantlydiffer between (supplementary materialTable and werestatisticallysignificantforobstacleheights0.2–0.5 occurred instep (supplementary materialTable body sizeonobstaclenegotiationstrategy(Fig. extension withobstacleheight.Quaildidnotdiffer significantlyfromotherspeciesinthemagnitudeof a similartrendofincreasingleg stance increaseswithobstacleheight,acrossspecies.Althoughquailexhibitgreatervariationinlegextension,they Fig. − RESEARCH ARTICLE (supplementary materialTable dynamics didincreaseinmagnitudewithobstacleheight of legstiffness and/orgreateruseofrotational legactuation. complex factorsinthemostcrouched species,suchasnonlinearity dynamics. Thevarianceinquail legtrajectorysuggestsmore angular trajectories,butnota significant difference inbody CoM appears toreflecthigherco-variance betweenleglengthand in theleglengthtrajectory(Fig. (Fig. increasing forceandlegextensionduringthelatterhalfofstance obstacle terrain,thevaultingbehaviourinstep 4).In profile correspondingtotheasymmetryin force (Fig. through legextensionduringunloading,withanasymmetric actuation trendsacrossterrainsandspecies.Birdsaddedenergy level terrain),withpeakGRFat20–45%ofstance(Fig. in theGRFwasapparentacrossspeciesandconditions(including unloading phase,orsecondhalfofstance.A pronouncedasymmetry Force profilesdeviatedfromthelevelterraintrajectoryin profiles retainedaprofilesimilartothatobservedonlevelterrain. level mean,evenduringnegotiationofobstaclesupto0.5 (Fig. possible priorities,suchasinjuryavoidanceandenergy economy. analysis belowoninterpretingthedatawithrespecttoalternative influence ofcompetingdemands.Consequently, wefocusour as adominantcontrolpriority, andinsteadappearstoreflectthe (Fig. breakpoint orshiftinstrategywithincreasingobstacleheight between ‘vaulting’ and‘crouching’ strategies,withnoevidenceofa 1, Across species,thedegreeofcrouchingonobstacleremained In additiontoconsistentlegforces,weobservedsimilar leg Force trajectoriesremainremarkablysimilartolevelrunning

.Virtual leglengthtrajectoriesforeachspeciesmeasuredinthepre-obstaclestep(step 4. Δ 2C). Theobservedbehaviourisinconsistentwithbodystability 2B, Fig. 2B), withpeakGRFwithin0.35bodyweights(BW)ofthe

E S3, S6),sothedifference inlegtrajectoryreflectsgreaterco-varianceangleandlength,notadifferencebody dynamics. inoverall Leg length (L/LTD) P 0.6 1.0 1.4 ). Instead,thevarianceinleg lengthtrajectoryinquail 0 4). Quailexhibitedmorevariancethanotherspecies

S5, step0,H 0.1 0.2 0.3 0.4 0.5L

− S1–S6). Theevidencethereforerefutesthe 1, duringtheanticipatorymanoeuvre(Fig. leg Quail 0.5 TD

). Deviationsinlegpostureandbody S5), butreflectedaconsistentbalance

S5). Thelargest shiftsinpeakforce 1.0 S5). Theloadingphaseoftheforce

4). Yet, the netchangein 1.0 0 Pheasant 0.5 −

2C; supplementary 1 wasachievedby

S3, S6,step

1.0 2B). 1.0 0

2B), L L Fraction ofstance E leg leg p Guinea fowl 0.5 work actuationcouldreplicatetheobservedforceandleg-length economy oflocomotion,wetestedwhetheramodelwithminimum- for obstaclenegotiation. 500-fold rangeinbodymassemploysimilarlegactuationstrategies posture-dependent actuation.Thus,wefindthatspeciesspanninga stance, and(2)scalingofthemagnitudenetworkthrough species: (1)positiveworkactuationthroughlegextensioninlate Thus, twokeyaspectsoflegactuationpatternsareconsistentacross by insertingandremovingenergy dependingonlandingconditions. actuation, whichadjustsbodymechanicalenergy onuneventerrain demonstrating aconsistentpatternofposture-dependentleg slope ofthisrelationshipwasremarkablysimilaracrossspecies, data setshownfor pheasants(allsteptypesandallterrains). stance. Regressionfitsare shownforeachspecies,witharepresentative and thebodyvelocityattouchdown), andworkdonebythelegduring cosseisadbd ie(i.5;R across speciesandbodysize(Fig. angle betweenthelegandbodyvelocityvector)netlimbwork positive linearcorrelationbetweenthelegloadingangle( and Daley, 2012;DaleyandBiewener, 2011). We foundasignificant previously reportedas‘posture-dependentactuation’ (Birn-Jeffery limb workproducedduringstanceandlandingconditions,apattern other species(below). height (Fig. Nonetheless, quaildoshowincreasinglegextensionwithobstacle correlation betweenlegloadingangle, Fig. To investigatetheimplicationsofbirdlegactuationpatternsfor Across species,weobservedaconsistentcorrelationbetweennet

.Across speciesandterrains,wefoundasignificantpositive 5. Net leg work (J/mg Lleg) –1 0 1 The JournalofExperimentalBiology(2014)doi:10.1242/jeb.102640

Ostrich (r Quail (r Pheasant (r Guinea fowl( Turkey (r 4), andposture-dependentactuationsimilartothatof 20 0 − 2 E 1). Inobstacleterrain,legextensioninthesecondhalfof =0.50) 2 2 p =0.57) =0.45) increase duringstep 2 =0.54) r 2 =0.36) Turkey 0.5 080 40 β TD β TD 2 − between 0.36and0.57).The 1 (supplementarymaterial (the anglebetweentheleg 0 60 Ostrich 0.5 β TD β 1.0 TD 3789 , the

The Journal of Experimental Biology 3790 RESEARCH ARTICLE targeting bodystabilityduringtheobstacledismount(0.1L Fig. series withthepassiveelements(Fig. mass-leg modelwithminimalworkappliedthroughanactuatorin and legdynamicscloselymatchthepredictionsofadamped-spring- 6,7).We foundthatstanceforce trajectories ofrunningbirds(Figs solution comparedwiththemeasuredvirtualleglengthofeachspecies(mean±s.d.). running (mean±s.d.)withforcepredictedbyminimal-workoptimisation.(C)Virtualfoot point)forthework-optimal leglength(distancebetweenbodyCoMand linear actuatorinserieswiththepassiveelements. Fig. identical tothoseusedforlevelrunning(Fig. body stability. We usedsimulationandtrajectory optimisationmethods suggest thatbirdstargetinjuryavoidanceandeconomyratherthan and measured(mean ±s.d.)strategiesandtheirrespective actuatorwork. the experimentally observedstep+1aerialphase.(B) GRFforthesimulated the immediatelyprecedingstep+0(red). Thethirdtrajectory(green)matches the constrainttomatchaerialphase oftheundisturbedstep hypothetical interpretationsofbody stability, actuatingwithminimalwork with three simulatedtrajectories.Thefirst twotrajectoriestargetalternative running. (A)Comparisonofthemeasured CoMtrajectories(mean±s.d.)and including legstiffness anddamping,fixedtothoseforguinea fowl level A Point-mass B A Damper

.Simulationspredictingtheforceandenergyconsequencesof 7. witha Asymmetricforceandleglengthtrajectoriescanbeexplainedbyminimal-workoptimisationappliedtoadamped-spring-massmodel 6. Spring

GRF (body weights) body 0 1 2 3 Pivot contact

0 Aerial target +1 +0 –2 –2 Aerial Simulated strategies

0.2 0.4 0.1L –1 leg Massless aerial phase stability actuator leg Observed Strict Linear l p Fraction ofstance –1

+0

C B Touchdown Leg length Total GRF 0.5 1.0 1.5 1 0 2 0 +1

6). Byfittingtwoparameters

Fraction ofstance

6), withmodelparameters, 0.6

Take-off +0 +1 . 1.0 0.5 (A) Schematicofthemodelusedtosimulaterunning.(B)ComparisonbirdGRFsinsteadyaerial 0.2 kg

Quail 0.8 1.0 Energy cost

(J/mg Lleg) +1 –2 leg +0 +1 − ) further 2 (blue)or 0 0.5 1.0 1.5 Pheasant 1.0 kg Work-optimal modelcontrol fluctuations inlegpostureandloadingacrossseveralsteps. posture-dependent actuationtonegotiateobstacleswithminimal economical energy managementthroughminimalactuation,using instead useunsteadybodydynamicsinastrategyprioritising birds donotdirectlytarget bodystabilityasacontrolpriority, but These simulations,alongwiththeexperimentaldata,suggestthat experimental data,evenforthesmallest0.1 rates, higherpeakforcesandgreaterlegworkthanobservedinthe that directlytargeting areturntosteadygaitrequiresfasterloading control target duringtheobstacledismount(Fig. stance. it ismosteconomicaltoactuatethelegduringsecondhalfof Thus, work-optimalsolutionsderivedfromthismodelsuggestthat extension oftheleg,similartoobservedlegtrajectories(Fig. model predictslegactuationinthesecondhalfofstancethroughnet goodness-of-fit betweenthemodelandexperimentaldata.The Table (MSE)=0.01–0.03, seesupplementarymaterialFigs across speciesforlevelterrainlocomotion[meansquarederror optimisation, wefoundgoodfitstoforceandleglengthtrajectories (leg stiffness anddamping)applyingwork-minimising We find, instead,acrossspeciesand terrainheights,thatbirds inconsistent withbodystability asthedirecttarget ofactive control. strategy, whileachievinggeneralstability(theydonotfall) is Moritz andFarley, 2004;MoritzandFarley, 2006).Thebirds’ Ferris etal.,1998;Grimmer al.,2008;MoritzandFarley, 2003; humans hoppingandrunningon varyingterrain(Ferrisetal.,1999; trajectory fromsteadygait.Such behaviourhasbeenobservedin that theycoulduseposturalchangestoavoiddeviationsin body active controlpriority, wewouldexpect,atleastforsmallobstacles, force–length dynamics.Ifbirdsdirectlytargeted bodystabilityasan external mechanicalworkbutminimisesfluctuationsin leg and externalmechanicalwork,versus‘vaulting’,whichrequires prioritises bodystability, minimisingfluctuationsinbodytrajectory spectrum betweentwohypotheticalextremes:‘crouching’,which obstacle. Potentialmanoeuvrestonegotiatethisobstaclespan a fold rangeinbodymassastheynegotiatedavisible,single-step We examinedrunning dynamicsofcursorialbirdsspanninga500- control priorities control asawindowObstacle intotask-level strategies negotiation DISCUSSION Finally, wefoundthatamodelsimulatingbodystabilityas S7 forfurthermodelanalysis].Allspeciesexhibitedsimilar The JournalofExperimentalBiology(2014)doi:10.1242/jeb.102640 Guinea fowl 1.2 kg Bird measurement Turkey 3.0 kg L leg obstacles (Fig.

7A) demonstrates

S1–S3 and Ostrich 117 kg 6C). 7B).

The Journal of Experimental Biology universal feature ofleggedanimallocomotion (Cavagna, 2006),but dismounting behaviour(Fig. the asymmetricforceandleglength trajectories(Fig. current modeldoesreplicatekey featuresofbirdrunning,including kinematics andposturalcosts into alegmodel.Nonetheless,the Future studiescouldinvestigate thisfurtherbyincorporatingleg force costsassociatedwithcrouching (McMahonetal.,1987). et al.,1994;SrinivasanandRuina,2006)increasesinmuscle from atrade-off betweencosts ofexternalmechanicalwork(Minetti obstacles usedbyrunningbirds.Theobservedbalancelikelyresults cannot predictthespecificbalanceof‘vaulting’ and‘crouching’ onto encode posturalgearingeffects onmuscleforce,andtherefore obstacle (Fig. birds increasedlegactuationinlatestancewhenvaultingonto the economical foranintrinsicallydampedleg.Consistentwith this, 7), andrevealsthatactuationthroughlegextensioninlatestance is asymmetric forceandleg-lengthtrajectoriesofrunningbirds(Figs of avianbipedallocomotion.Themodelsuccessfullyreplicates the supports economicalenergy managementasakeycontrolpriority vertebrate leggedlocomotion. species ofavianbipedssuggeststhatitmaybeageneralfeature observation ofposture-dependentactuationinhumansandseveral and work(DaleyBiewener, 2011; Daley et al.,2009).The intrinsic dynamicsandfeedback-mediatedchangesinmuscleforce Deviations betweenanticipatedandactuallegloadingleadtoaltered 1979; DonelanandPearson,2004;Engberg andLundberg, 1969). delays (DaleyandBiewener, 2011; Daleyetal., 2009;Dietzetal., in anticipationofstance,becausesignificantneuromuscular feedback control,withthefeedforwardactivationstartinglateswing, activity isdeterminedthroughacombinationoffeedforwardand mechanisms. Invertebrateleggedlocomotion,stancephasemuscle including intrinsicmusculoskeletalpropertiesandreflex arise fromsharedfeaturesofvertebratelocomotorsystems, negotiating obstacles(Mülleretal.,2012).Thisphenomenonmay negotiating obstacles(Birn-Jeffery andDaley, 2012),andhumans (Daley andBiewener, 2006;Daleyetal.,2007),pheasants also beenpreviouslyobservedinguineafowlnegotiatingdrops actuation acrossspecies(Fig. through directcontrolofbodyCoMtrajectory. energy management,viaposture-dependentactuation,ratherthan Thus, birdsmayachievegeneralstabilitythrougheconomical coinciding withpredictionsofourminimum-workmodel(Fig. occurs inlatestance(DaleyandBiewener, 2011; Daleyetal.,2009), (Daley andBiewener, 2011). Additionally, posture-dependentwork towards thetotalmechanicalenergy ofthenominalsteadygait touchdown elicittheactuationnecessarytoreturnsystem dynamics toworkoutput.Alteredlegpostureandloadingat posture andloading,becauseitdirectlylinkslegforce–length Posture-dependent actuationalsohelpsattenuatefluctuationsinleg has astabilisingeffect onuneventerrain(SchmittandClark,2009). absorption (Fig. mechanical energy ofthebody, throughenergy insertionand control priority. Posture-dependent actuationregulatesthetotal economical whole-bodyenergy managementasakeylocomotor predominant controlpriorityinuneventerrain. birds directlytarget stabilityofbodyCoMtrajectoryasa loading acrossmultiplesteps.We thereforerejectthehypothesisthat and ‘crouching’ thatminimisesfluctuationsinlegpostureand negotiate theobstacleusingaconsistentbalancebetween‘vaulting’ RESEARCH ARTICLE Our reduced-order, minimum-workmodelofrunningfurther We foundastrikingsimilarityintheslopeofposture-dependent The obstaclenegotiationbehaviourofbirdsisconsistentwith

4). However, thesimpleprismaticlegmodel doesnot 5), andmodellingstudieshavedemonstratedthatit

7). Theforceasymmetrymay bea 5). Posture-dependentactuationhas

6) andobstacle

6).

6, for obstaclesupto0.5 in runningbirds.Peaklegforcesremainedwithin0.35 load regulationforinjuryavoidanceasakeypriorityoflegcontrol governing legcontrolinrunningbirds. supports economicalenergy managementaskeytask-levelpriority explanatory reduced-ordertemplateofanimallocomotionand our minimum-workactuationmodelprovidesamoreaccurateand reproduce it(Blickhan,1989;McMahonandCheng,1990).Thus, energy-conservative models,suchasaspring-massmodel,cannot muscle stresses requiredtosupportbodyweight (Biewener, 1989; towards moreupright,straight-legged posture,whichreducesthe 1987; Taylor etal.,1982).Asanimalsincreaseinsize,they tend (Biewener, 1989; HoytandTaylor, 1981;Moreetal.,2010;Nagy, and Dial,2000;Walter andCarrier, 2002)andphysiology et al.,2000;Iriarte-Díaz,2002; JacksonandDial,2011; Tobalske 2012; KilbourneandHoffman, 2013),locomotorperformance (Hoyt Body sizeaffects morphology (Christiansen,1999;Doubeetal., level prioritiesgoverninglegcontrolinrunninganimals. economy andinjuryavoidancearecrucialcloselycoupled task- overall, ourexperimentalandmodellingevidencesuggestthat both changes ingearing(Biewener, 1989;McMahon etal.,1987).Thus, obstacle, whichwouldincreasemuscleforcecosts,because of may beoffset byavoiding excessively crouchedposturesonthe The costofexternalmechanicalworkbyvaultingontotheobstacle Minetti etal.,1994;Srinivasan,2010;SrinivasanandRuina,2006). strongly onbothmuscleworkandforce(KramTaylor, 1990; expenditure. Themetabolicenergy costoflocomotiondepends economy asapriority, becauseminimisingforcesreducesenergy control priority. Daley andBiewener, 2006),suggestinginjuryavoidanceasakey previous studies(Birn-Jeffery andDaley, 2012;Blumetal.,2014; similar peakforcesacrossuneventerrain,bothinthisand (Guo etal.,1994;Verheyen etal.,2006).Birdsconsistentlypreserve repetitive loadinginjuryifinsufficient repairoccursbetweenbouts submaximal increasesinforcecanleadtomicro-damageand to fourtimespeaksteadylocomotorforces(Biewener, 1990).Even dangerously towardssafetyfactorsofvertebratebone,whicharetwo et al.,2014;Vejdani etal.,2013).Theseforcescouldencroach example, increasingby+2–3 However, thisstrategycanresultinlarge peaklegforces–for stability (Blumetal.,2014;Ernst2012;Vejdani etal.,2013). minimise deviationsinbodyCoMtrajectory, prioritisingbody but notobservedinanimals,istooptimiseswing-legtrajectory 2010). A swingcontrolstrategythat hasbeenhypothesisedintheory, crucial foravoidingfalls(Blumetal.,2011; DaleyandUsherwood, terrain dropbeforethelegmissesstanceentirely, andistherefore 2014). Late-swingretractionvelocityalsodeterminesthemaximum minimise fluctuationsinlegloadinguneventerrain(Blumetal., specific retractionvelocitytunedtotarget landingconditionsthat (Birn-Jeffery andDaley, 2012;DaleyandBiewener, 2006),withthe use aswing-legtrajectoryinvolvinglegretractioninlateswing Usherwood, 2010;Karssenetal.,2011; Vejdani etal.,2013).Birds between swingandstancedynamics(Blumetal.,2014;Daley leg trajectoryindetermininglandingconditions,andthecoupling detail, previousstudieshavedemonstratedthecrucialroleofswing- While thecurrentstudydidnotexamineswing-legdynamicsin crucial roleincontrollinglandingconditionstoregulatelegloading. priorities? Does bodysize influencenon-steadylocomotorcontrol The observedobstaclenegotiationstrategyisalsoconsistentwith Regulation ofpeakforcesonuneventerrainalsofurthersupports The JournalofExperimentalBiology(2014)doi:10.1242/jeb.102640 L leg . Swinglegtrajectorylikelyplayeda BW fora0.4L leg downward step(Blum

BW oflevel 3791

The Journal of Experimental Biology 3792 RESEARCH ARTICLE embracing the looser definitionofstability as ‘fallavoidance’, (Ernst etal.,2012).Ourresults suggestadifferent approach, nominal gait(Erezetal.,2012), orrejectingperturbationsentirely perturbed (DaiandTedrake, 2012),planningrapidreturns toa 2012), designinggaitsthatresult insmallergaitdeviationswhen locally stabilisinganominalgait withfeedback(Bhounsuleetal., (Westervelt etal.,2007).Thisapproachtakesmany forms,e.g. maintains thesystemwithinknowndynamicsandcontrolauthority stability asadirectcontrolpriorityiscommonplacebecause it In engineeredsystems,suchasrobotsandprosthetics,using body priorities areobservedamongleggedanimalsindifferent clades. bipeds). Futureworkshouldaddresswhethersimilarcontrol a groupofanimalswithsimilarlocomotorstyle(e.g.striding to ashiftincontrolprioritiesandobstaclenegotiationstrategywithin present studysuggeststhatbodysizealonedoesnotnecessarily lead and Biewener, 2006;Satoetal.,2012;Watson etal.,2002).The substantial changesinbodydynamicsandlegposture(Kohlsdorf animals havealsoobservedanticipatorystrategiesinvolving Nonetheless, previousobstaclenegotiationstudiesinsmaller result indifferent specificstrategiesamongdifferent clades. mechanisms onarelativelyshortertimescale.Thesefactorsmay physiological delays(Moreetal.,2010),andmayusefeedback animals (e.g.insects).Smalldonotsuffer fromlong this studyarelarge relativetothebodysizerangeamongextant Full, 2008;Watson etal.,2002).Additionally, theanimalsusedin options (Olberdingetal.,2012;Spagna2007;Sponberg and allows greaterintrinsicstabilityandalarger rangeofbehavioural strategies tonegotiateobstaclesbecauseincreasedlegnumber and legnumber(e.g.quadrupeds,hexapods)mayusedifferent across clades.Animalswithsubstantiallydifferent locomotormode other animalorders.However, thespecificstrategiesusedmayvary body size,andwesuspectthatsimilarexamplesmaybefoundin dinosaurs andtheirbirddescendants. reflect asharedheritageofbipedalagilityinthelineagetheropod change. We suggestthatunifiedlegcontrolamonggroundbirdsmay negotiate larger obstacleswithminimalexternalworkandpostural similar bodysize(Robertsetal.,1998b),whichmayallowthemto Bipeds tendtohavelongerleglengthscomparedwithquadrupedsof selection forrobustandeconomiclocomotioninuneventerrain. dinosaurs andtheirbirddescendants(Farlowetal.,2000)mayreflect Garcia, 2002),evolutionofstridingbipedalismamongtheropod the largest theropodsmaynothavebeenfastrunners(Hutchinsonand and thebird-liketroodontids(PadianChiappe,1998).Although non-avian theropoddinosaurs,suchasVelociraptor, adromaeosaur Garcia, 2002).Birdssharenumerousfeaturesoflegmorphologywith behaviour ofextinctanimalsfromfossilevidence(Hutchinsonand among livingandextinctanimals,allowingustobetterreconstructthe provide insightintotheco-evolutionofbehaviourandmorphology important factorsinfitness. limited, thus,injuryavoidanceandeconomyarelikelytobe injuries canresultinpredation,andfoodenergy resourcesareoften priorities, irrespectiveofbodysizeandlegposture.Inthewild, economical energy managementandinjuryavoidanceaskey and similarlegactuationpatterns.Theobservedmanoeuvressuggest range inbodymassusedconsistentobstaclenegotiationmanoeuvres influence obstaclenegotiationstrategies.Birdsspanninga500-fold scaling trendsinmusculoskeletalstructuredonotsubstantially Biewener, 2005).Here,wepresentfindingsthatsuggestthese Potential implications for control of legged robots legged Potential implications for of control Birds donotexhibitashiftinobstaclenegotiationstrategywith Understanding howbodysizeinfluencesbipedallocomotioncan without encodinganexplicitpreferenceforasteadygait. stability, optimisingdynamicsbasedonkeytask-levelpriorities animals, controlapproachesmustembraceamorerelaxednotion of prosthetics tomatchtherobust,agileandeconomiclocomotionof control inrunningbirds.We suggestthatforbipedalrobotsand stability ofbodyCoMtrajectory, perse,asadirectpriorityof direct targeting ofanominaldesiredtrajectory).Ourfindingsrefute may beaconsequenceofthesepriorities,notdirectobjective(not mechanical energy. Theobservedconvergence towardsteadygaits and (3)applyingminimalworkactuationtomanagethebodytotal (2) regulatingpeakforceandlegpostureforeconomysafety priorities are:(1)ensuringleg–groundcontacttoavoidfalls,while protocols didnot require anyinvasiveorsurgical procedures. ‘Kinematics andkineticsinbirds runningoveruneventerrain’.The Welfare Committeeapprovedallproceduresundertheprojectprotocol title effects onmedio-lateralstability. The Royal Veterinary CollegeEthicsand dynamics (Fig. (Fig. actuation duringstance,throughlegextensioninthelatterhalfofstance safe landingconditions(Blumetal.,2014),andapplyingcost-minimising management inuneventerrainbycontrollingswinglegtrajectorytotarget Birds mayachievesafelegforcesandeconomicalstep-to-stepenergy have emergedfromthisandotherrecentstudies(seeDiscussion). and legcontroltargetsofrunningbirds,highlightingprinciplesthat Fig. common pheasant( northern bobwhitequail( for fivecursorialgroundbirdspeciesspanninga500-foldbodymass range: We collectedbothkinematic(bodyandlegmotion)kinetic(GRF)data series withthepassiveelements(Fig. The modelisadamped,spring-masssystemwithanactuatorin 8. economical bipedallocomotion,schematicallyillustratedinFig. unified modelandsetoftask-levelcontrolprioritiesforrobust The findingshere,inthecontextofpreviousstudies,supporta systems (BylandTedrake, 2009). has beenrecentlyextendedtotheanalysisandcontroloflegged consistent withthemathematicalconceptof‘metastability’,which Experimental protocol MATERIALS ANDMETHODS Conclusions attenuating fluctuationsinlegpostureandloading. in Vetwrap obscured legandbodymarkersso the distalendofeachwingwaswrapped had theirprimarywingfeathersclipped topreventflight.Theostrich’s wings ( American turkey( guinea fowl( Struthio camelus

.Schematicillustrationofthehypothesisedtask-levelpriorities 8. 6). Posture-dependentactuationtightlycouplesswingandstance Control target: L TD v TD β TM TD roiy Safeforcesandminimalwork Priority: The JournalofExperimentalBiology(2014)doi:10.1242/jeb.102640 Stance to restrictwingfanning.Thisdidnot appeartohaveadverse

Numida meleagris, 5), andallowseconomicalenergymanagementwhilealso L(t) , Meleagris gallopavo θ N Phasianus colchicus, TD =4, mass116.8±6.1 L(t) asafunctionofβ Colinus virginianus Stance Swing N =5, mass1.24±0.30 , L(t) TD N kg). Allbirds,excepttheostriches, N

6A), andthetask-levelcontrol =4, mass1.03±0.21 =6, mass3.0±0.3 , θ(t) N v β Safe landingconditions TD =6, mass0.22±0.02 TD θ(t), Ltotargetβ Stance Swing L(t) kg), wildNorth θ kg) andostrich TD kg), helmeted TD kg),

The Journal of Experimental Biology (0.6×0.9 excluding thequail, therunwaycontainedsix Kistlerforceplates where formula: similarity, withouttheconfoundingeffect oflegposture,usingthefollowing a nominalleglengthbasedonbodymassandassumptionsofgeometric to anisometricallyscaledleglengthreferencevalue.We thereforecalculated differing bodymassshouldbebasedonscalingofobstacleheightsrelative Consequently, wereasonedthatthefairestcomparisonbetweenanimalsof amplify theapparentstabilityofsmalleranimalsfortheirbodymass. posture ofsmallbirds,scalingobstaclesbasedonhipheightwould ‘mid-stance’ runningposture,and(2)becauseofthesubstantiallycrouched definitively measured,becausestandingposturevariesconsiderablyfrom reasons: (1)birdsdonothaveasingle‘true’ hipheightthatcanbe the obstaclesbasedonabird’s hipheightwouldbeproblematicfortwo animals makesitchallengingtoteaseaparttheirrespectiveeffects. Scaling conditions. Yet, theco-variancebetweenlegpostureandbodymassin species, wewantedtocomparebehaviourinappropriatelyscaledterrain running (Fig. the ostrichwhenmeasuredatmid-stanceduringmoderate-speedlevel lengths. Ourpostureindexvaluesrangedfrom0.36inthequailto0.74 index’ equaltotheratioofhipheightsumhindlimbsegment Gatesy andBiewener(GatesyBiewener, 1991)basedona‘posture Force datawerepre-filteredusing a low-passfilterof100 We collectedGRFdataat500 uneven terrain,astrategythatsuggests bodystabilityasacontrolpriority. strategies (‘crouching’)toattenuate deviationsinbodyCoMtrajectory obstacle allowsustoevaluatetheextentwhichtheyemploylegpostural mechanical work(Fig. to achieveasteadygaitisplausibleoptionthatcouldminimiseexternal foot clearancelimits.However, forsmallobstacles,useofposturalstrategies required onceobstaclesreachheightsthatchallengestancepostureor swing pronounced forsmallobstacles.A shiftawayfromsteadygaitisclearly comparisons becausethepotentialfordifferent strategiesismost obstacle negotiationacrossspeciesisthemostappropriateforscaling RESEARCH ARTICLE length ( ostriches ranoverobstacleheightsscaledbetween0.1and0.5nominalleg necessarily reflectanoptimisedstrategy. perturbation, whichrevealsintrinsicstabilitymechanismsbutdoesnot recovery totheunperturbedgaitmightbeunreasonable,oranunexpected single-step perturbationcontrastswithapersistentterrainchange,forwhich upon theobstaclebeforesteppingbackdown(not‘hurdling’).Thisvisible, stability, minimalwork,safeforces,etc.).Theobstaclerequiredasinglestep them tooptimisebehaviouralstrategybasedontask-levelpriorities(e.g. ample distance,timeandpractiserunstoanticipatetheobstruction,allowing considerations forthebirdsandhandlers.However, comparisonof0.1 (for theostriches). smaller species),orapenatoneendcontainingfewmembersofthe flock forth acrosstherunwaybylocatingdarkrestingboxesateitherend (for shifts inbehaviourtojumping.Thebirdswereencouragedrunbackand (continuous stridingwithpositiveforwardvelocity),toavoidcategorical complexity, werestrictedobstacleheightstothosethebirdscouldrunover so itwasnotpossibletomanoeuvrearoundit.To minimiseexperiment encountering it.Theobstaclespannedthemedio-lateralwidthofrunway, length ateitherendtoallowaccelerationasteadyspeedbefore that crouchedposturesreflectincreasedpriorityforstabilityonroughterrain. crouched species.We feelthisisafair, conservative testforthehypothesis relative tomid-stancehipheight,obstacleswerelarger forthemore (approximately thatofaturkey).Thisobstaclescalingchoicemeansthat, selected toobtainaleglengthproportionalanintermediateposture Data collection andprocessing Level terrainrunningservedasacontrolforeachspecies.Allbirdsexcept In thisstudy, birdsranoverterrainwithasingle-stepvisibleobstacle, The ostricheswererestrictedto0.1 Each obstaclewasplacedinthemid-sectionofarunwaywithample L L leg leg m; model9287B, Hook,Hampshire,UK).Because ofthelack ). A substantialscalingeffect onlegposturehasbeenreportedby is leglengthand 3). To compareintrinsicstabilityandcontrolstrategiesacross

1). Comparingspeciesnegotiatingasimilarlyscaled

m Hz fromforceplatesembeddedinthe runway. Lm leg is bodymass,andthecoefficient 0.2was = . (1) , 0.2 L 0.33 leg obstacles becauseofsafety

Hz. Forallbirds L leg ran anANOVA withthefactorsobstacleheight, steptypeandtheir negotiation, notdifferences insteady-stategait. statistical differences amongspeciesreflectdifferences relatedtoobstacle value, thusmeasuringthedeviation fromsteadygait.Thismeansthatany difference betweentheobstacleterrainvaluesandlevel mean included speedasacovariateinthe statisticalanalyses. restricted thedatatonormalisedvelocitiesbetween0.75and2.00 and control fortheeffects ofspeed inthecomparisonsacrossspecies,we ostrich ranatloweraveragespeedsthantheotherspecies.Therefore, to Average forwardspeeds differed amongspecies;inparticular, thequailand terrain dataforeachspecies. average trajectoriesand95%confidenceintervalsweregeneratedfromlevel (step 0)anddismountingtheobstacle+1).Asacontrolreference, procedures anddatacollectionprotocolwereotherwiseidentical. (0.12×0.2 different runwayforthequail,containingtwo‘Squirrel’ Kistlerplates resolution inthemodel9287Bforceplatesforsmallanimals,wecreateda length dimensionless quantitiesbasedonbodymass,gravityandnominal leg individual sizedifferences, all variablesintheanalysiswerenormalisedto comparisons acrossspeciesandminimisevarianceduetowithin-species completed usingMATLAB R2012awiththeStatisticstoolbox.To allow All statisticaltestswererunfollowingchecksfornormalityand were were calculatedforstepsapproachingtheobstacle(step touchdown ofthecontralateralfoot.Inobstacleterrains,averagetrajectories leg postureoverthestepcycle,definedastouchdownofonefootto and Daley, 2012).We thencalculatedmechanicalenergies, peakforcesand conditions obtainedfollowingpreviouslydescribedmethods(Birn-Jeffery 333; andostrich,25. for theobstacletrials:quail,362;pheasant,163;guineafowl,240;turkey, quail, 96;pheasant,33;guineafowl,91;turkey, 255;andostrich,39.And selected, thenumbersofleveltrialsincludedinstatisticalanalysiswere: step cyclesforallsubsequentanalysis.Onceonlysteadytrialshadbeen non-steady strategiesforobstaclenegotiation.Thedataweresegmentedinto the initialapproachbeforeencounteringobstacle,butdoesnotrestrict forward speed.Thiscriterionminimisesthevarianceduetoaccelerationin fore–aft impulsecriterioncorrespondedtoamaximum10%changein corresponds toperfectlysteadyforwardlocomotion.Acrossspecies,this s.d. oftheleveldatadistributionforeachspecies.A netzeroimpulse the fore–aftimpulseof‘step selected steadyapproachtrialsbyrestrictingtheanalysistoinwhich in theinitialapproachtocentreofrunway. Inpost-processing,we in whichthebirdranastraightlineandappearedsteadytohumaneye six trialsperconditionindividualwithineachspecies.We includedtrials where the‘on’ obstaclestepwasdefinedas‘step0’.We collectedatleast the experimentalandmodellinganalyses. sagittal plane,consideringonlytheverticalandfore–aftdynamicsinboth with theforceplates.Forsimplicity, alldataanalyseswererestrictedtothe (Hedrick, 2008).Kinematicrecordingdevicesweretriggeredsynchronously runway. Sagittalplane2DdatapointsweredigitisedintheDLTdv5 code HSV wascollectedusingtwolateralviewcamerasoneithersideofthe Dättwil, Switzerland).Papermarkerswereplacedonthesamelandmarks. collected usinghigh-speedvideo(HSV)cameras(AOSTechnologies AG, maintaining Qualisysmarkersontheostriches,ostrichdatawere Sweden) placedevenlyaroundthefieldofview. Becauseofdifficulties with kinematics wererecordedusingeightto12Qualisyscameras(Gothenburg, effective leglengthandangle.Forallbirds,excepttheostriches, foot markerswereaveragedtoestimatepositionandcalculatethe averaged foraninitialestimateofthebodyCoMvelocityandposition.The tarsometatarsalphalangeal jointanddigitIII.Thebackmarkerswere caudally onthebirds’ backandonthefeetlocatedat Statistical analyses For thespecieswith multipleobstacleheightconditions (galliforms),we For thestatisticalanalysisofobstacle negotiationdynamics,wetookthe We collectedkinematicdataat250 We twice-integratedforcestoobtainbodyCoMmotion,usinginitial Step typesacrosstherunwaywereidentifiedwithrespecttoobstacles, L leg m; modelZ17097,Hook,Hampshire,UK),buttheexperimental (Birn-Jeffery andDaley, 2012;McMahonandCheng,1990). The JournalofExperimentalBiology(2014)doi:10.1242/jeb.102640 − 2’ (twostepsbeforethecentre)waswithin±1

Hz frommarkersplacedcraniallyand − 1), ontheobstacle 3793

The Journal of Experimental Biology where least-squares regressiontotestforalinearrelationshipbetween significant (seesupplementarymaterialTables completed using‘multcompare’ ifthemaineffects werefoundtobe Post hoc a continuouscovariateandaninteractiontermbetweenspeedspecies. as arandomfactor, theinteractionbetweensteptypeandspecies,speedas including ostrich,usinganANOVA withsteptypeasafixedeffect, species 3794 RESEARCH ARTICLE for eachspeciesand convertedthemintoparametersand boundaryconditions Our dataprocessing methodologytookaveragedGRF andCoMtrajectories where equations ofmotionfortheactuatedmodelareasfollows: accelerations. Thislinearactuatorcanonlyactintheaxialdirection.The optimiser ultimatelyfoundsolutionsthatdidnotrequireunrealistic of theactuator, e.g. accelerationorlengthlimits,althoughthetrajectory material Fig. that themodelallowsarbitraryforce–lengthtrajectories(supplementary series withaspringytendon.Thismodeldecouplesforceandposture,such include anaxialactuatorinserieswiththespring,analogoustoamuscle in parallelwiththelinearlegspring.To reinsertenergy intothesystem,we energy. We modelledtheinherentleg dissipationasalineardamper, acting and anactuatorinserieswiththespringdampertoreplacelost conservative regimebyaddingadampertosimulaterealisticenergy losses, stores andreleasesenergy conservativelyduringstance. SLIP modelhasacharacteristicallysymmetrichalf-sineshapeasthespring that connectsthebodyandground.ThetotalGRFexertedbylegin leg, africtionlesspivotatthepointofgroundcontact,andlinearlegspring et al.,2001)runners.Thismodelfeaturesalumpedmassbody, amassless and Biewener, 2006; McMahonandCheng,1990)robotic(Altendorfer exchange, CoMtrajectoriesandGRFofbiological(Blickhan,1989;Daley The SLIP modelofrunninghaslongbeenusedtotheenergy conservative variantofthespring-loadedinvertedpendulum(SLIP)model. quantitatively analysethetrajectoriesofbirdlocomotion,particularly, anon- We usedasimple,reduced-order dynamicalmodel(Fig. Tables Tables correction (Holm,1979;Rice,1989)(seesupplementarymaterial variable, weran species. Ifthemaineffects werefoundtobesignificantforaspecific speed asacontinuouscovariateandaninteractiontermbetween interaction, speciesandtheinteractiontermbetweensteptype, gravitational acceleration( coordinates ofthebodymassrelativetoafoot-pointorigin,withunsigned velocity ofthepassiveleglength(Fig. removed fromtheregressionforvaluesgreaterthan3s.d.mean. including allstepsinlevelandobstacleterrainconditions.Outlierswere leg work.A singleregressionwasfitforalldatafromeachspecies, Processing measurements into model boundary conditions into modelboundary measurements Processing Modelling spring stiffness anddampingcoefficient, respectively. For theregressionanalysesshowninFig. To accountforGRFasymmetry, wetook ourmodeloutoftheenergy- We separatelyanalysedthe0.1

F l S5–S6) werecompletedusingMATLAB function‘multcompare’. S4–S6). Thepairwisecomparisons(supplementarymaterial a leg is theactuatedleglength, pairwise comparisonswithsequentialBonferronicorrectionswere is axiallegforce,

S1). We didnotplaceanyinherentlimitationsonthemotion F leg post hoc = ⎩ ⎪ ⎨ ⎪ ⎧ , otherwise 0, llc llcl l kl cl l kl (),if 0 () pairwise comparisonswithasequentialBonferroni pp0 p 0p p 0p g −− ≥ −− −− ), bodymass(m l t lxy  y is totalleglengthand t lll = =+ x  pta = = Fy  l ml L p leg Fx

leg 6A). Parametersk ml is thepassiveleglengthand 22 leg t − t − obstacle dataacrossallspecies ,( g ,(5) ) and: 4, weusedreducedmajoraxis ,(3) ,(6)

S1–S3). x , and y are theCartesian c are themodel ,(4) β TD

6A) to l ̇ and net p is the 2 ) of themodel. spite ofthegreateroptimiserfreedomstrengthenscaseforvalidity dynamics. We argue thattheclosetrajectorymatchestomeasureddatain select themostenergy-efficient optionwhilestillachieving theobservedgait lengths anddistancestraversed,allowingtheoptimisermorefreedomto the aerialphasepermitsmoresolutionswithslightlydifferent take-off leg unnecessarily constrainingtotheoptimisationproblem.Instead,targeting phase wouldseemanobviouschoice,targeting asingleexactstateisoften While targeting theprecisemeasuredtake-off stateforthe measuredstance magnitude, velocityangle,verticalposition,andnotthehorizontalposition). intersect thestatetrajectoryofsubsequentaerialphase(velocity for whichthework-optimal solutionprovidedthe closest fittothemean 2.23×10 equations ofmotionwereintegratedusingMATLAB’s ode45(tolerance as implementedbyMATLAB’s fmincon)wasusedforoptimisationandall distance duringthefullstepcycle.SequentialQuadraticProgramming(SQP, no morethan1s.d.fromthemean,whiletravelingsamehorizontal measured CoMtrajectoryandthepoint-massplayback,adjustingthemby minimise thediscrepancy. We minimisedtheEuclideandistancebetween angle, velocitymagnitudeandangle)flightphasedurationto essence, adynamicaldisagreement). measured birdCoMtrajectoryandthe‘point-massplayback’ simulation(in point measurementcanleadtosignificantdeviationsbetweenthemean- sensitive toTDconditions,meaningthatevensmallerrorsofthissingletime- CoM trajectory. However, point-masslocomotionmodelsareinherently should seeanintegratedCoMtrajectorythatmatchesthemeanmeasuredbird touchdown (TD)conditionsand‘playback’ themeasuredbirdGRF, we model tobeuseful,ifwesimulateapointmasswiththeempiricallymeasured restricted toaerialrunningtrials(notwalkingorgroundedrunning).Forthe for theactuatedmodel.Theexperimentaldatausedmodellingwere parameters While allothermodelparameters wereexperimentallymeasured,the where Ruina, 2006): the netunsignedwork,asimpleproxyformetaboliccost(Srinivasanand optimisation foundtheactuator’s leg-extensiontrajectorywhichminimises mass andlandingconditionsfromprocessedexperimentaldata.The optimisation. Foreachspecies,thismodelwasgivenaveragemeasuredbird optimal GRFforasimplifiedactuatedmodel(Fig. To facilitateenergy-optimal control,wenumericallysolvedforthework- velocity oftheactuatorthrustand normalised springstiffness (kL optimisation studies(SrinivasanandRuina,2006),| use smoothedapproximationoftheabsolutevaluefunction,asusedinprior coefficient ( Parameter search optimisation Trajectory revealing different solutions ofanysignificance. MATLAB’s fmincon)anddifferent initialguesseswerespot-checked,never the optimizationproblemusinganSQP solver(implementedusing (much finerresolutionsdidnotyieldanysignificantdifferences). We solved discretising theinputtapeintoa20-segmentpiece-wisedifferentiable curve more reliabletrajectorysolvingwithawiderarrayofinitialguesses, and speedtoavoidoverlyconstrainingtrajectories. processing, allowingfordifferences intotaldistancetravelled,steplength to findsolutionsthatsatisfiedtheboundaryconditionscalculatedby data small (0.001).We alsoimposedhardequalityconstraintsontheoptimiser values {k two-dimensional tableofwork-optimal trajectoriesforarangeofparameter the trajectoryoptimisationwaslooped insideagriddedsearch,producing Final statetargets forthetrajectoryoptimisationareconstrainedto Using optimisation,weadjustthefourTDstatevariables(leglength,leg Using amultiple-shootingformulation(BockandPlitt,1984)allowed for J − is thevalueofobjectivefunction, 14 norm ). k c The JournalofExperimentalBiology(2014)doi:10.1242/jeb.102640 / and m =[7:0.5:17] and √ — g c / must befittedforthebirds.To fitthesetwoparameters, L — leg )}. We thenselectedtheparametersforeachspecies JFlt leg c = / norm m t ∫ s g 0 t is thedurationofstancephase.We s ) andc =[0.0:0.05:0.7], wherek  a ,(7) d, norm is thenormaliseddamping F is thelegforce, x

6A) usingtrajectory | ≈√ — x 2 + — ε – 2 , whereε norm l ̇ a is the is the is

The Journal of Experimental Biology material Table on theparametersofthesebest-fittrajectoriesareprovidedinsupplementary poorly matchedparameter/boundaryconditioncombinations.Moredetails this immediate(andtypicallybrief)periodofworkwasassociatedwith subset thatperformedactuatorworkattheinstantoftouchdown,because that performedsimilarlywell.Amongthesesolutions,weeliminateda clearly performedbetterthanothers,therewasoftenalarge setofsolutions measured GRFtrajectory. Whilesomeregionsofthisfittinglandscape reflect betterqualityfits,asdefinedbyMSEbetweenpredictedand fitting landscape(seesupplementarymaterialFig. http://jeb.biologists.org/lookup/suppl/doi:10.1242/jeb.102640/-/DC1 Supplementary materialavailableonlineat PMC forimmediaterelease. Program fundedsimulations(RGY0062/2010toM.A.D.andJ.W.H.). Depositedin comparative experiments(BB/H005838/1toM.A.D.).TheHumanFrontierScience The BiotechnologyandBiologicalSciencesResearchCouncil,UKfundedthe the paper. optimisations. D.R.co-supervisedsimulations.A.V.B.-J., C.M.H.andM.A.D.wrote and Y.B. collectedandanalysedexperimentaldata.C.M.H.ransimulations supervised experiments.J.W.H. plannedandco-supervisedsimulations.A.V.B.-J. All authorsdiscussedandcommentedonthemanuscript.M.A.D.designed The authorsdeclarenocompetingfinancialinterests. thank R.Fisher, S.Warner, J.GordonandA.Channonforhelpwithexperiments. We thankM.Srinivasanfortechnicaladviceontrajectoryoptimisation.We also data, potentiallyrefutingthework-minimisinghypothesis. Figs of agoodmatchbetweenmodelanddata(seesupplementarymaterial parameter values,beforeselectingthebestfittodata,therewasnoguarantee because thesetofsolutionswereallworkoptimalfortheirrespective prediction forthesteadyrunningofeachspecies(Fig. measured GRF, asmeasuredvia MSE. Theresultwasafittedwork-optimal RESEARCH ARTICLE iwnr A. Biewener, lxne,R . aoy .M . ju .adJys A.S. Jayes, and R. Njau, G.M.O., Maloiy, R.M., Alexander, References Supplementary material Funding Author contributions Competing interests Acknowledgements iwnr A. Biewener, lm . edn,H . inJfey .V,Hbci .M,Hrt .W n Daley, and J.W. Hurst, C.M., Hubicki, A.V., Birn-Jeffery, H.R., Vejdani, Y., Blum, A. Seyfarth, M. and Günther, M.A. Daley, and A., Birn-Jeffery, H. Y., Wagner, Blum, S., Grimmer, H., Geyer, A., Seyfarth, R., Blickhan, R. Blickhan, M.A. Daley, and A.V. Birn-Jeffery, A. Biewener, Jr, H.B., Brown, A. Ruina, M., and J. Buehler, Cortell, P. A., Bhounsule, H., Komsuoglu, N., Moore, R., Altendorfer, ok .G n lt,K.-J. Plitt, and H.G. Bock, y,K n erk,R. Tedrake, and K. Byl, 250 mechanics. posture enhancerunningstabilityandrobustness? running oftheostrich( 1040-1064. of forceregulationratherthandisturbance rejection. M. A. 220. (2007). Intelligencebymechanics. 1217-1227. terrain throughactivecontroloflandingconditions. 1665-1676. Mobile Machines(CLAWAR) D.E. Conference onClimbingandWalking RobotsandtheSupportTechnologies for Koditschek, and energy-efficient, dynamicwalkingrobot.In R. Full, U., Saranli, biologically inspiredhexapodrunner. D., McMordie, pp. 243-247.Budapest,Hungary:IFAC. optimal controlproblems.In Searches forthebest-fittingparameters, S1–S3). Therefore,themodellingapproachcouldhavefailedtofit , 1097-1103. (2014). Swing-legtrajectoryofrunningguinea fowlsuggeststask-levelpriority (1989). Thespring-massmodelforrunningandhopping. Science

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