Locomotion Stabilization with Transition between Biped andQuadruped Walk based on Recognition of Slope

Hiroyoshi Sawada*, Kousuke Sekiyama*, Mikiko Kojo*,Tadayoshi Aoyama*, Yasuhisa Hasegawat and Toshio Fukuda*

*Department of Micro System Engineering, Nagoya University, JAPANtDepartment of Intelligent Interaction Technologies, University of Tsukuba, JAPAN

Abstract- The applicative field of activities of robots who haveonly one locomotion strategy is limited. As means of enhancingthe mobile range, it is necessary to have various locomotionmodes. Therefore, we focus on dynamic transitions betweenseveral kinds of locomotion modes adapting to environmentalchanges. In this paper, we aim to realize stable locomotionalong some unknown test courses consisting of flat and slopewith transition between biped and quadruped walks. To achivethis transition, we propose a method to recognize a slope, adesign of the transition motion, and a technique for modifyingathe trajectories of quadruped walk to move between flat andslope. By experiments, we verify that the proposed methods can Figure 1. Concept of Multi-locomotion robotsuccessfully be applied to both upslope and downslope cases.

I. INTRODUCTION Then, we focus on transition between biped and quadrupedRecently, robots which work in human society have been walk based on recognition of terrain. As an elementary exam-

developed, such as entertainment robots and lifestyle support ple, in this paper, we aim to realize locomotion stabilizationrobots. These robots need to have greater locomotion adapt- with transition between biped and quadruped walk based on

ability than industrial robots designed for a task. Because there recognition of a slope. The robot changes locomotion mode

are various terrains in human society, such as stairs and slopes, from biped to quadruped walk in front of a slope. Because

Therefore, they have to recognize terrain and perform stable quadruped walk has an advantage in stablity compared withlocomotion autonomously. Then, many studies on locomotion biped walk. To realize this objective, we propose followingadaptatability have been carried out. three things. First, we propose a method to estimate slopeA leg-wheel robot which can move on unknown rough angle and distance from starting point to boundary between

flat and slope with a laser range finder. In addition, this methodterrains by using only information of internal sensors has beenis aple tobt nusoeadadwsoe eody

developed [1]. This robot has an advantage that it can useseveral locomotion modes adapting to various terrains. How- we design transition motion between biped and quadrupedever, the robot cannot obtain environmental information with posture. Although continuous transition from quadruped to

only internal sensors until it moves there. If external sensors biped walk have been realized on a simulation [7], in this

are also used for recognition, the robot can estimate terrain paper, the robot stops walk to transit posture in order that theand seec ocmtinmoenadace snohrxmpemotion is conducted safely. Finally, we propose a method toand select locomotion mode in advance. As another example moi h retre fudue akt oeaon

of adaptation to environment, behavior transitions between y qunbiped and quadruped walk based on gradient of slopes have boundary between flat and slope, to avoid fallind down.

been demonstrated by using the bifurcation phenomenon [2]. Although gait planning of quadruped walk in 3D environment

However, gradient is not the information which is estimated have been realized [8], we deal with trajectory generationfrom sensors. Therefore, also in this example, it can be said based on estimated information with a sensor. By experiments,

environmental recognition is required for realization we verify proposed techniques can be applied to both upslopethat priori. and downslope cases, and show that stable locomotion with

ofgaunstonom s lockgromoti trnstinhavedevelopedMul transition between biped and quadruped walk is realized.Against this background, we have developed Multi-qlocomotion robot [4] (fig.1). With this robot, we aim torealize adaptive locomotion transltion based on environmental II. MULTI-LOCOMOTION ROBOTrecognition. Therfore, this robot has several locomotion modes Multi-Locomotion Robot is a novel bio-inspired robot whichsuch as biped and quadruped walk, and brachiation. There can perfoim in stand-alone several kinds of locomotion suchhave been proposals of control methods for several locomotion as biped walking, quadruped walking, and brachiation. Wemodes [3]-[6] and verification of consumption energy [5] until built and developed Gorilla Robot III as a prototype of Multi-now. Autonomous transition between these locomotion modes Locomotion Robot. Overview and link structure of Gorillabased on environmental recognition is the current task. Robot III is shown in fig.2. Its height is about 1.0 [in] and

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j.fi6 jfi,0 j.jAO Iq-) finder, Al is the distance from the starting point to the centerof the laser range finder. These values can be calculated by

Figu ria rt IIsolving the inverse kinematics. Then, a point on the groundFigure 3. surface can be described as (xi,za).

afolw:DOlej5O2Olu Each jito Atheboundr between faslopefor inxfigl4,ahsmtraigh

is ~ ~ ~ ~ ~ ~ ~ ~ ~~~ ~ln iscetrated bylesromtropte ocnrl DD as plcbei ast-omsquaren mehodwithopointwurhichreboard,~ ~~ ~ ~ ~~ ~ ~~meZounte.ord and poe Zmae Zmitotieterb.inqaupdosr,thrbtcand Zstmaaethes z-oordiateso

Asaensorfigureo 2.io Goril rlobot ai ofse theg points onslopei iia a.

2 22 )3h-dicosa)

installed~~ ~ ~~ whrat ise thek nubeofe points which3) meet angula.esZuti.

0.m Then,an andimu rangear gn as flTOwS

Fecmeaisaloigurled3. L o telaserrange finder- ardtana f (

weight is abheo 22.0n g[kg].n flahmead nilceIs structure is d nae

asfllw:6IO. lgDOFOarm,U2NDOF lubrEachE jon Alhogwnered taen anlupslopei for.5exmpe,spothis gmetodist

ist19o audy svm rC uetsapplicaed in case-sqomes adeownlthonpein.FThermoreboard,gcounter badscmanh powerg tharesetoutsidthe robot . in quadruped posture, thet cn e e iormati o

Asgarsensoroforlrecognition ofserr le pointansima wh.installed at theon neck ofrese the rooqF

wist06 [deg]sctanpangular rangefise240e[deg],iscantitem i

0.1r[is],andmaxrimumss rhangheirofrdtecioniis 4.0teatt[pin]. Th AND QUADRUPEDPOSTURE

rotatio axes o motersare pith and yw axes.In addiionnaiALcmtio numoder fpit hc etZnn< i

wiebcamyunderaisalsointled nex tothe las finer raneige afer.1) B w In b walk, (w)

II.recogniTUNOzASOea3DopinvethexzDpnuu shownceIn fig.5, The isupportinglpoint G L-m

ofelaser isabout220[kg].Tho thpecnicud a e to bitneiondacisanedasfigurel4s:6DOFschemat sOw tat t rOblmeasurE ant heeliogh fre fe and the graitpeyr aetplnetCG [the, tebunnwen lopeinnterboied powser Tre lserunsd the prolt n

Csartesanscorordinatessogthatitheiroriginp, i locatedrathe pointe Fn 1hFostaie1n de

recognized at sloe inekothex-zb2D suFace3. Itanfgul,ariesolthe onge[ j LzLdirectly6under] thenlaseulr rangefinde and [desgn, santmeto tos 1VESG OF ±RNITO JEWE BI (6)of laser anto thexdwnwar drection, andectio is the disanc whrThie AlNgt ofUtheUPEnDulmPOTREfrigt9,wbeweenthmer cetealofisaldettthelaserrnefner randgte pointer on Bpdwlig nbpdwak emdlterbta

the ground surface. These data are obtained from the laser on the constrainedcplane desi asrange finder. In addition, h is the heighteo the laser range eq ( )c

ZG =kSc±kyYG±ZC , (7)

withthesagittalplaneTherefore,wedeinethesy fwherekq andko are parameters determining the gradient ofn c s sn the constrainedXplane, z is the z-intercept. If eq.(8)is satisfied,

y z~~~~~~~~~~~~~~~xFigure 4. Measuring an slope Figure 5. Robot modeled as 3D penulum

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COG moves on it. ° Swing LegFk1 *:Stance Leg ~~~~~~~".Moving Directionr-kx O:Sac e

[fe-L fY- fZ-mg]L-k2=O * (8) (1) (2) o (3)*~~~~~~~~~~ ' SM_Substituting eq.(7) into eq.(8) gives f.

mgr (9)9 Izc

Substituting eq.(9 )into eq.(6) yields the following equations. (4) (5) (6)g

?- ?G (10)

{YG = g YG------- ----oSolving eq.(10), eq.(11) are obtained. * S

f xc(t)=C exp( p(g/Zc) +C2exp(- g) (11) Il. yG(t) =C3 exp( g/Zc) ± C4 exp(- g/ ) Figure 6. Crawl gait

where C1, C2, C3, and C4 are given by following conditions.

x(ti) a-- , xt=-a (12 the robot then swings the front and rear legs on its other side2 2 and adjusts its COG accordingly (Fig. 6(4)-(6)).

yc(ti) = v , y0(t2) -v (13) This shows that the Intermittent Crawl Gait is capable ofwhere a is the length of stride, tl, t2 are the times when performing a forward motion that follows a zigzag COGone foot contacts the ground, and when the other does, trajectory.respectively. In addition, v is the velocity of COG at tl. Next, we will describe the design method of a zigzag COG

Furthermore, we design the motion of the idling foot (xf, trajectory. The COG trajectory is determined by ensuring thevyf, zf) as shown in eq.(l4). projecting point of the COG is located among the static stableyf,zf)as

shown in eq.(14).domains provided by the support polygon. In this paper, the

rf (t) Cf it3 + Cf2t2 + Cf3t + Cf4 position of the projective point of the COG is decided bygzf = /(1b I - (14) setting up the stability margin. The stability margin degree

yf(t) 1nis the distance from the projecting point of the COG to thetyf (t) = zf (t) tan Ovoll neighborhood of the nearest support polygon (SM in Fig. 6),

where 0,01, is the roll angle of the ancle joint of supporting and is the evaluation index of the simplest static stability [17].foot, Cf i, Cf 2, Cf 3, and Cf 4 are given by following condi- Thus, by establishing the stability margin, the projecting pointtions. of the COG is determined, and the COG trajectory is projected.

Xf (ti) =-a , Xf (t2) = a (15) B. Design of transition motionf (ti) = 0 , f (t2) = . (16) This section describes the transition from biped to

Then, the joint angles are given by solving the inverse kine- quadruped posture. Before transiting the posture between

matics. In addition, the number of steps nb are decided with biped and quadruped stance, the robot stops walking. The

Is.2) Quadruped walking: In this paper, we use crawl gait

as a quadruped walking (fig.6) to move on flat or slope. Inthis gait, the robot's motion is separated from its leg movingparts and COG moving parts. So the robot realize more stablequadruped walking than in case of legs and COG moving l \simultaneously. And we can give the robot its The intermittent _ _crawl gait has been successfully used by robots walking on (A) (B) (C)steep slopes is a widely used control method [10], [11], [ 12], Figure 7. Between biped posture and quadruped posture[13], [14], [15].With Multilocomotion robot, the gait has been It.obtained [16]. Its crawl gait pattern is described below. ---c m=o b Ga Ca

First, the robot swings its rear and front legs on one 3so Mtr\ '\Caside forward while at the same time maintaining the COG Oh--^ip Okne lb

projection in the support polygon (Fig. 6(1)-(2)). Second, the \ ma<5 0,2'robot's state transitions from three-point grounding to four- Gank i 11112N3d\point grounding. Third, the robot changes the COG inside a if 1

new support polygon (Fig. 6(3)). Using the same technique, Fiur 8. Deiito ofteaamtr

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transition motion is designed on 2D model shown in fig7. are kept to the ground.(A) shows the biped posture, (B) shows the moment thatfront legs are leaving or touching the ground, and (C) shows 1 ±+ 12 - 2torlllcos(w - Ohip) (28)the quadruped posture. The design of motion is divided into ±2+2 -2following two phases. Between (A) and (B) we control the Ob = COS 21b +tor 11 (29)joint angles to keep COG right above the rear feet, and to 21bltorkeep all the feet to the ground between (B) and (C). Fig.8 I 2 2shows difinition of the parameters. The trajectories of Oanmk, VI ± 112Sfl2arik) ±(if ±112COSOarik), (30)Okine, and Ohip between (A) and (B) are designed as eq.(17). (12 +( b12_) (31)

Oankk(t) aal bal Cal dal 1 fOkne,(t) j akl t3+ Lbkl t2+ Cklj t+ dkl2 (17) If=tn_l + 112CO80an (2

L Ohip (t) J Lahl bhl L Ch(7L d) O= tan Id + ll2Osinank Jwhere the coefficients of eq.(17) are determined from eq.(1 8) 1 _2+ 12-_12to eq.(21). Od = 2C1 (33)

[Oank(tA) Okine(tA) Ohip(tA) ]= [OAOnThe Ship ] P8) Then, o osho and Ake are described as eq.34 and eq.35.[rank(tLA) kner(LA) hip(LA)] T= [0 0° ]T (19) Osho Oa +Ob (34)Oank (tB) Ockne(tB) Ohip(tB)] - arik fb^rie O/jf20)ahOkne = - Oanrk + Ohip - Osho - Oc - Od * (35)

[&irikLB) Ore(L) Oh~(LB) T= [0 0 01T (2)2Oank (tB) Okine,(tB) Ohip(tB)]21)=[°°°V. METHOD TO MODIFY THE TRAJECTORIES OF

where OA and 0B are the joint angles at (A) and (B), tA and QUADRUPED WALKtB are the times at (A) and (B) , respectively. Then, Osho iS A. Method to modify the feet trajectoriesfound under the condition that COG is kept right above therear feet. To realize smooth locomotion aroud the boundary between

flat and slope, we designed feet position of landing and

Osho =arcsin( 1 [M2C12s . modified the trajectory of COG. First, the modified height ofmaca Ll2Oarik the robot's feet, at the time when they go beyond the boundary,

+mll (ll2 sinOanmk + Cll SinOkne) are given as eq.(36).

+mtor(ll2sin0ank + Illlsin0kftne + ctorsin0thip) ZSW (x - d) tan . (36)

+ma(ll2sin0ank l+IllSin n,re +± torSin0hip)}1V2) where 0 is the slope angle estimated with information fromthe laser range finder, x is the quad stride and d is the distancefrom the feet position before moving to the boundary flat and

where m, 1, and c are the parameters of the robot shown in slope in fig. 9.fig8.

Then, the trajectories of Oank and Ohip between (B) and (C) B. Method to modify the COG trajectoryare designed as eq.(23).

Secondly, after the feet reaching slope, the COG trajectoryF Oank (t) 1 F aa2 1 +F ba2 t2 +F Ca2 1 t+F da2 1 (23) is revised as fellows. In fig.l0, when the robot goes beyondOhip (t) [ah2 [bh2 [Ch2 j [dh2 J the boundary, it is assumed that the robot walks on the ground

where the coefficients of eq.(23) are determined from eq.(24)to eq.(27). LRF

[Sark(LB) Ohjp(LB) ] = [O° B] T, (24)

[rikL)O~(B 1T [0C1 (25 (X ),ZOank (tLC) Ohip (tLC) [=Lank TShip (26)

[&ank(tC) Ohip(tC) ]T [0 ° ] (27)

where tB and 00 are the joint angles at (B) and (C), LB and d__Lc are the times at (B) and (C) , respectively. Then, 1 and 0 I Ishown in fig.8 are found under the condition that all the feet Figure 9. Planning the position of landing

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x/2 TABLE I2+iGLPF CONDITION OF EXPERIMENT 1

zc ~ _

[deg] IS[m] TB[S] |VB[S] |TQ[S] VQ[S] |TB Q[S]]15.0 1.0 2.00 0.100 8.00 0.0675 10.0

ZJ i AW« W TABLE II

RESULTS OF EXPERIMENT 1

X t b~ ~ ~ ~ ~ ~ ~ ~ ~ X~~~~[deg] l s[m] |nb|_ _ 16.3 T0990T1 21

TB, VB are the period and the velocity of biped walk, and TQ,Figure 10. Modification of COG position VQ are those of quadruped walk. Tablell shows the estimated

parameters. Scaned data with LRF are shown in fig.12 and

tilted at . Using the feet modified value zsWS we design the fig.13 shows snapshots of Experiment 1angle / as eq.(37).

400

/3= arcsin (j)wac. (37) 6030,1 """b 200100

where b is the distance from front feet to rear feet. This 0 W

parameter is a fixed number because of the quad stride doesn't -1000 500 1O0 1500 2000 2500 3000

change. Then the value of the modified COG height is given X-coordinate[mmn]by eq.(38). Figure 12. Estimated shape of terrain 1

Zcogtan (38)

In the same way as feet modifications, COG trajectoryis adjusted with the z axis direction.The above-mentionedmethod adjusts only side motion, right or left side. The robotrepeat this motion, so it ascend on a discontinuous plate. t-O[s] t=7[s] t=14[s]On the flat, prejective point of COG is fixed on the stabilitymargin(fig6). In the case of moving on the slope, projectivepoint of COG is shown as figil1. The COG trajectorys areneeded to change for the purpose of this point existing insidesuppurt polygons. When the robot steps on slope completely,its prejective point of COG altered during one moving phase. t=21 [s] t=28 [s] t=35 [s]So the robot is capable of adjusting to both flat and slope.

VI. EXPERIMENT

A. Experiment ]

In this experiment, the robot walks from flat to upslope. Atfirst, it estimates the slope information (¢b and IS) in biped t42E49 EES ~~~~~ ~ ~ ~~~~ ~ ~~~~~~~~~~~~~~~~~t=4[s]t=4IS]t56 ,S,posture at the stating point. Based on it, nb is desided. Then, Figure 13. Snapshots of Experiment 1the robot starts biped walk and stops it at nb steps to transit toquadruped posture. Finally the robot climbs up the upslope inquadruped posture. Tablel shows the experimental condition. B. Experiment 2

In this experiment, the robot walks from flat to downslopein the same way as Experiment 1. Tablelll shows the experi-mental condition. Fig.14 discribe the shape of terrain 2 givenby LRF. TableIV show the estimated terrain and parameters.And snapshots of Experiment 2 are shown in fig.15.

t, \ ,_ ~~~~~~~C.Discussioniv, _ ~~~~~~~~Theerror range of ¢b was within ±1.5[deg]. That Of ls wasC_ ~~~~~~~~~~within±O.02[m]. Although stable locomotion was realized to

Projcctivc Point ofCOG an extent in experiment, the accuracy of slope estimation isnot enough. Therefore, we are planning to use other sensors

Figure 11. Projective Point of COG together for terrain estimation.

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TABLE IIICONDITION OF EXPERIMENT 2

I[deg] lS[m] TB[S] VB[S]I TQ[S]I VQ[S]I TB<Q[S] E I10.0 0.7 2.00 0.100 8.00 0.0675 10.0 E 'lI

-200 .3-400

TABLE IVRESULTS OF EXPERIMENT 2 X-coordinate[mm]

|[deg] Ts [ml nb Figure 14. Estimated shape of terrain 29.95 0.72 3

VII. CONCLUSIONS AND FUTURE WORKS

A. Conclusions

In this paper, we made following three propositions. The t=0[s] t=3[s] t=7[s]first was a method to recognize an unknown slope with thelaser range finder. The second was the design of transitionmotion between biped and quadruped posture. The third was atechnique for modifying the trajectories of quadruped walk. Byexperiments, we verified the proposed methods can be appliedto both upslope and downslope cases, and showed that stable t=14 [s] t=21 [s] t=28 Es]locomotion with transition between biped and quadruped walkhave been realized.

B. Future Works

Although we dealt with only biped walk and quadrupedwalk in this paper, we will deal with other locomotion modes t=35 [s] t=42 [s] t=49ss]such as brachation and ladder climbing for transition. Fur- Figure 15. Snapshots of Experiment 2thermore, we will poropose environmental recognition withinformation from other sensors for example inclination sensorand gyroscope. [11] Hirose S., Tsukagoshi H., and Yoneda K. (2001): "Normalized Energy

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