• 검색 결과가 없습니다.

Analysis on Effective Walking Pattern for Multi-Legged Robots

N/A
N/A
Protected

Academic year: 2021

Share "Analysis on Effective Walking Pattern for Multi-Legged Robots"

Copied!
7
0
0

로드 중.... (전체 텍스트 보기)

전체 글

(1)

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].

(2)

.

[2]. ,

[3].

,

[4] [5].

(walking robot)

. ,

,

. ,

(maneuverability) (balance)

. ,

. .

,

. (walking

balance)

. 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. 4

4

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

(3)

. 1(b)

Sony [12] [13].

. 1(c) Boston Dynamics

4 [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), or

s2(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.

, , . ,

. ,

(walking

balance 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 (foot

polygon) ,

(walking performance index) .

5.1

,k

(N ) [1].

N = (2k − 1)! (7)

(4)

,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 → f1

III f1→ f3 → f4 → f2 → f1 Fig. 4(b) IV f1→ f3 → f2 → f4 → f1

V f1→ f4 → f2 → f3 → f1 VI 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) .

(5)

(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

(6)

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.

(7)

[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 irregular terrain, 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-wheel robot 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, “Rough terrain locomotion of a leg-wheel hybrid quadruped robot,” in Proc. of IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 1090-1095, 2006.

[6] S. Cordes, K. Berns, and I. Leppanen, Sensor com- ponents of the six-legged walking machine LAURON II, 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: hexapedal robots 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, A leg configuration measurement system for full-body pose estimates in hexapod robot, IEEE Transactions on Robotics, vol. 21, no. 3, pp. 411-422, 2005.

[10] K. Arikawa and S. Hirose, Development of quadruped walking robot TITAN-VIII, in Proc. of IEEE/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. on Advanced Robotics, FD1: Humanoid and Walking Robots 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, and M. Fujita, Autonomous evolution of dynamic gaits with two quadruped robots, IEEE Transactions on Robotics, vol. 21, no. 3, pp. 402-410, 2005.

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

[15] M. Raibert, K. Blankespoor, G. Nelson, R. Playter, and the BigDog Team, BigDog, the rough-terrain quadruped robot, in Proc. of the 17th World Congress 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- low

2004 ∼ 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]

수치

Fig. 1. Quadruped walking robots
Fig. 3. Foot polygons , . , 3 , , (C g (x g (t), y g (t))) . x g (t) = {x 1 (t) + x 2 (t) + x 3 (t)}/3 (1) y g (t) = {y 1 (t) + y 2 (t) + y 3 (t)}/3 (2) , x i (t)(i = 1, 2, 3) y i (t)(i = 1, 2, 3) x- y-
Fig. 4. Walking patterns of a quadruped robot
Fig. 6. Centroid trajectory of foot polygons during the walking task
+2

참조

관련 문서