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Analysis on Effective Walking Pattern for Multi-Legged Robots Byoung-Ho Kim Bio-Mimetic Control & Robotics Lab., School of Electrical and Mechatronics Eng., Kyungsung Univ., Busan, 608-736, Korea . 4 , . , . ,4 . , 4 . : , , , Abstract A proper walking pattern is to be assigned for a walk of multi-legged robots. For the purpose of identifying a good walking pattern for multi-legged robots, this paper consider a simple model of quadruped robotic walking and analyze its walking balance based on the centroid of foot polygons formed in every step. A performance index to estimate the walking balance is also proposed. Simulation studies show that the centroid trajectory of foot polygons and the walking balance in a common quadruped walking are different according to the walking pattern employed. Based on the walking balance index and a bio-mimetic aspect, a useful walking pattern for quadruped robots is finally addressed. Key words : Multi-legged robot, Walking pattern, Centroid trajectory of foot polygon, Walking balance 1. (mobile robot) , , , , . , . . (1) , (2) , (3) [1].

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Page 1: Analysis on Effective Walking Pattern for Multi-Legged Robotsks.ac.kr/kimbh/paper-pdf/DomesticJournal/2009_KIIS_V19_N5.pdf · balance in a common quadruped walking are different according

Analysis on Effective Walking Pattern for Multi-Legged Robots

Byoung-Ho Kim

Bio-Mimetic Control & Robotics Lab., School of Electrical and Mechatronics Eng., Kyungsung Univ.,Busan, 608-736, Korea

.4

,. , . , 4

., 4 .

: , , ,

Abstract

A proper walking pattern is to be assigned for a walk of multi-legged robots. For the purpose of identifying a goodwalking pattern for multi-legged robots, this paper consider a simple model of quadruped robotic walking and analyzeits walking balance based on the centroid of foot polygons formed in every step. A performance index to estimate thewalking balance is also proposed. Simulation studies show that the centroid trajectory of foot polygons and the walkingbalance in a common quadruped walking are different according to the walking pattern employed. Based on the walkingbalance index and a bio-mimetic aspect, a useful walking pattern for quadruped robots is finally addressed.

Key words : Multi-legged robot, Walking pattern, Centroid trajectory of foot polygon, Walking balance

1.(mobile robot)

, ,

, ,. ,

.

.(1) , (2)

, (3)[1].

Page 2: Analysis on Effective Walking Pattern for Multi-Legged Robotsks.ac.kr/kimbh/paper-pdf/DomesticJournal/2009_KIIS_V19_N5.pdf · balance in a common quadruped walking are different according

.

[2]. ,

[3].,

[4] [5].

(walking robot). ,

,

.,

(maneuverability) (balance). ,

.

.,

. (walkingbalance)

. 6[6]- [9].

4

. ,

4. 4 4

. 4,

[10] [3]. ,(center of gravity)

. ,(equilibrium)

,

. 4[11] ,

(essential issue) .

. 4,

(foot polygon)(walking performance index)

. ,4

.

2. 44

1 4 .

(a) Titan VIII [10] (b) AIBO [13]

(c) BigDog [15]

1. 4

Fig. 1. Quadruped walking robots

2. 4

Fig. 2. Model of a quadruped robot

1(a) Titan VIII(Tokyo Institute of Technology) 4

[10]. Arikawa Hirose

Page 3: Analysis on Effective Walking Pattern for Multi-Legged Robotsks.ac.kr/kimbh/paper-pdf/DomesticJournal/2009_KIIS_V19_N5.pdf · balance in a common quadruped walking are different according

. 1(b)Sony [12] [13].

. 1(c) Boston Dynamics4

[14].

.

,

4 2 .

3.2 4

. ,(platform)

.

(a) (b)

3.

Fig. 3. Foot polygons

,. ,

3,

,(Cg(xg(t), yg(t)))

.

xg(t) = {x1(t) + x2(t) + x3(t)}/3 (1)

yg(t) = {y1(t) + y2(t) + y3(t)}/3 (2)

, xi(t)(i = 1, 2, 3) yi(t)(i = 1, 2, 3)x- y- .

,.

xg(t) =1

s1(t) − s2(t){s1(t)xg1(t) − s2(t)xg3(t)

+yg3(t) − yg1(t)} (3)

yg(t) ={

s1(t){xg(t) − xg1(t)} + yg1(t), ors2(t){xg(t) − xg3(t)} + yg3(t)

(4)

, xi(t)(i = 1, 2, 3, 4) yi(t)(i = 1, 2, 3, 4)x- y- .

s1(t) �f1f2f3 (Cg1(t))�f1f3f4 (Cg2(t))

, s2(t) �f1f2f4(Cg3(t)) �f2f3f4 (Cg4(t))

.

4.

,,. ,

.,

(walkingbalance index) .

IB = min(rj(t)), j = 1, · · · , n (5)

, min(rj(t)) rj(t). n

3 , 4. 3 j

(rj(t)) .

rj(t) =√{xg(t) − xj(t)}2 + {yg(t) − yj(t)}2. (6)

(5) , (IB)

,

.

5.

4.

, 4 (footpolygon) ,

(walking performance index).

5.1

, k(N ) [1].

N = (2k − 1)! (7)

Page 4: Analysis on Effective Walking Pattern for Multi-Legged Robotsks.ac.kr/kimbh/paper-pdf/DomesticJournal/2009_KIIS_V19_N5.pdf · balance in a common quadruped walking are different according

, q! q (factorial) . ,4 5040

.,

. ,4

,, 1

.

(a)

(b)

4. 4

Fig. 4. Walking patterns of a quadruped robot

1.

Table 1. Walking patterns starting from the first leg.

Case Order of foot step Remarks

I f1 → f2 → f3 → f4 → f1 Fig. 4(a)II f1 → f2 → f4 → f3 → f1III f1 → f3 → f4 → f2 → f1 Fig. 4(b)IV f1 → f3 → f2 → f4 → f1V f1 → f4 → f2 → f3 → f1VI f1 → f4 → f3 → f2 → f1

2.

,

. x-y-

.

xi(t + dt) = xi(t) + pirand(1), i = 1, 2, · · · , 4 (8)

yi(t + dt) = yi(t) + pirand(1), i = 1, 2, · · · , 4 (9)

, rand(1) 0 1(random) . pi

,, 0.05

. (step)dt 5ms .

5.2 4

. 4

, 4,

. ,

.

.,

,. , (behavior)

.

5.

Fig. 5. Reference foot trajectory for the walking task

, 2. ,

1.

, 5 .(8) (9) .

Page 5: Analysis on Effective Walking Pattern for Multi-Legged Robotsks.ac.kr/kimbh/paper-pdf/DomesticJournal/2009_KIIS_V19_N5.pdf · balance in a common quadruped walking are different according

(a) Case I: f1 → f2 → f3 → f4 → f1 (b) Case II: f1 → f2 → f4 → f3 → f1

(c) Case III: f1 → f3 → f4 → f2 → f1 (d) Case IV: f1 → f3 → f2 → f4 → f1

(e) Case V: f1 → f4 → f2 → f3 → f1 (f) Case VI: f1 → f4 → f3 → f2 → f1

6.

Fig. 6. Centroid trajectory of foot polygons during the walking task

Page 6: Analysis on Effective Walking Pattern for Multi-Legged Robotsks.ac.kr/kimbh/paper-pdf/DomesticJournal/2009_KIIS_V19_N5.pdf · balance in a common quadruped walking are different according

6 1

. ,(1) ∼ (4)

. , 6(a) (Case I: f1 → f2 → f3→ f4 → f1) . ,

, , ,

.,

.,

. ,,

..

, 4.

. ,

. ,

.,

,. , 6

,,

.1

. , (5) ,

IB

.7 1

.,

(Case III: f1 → f3 → f4 → f2 → f1).

(Case V: f1 → f4 → f2 → f3 → f1).

, , (Case II:f1 → f2 → f4 → f3 → f1)

.,

, ,.

.

7.

Fig. 7. Balance index for the walking task

, 7, (Case III)

4.

6.

., 4

.

[13] [9] [16]

. , 4

,(Case III)

4.

,,

(random walking) .

[1] R. Siegwart and I. R. Nourbakhsh, Introduction to au-tonomous mobile robots, The MIT Press, 2004.

Page 7: Analysis on Effective Walking Pattern for Multi-Legged Robotsks.ac.kr/kimbh/paper-pdf/DomesticJournal/2009_KIIS_V19_N5.pdf · balance in a common quadruped walking are different according

[2] Y. Hada, H. Gakuhari, K. Takase, and E. I. Hemeldan,“Delivery service robot using distributed acquisition,actuators and inteliigence,” in Proc. of IEEE/RSJ Int.Conf. on Intelligent Robots and Systems, pp. 2997-3002, 2004.

[3] J. Estremera and P. G. deSantos, Generating contin-uous free crab gaits for quadruped robots on irregularterrain, IEEE Transactions on Robotics, vol. 21, no.6, pp. 1067-1076, 2005.

[4] S. Nakajima, E. Nakano, and T. Takahashi, “Mo-tion control technique for practical use of a leg-wheelrobot on unknown outdoor rough terrains,” in Proc.of IEEE/RSJ Int. Conf. on Intelligent Robots and Sys-tems, pp. 1353-1358, 2004.

[5] M. Takahashi, K. Yoneda, and S. Hirose, “Roughterrain locomotion of a leg-wheel hybrid quadrupedrobot,” in Proc. of IEEE/RSJ Int. Conf. on IntelligentRobots and Systems, pp. 1090-1095, 2006.

[6] S. Cordes, K. Berns, and I. Leppanen, Sensor com-ponents of the six-legged walking machine LAURONII, in Proc. of IEEE Int. Conf. on Advanced Robotics,pp. 71-76, 1997.

[7] U. Saranli, M. Buehler, and D. E. Koditschek, RHex:a simple and highly mobile hexapod robot, Int. Jour.of Robotics Research, vol. 20, no. 7, pp. 616-631,2001.

[8] J. G. Cham, S. A. Bailey, J. E. Clark, R. J. Full,and M. R. Cutkosky, Fast and robust: hexapedalrobots via shape deposition manufacturing, Int. Jour.of Robotics Research, vol. 21, no. 10-11, pp. 869-882,2002.

[9] P.-C. Lin, H. Komsuoglu, and D. E. Koditschek, Aleg configuration measurement system for full-bodypose estimates in hexapod robot, IEEE Transactionson Robotics, vol. 21, no. 3, pp. 411-422, 2005.

[10] K. Arikawa and S. Hirose, Development ofquadruped walking robot TITAN-VIII, in Proc. ofIEEE/RSJ Int. Conf. on Intelligent Robots and Sys-tems, pp. 208-214, 1996.

[11] B.-H. Kim, “Centroid-based analysis of quadruped-robot walking balance,” in Proc. of Int. Conf. onAdvanced Robotics, FD1: Humanoid and WalkingRobots Session, 2009.

[12] M. Fujita and H. Kitano, Development of an au-tonomous quadruped robot for robot entertainment,Autonomous Robots, vol. 5, pp. 7-18, 1998.

[13] G. S. Hornby, S. Takamura, T. Yamamoto, andM. Fujita, Autonomous evolution of dynamic gaitswith two quadruped robots, IEEE Transactions onRobotics, vol. 21, no. 3, pp. 402-410, 2005.

[14] Http://www.bostondynamics.com/, Boston Dynamicscompany, USA.

[15] M. Raibert, K. Blankespoor, G. Nelson, R. Playter,and the BigDog Team, BigDog, the rough-terrainquadruped robot, in Proc. of the 17th WorldCongress The Int. Federation of Automatic Control,pp. 10822-10825, 2008.

[16] K. Seo, J. Choi, and Y.-W. Cho, Automatic gait gen-eration for quadruped robot using GA with an en-hancement of performance, Jour. of Korean Insti-tute of Intelligent Systems, vol. 18, no. 4, pp.555-561,2008.

(Byoung-Ho Kim)2001 : ( )1995 ∼ 2001 :

2002 ∼ 2004 : Ritsumeikan () JSPS Post-Doctoral Fel-

low2004 ∼ 2005 : RIKEN

( )2005 ∼ :

2006 ∼ 2008 :2009 ∼ :

: intelligent mobile manipulation, walking algorithm,humanoid robots, biomimetic mechanism modeling and control,multi-fingered robot/artificial hands and multiple arm control,macro/micro mechanism and intelligent control, and neural net-work applications.E-mail : [email protected]