Two Arms Design and Dynamic Analysis of Biped Walking

Robot

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...

()

()

()

2007 2

Two Arms Design and Dynamic Analysis of

Biped Walking Robot

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In this paper, I designed and constructed two light-weighted 12 d.o.f

robot arms for the humanoid robot and studied its kinematics model. The

weight of one arm is light enough to be 9 Kg but capable of delivering

10Kg pay load.

To find out the characteristics of the robot arm, an analysis on the

kinematics and dynamics was performed. For appropriate design of the

motor capacity, a computer simulation based on the analysis on the

kinematics and dynamics was performed. Through this, the required

torques for delivering the payload were capable of measuring.

Since an ultra-light robot arm despite of heavy pay load was designed,

an FEM analysis was performed using ANSYS tool to estimate deformation

of the robot link. The accuracy of the analysis was verified through the

actual pay load test measuring the deformation of the robot link.

K

im i

V

L Lagrangian ( )VKL =( )S (skew symmetric matrix)

iI i (inertia moment)

vciJ i (Jacobian)

iJ i

D

C (Coriolis)

i i

iO i

iq i

il i

cil i

id

iF

i

H

Q

iM

AbstractAbstractAbstractAbstract

1 1 1 1 .......................................................................... 1

2 2 2 2 ........................................ 3

2.1 .......................... 5

2.2 ......................................... 8

2.3 ................................ 11

3 3 3 3 ................................ 13

3.1 ................................................... 13

3.2 ................................................................. 17

3.3 .......................................... 21

3.4 .......................................... 28

3.4.1 ............ 28

3.4.2 ......... 31

3.4.3 ............ 33

3.3.4 ....................... 35

3.3.5 ............... 35

4 4 4 4 ........................................ 37

4.1 4 ................. 37

5 5 5 5 ............................ 42

5.1 .......................................................... 42

5.2 .......................................................... 43

5.3 .................................................. 45

5.4 ...................................................... 45

6 6 6 6 ........................................................................ 48

............................................................................... 49

Table 2.1 Specification of the KUBIR-2 ..................................... 10

Table 2.2 Degrees-of-freedom of the KUBIR-2 ......................... 10

Table 3.1 Link parameter for the KUBIR-2 arm ........................... 14

Table 4.1 Constants of the load torque in each joint .................. 39

Table 5.1 Material property ....................................................... 43

Table 5.2 Element type and number .......................................... 43

Table 5.3 Displacement FEM of the KUBIR-2 arm ...................... 43

Table 5.4 Experiment result of displacement of the KUBIR-2 arm

.............................................................................................. 46

Table 5.5 Adjusted displacement by servo motor ........................ 46

Fig. 2.1 Structure of the KUBIR-1 arm ........................................ 3

Fig. 2.2 Structure of the KUBIR-2 arm ........................................ 4

Fig. 2.3 Structure of for bar link ................................................. 5

Fig. 2.4 3 dimensional model of the one axis actuator ................. 6

Fig. 2.5 Structure of the one axis actuator.................................... 7

Fig. 2.6 Structure of the two axis actuator.................................... 7

Fig. 2.7 System composition of the KUBIR-2 arm ........................ 8

Fig. 2.8 3 dimensional model of the KUBIR-2 arm ..................... 12

Fig. 3.1 D-H coordinate frame assignment for the KUBIR-2 arm ..14

Fig. 3.2 Four-bar-link structure for shoulder joint ....................... 28

Fig. 3.3 Four-bar-link structure for elbow joint .......................... 31

Fig. 3.4 Four-bar-link structure for wrist joint ............................ 33

Fig. 4.1 Torque analysis of the shoulder joint ............................. 37

Fig. 4.2 Torque analysis of the elbow joint ................................ 38

Fig. 4.3 Torque analysis of the wrist joint ................................ 38

Fig. 4.4 Load torque of the shoulder joint ................................ 40

Fig. 4.5 Load torque of the elbow joint ..................................... 40

Fig. 4.6 Load torque of the wrist joint ....................................... 41

Fig. 5.1 Finite element model ................................................... 42

Fig. 5.2 FEM result of KUBIR-2 arm .......................................... 44

Fig. 5.3 Comparison result of FEM analysis and experiment ........ 47

Pic. 5.1 Experiment setup of the KUBIR-2 arm for displacement

measure ................................................................................. 45

1

1 1 1 1

.

. ,

HRP-2, I-FOOT, KAIST [1-3] 50kg

.

.

,

, .

[4], 2R SCARA 3R

, , [5],

[6],

[7], A Mechatronics

Approach to the design of light-weight arms and multifingered hands[8]

.

. 2

2

. 3

. 4

. 5 .

6 .

3

2 2 2 2

(KUBIR-1) 5

. 0, 1 DC

2 DC -

(gripper) 3, 4

RC . Fig. 2.1

.

(KUBIR-2) .

6 . 0, 4 DC

1, 2, 3, 4 4

. Fig. 2.2 .

Fig. 2.1 Structure of the KUBIR-1 arm

4

Fig. 2.2 Structure of the KUBIR-2 arm

5

2.1

KUBIR-2

. ,

.

,

. KUBIR-2 4

.

. Fig. 2.3 .

Fig. 2.3 Structure of four bar link

6

1 2 1

1.5kg 2 3.5kg . Fig. 2.5

3 Fig. 2.6, 2.7 1 2

.

Fig. 2.4 3 dimensional model of the one axis actuator

7

Fig. 2.5 Structure of the one axis actuator

Fig. 2.6 Structure of the two axis actuator

8

2.2

(KUBIR-2) 173cm, 92kg, 13,

12, 4 29 .

CCD 2

. 6

yaw-pitch-pitch-pitch-roll-pitch

(ball screw) 4

. 6

yaw-roll-pitch-pitch-pitch-roll

.

9

Fig. 2.7 System composition of the KUBIR-2

10

Table. 2.1 Specification of the KUBIR-2

Height 160[cm]

Weight 75[kg]

Actuator

Arm

DC Servo motor + Harmonic speed reducer

DC Servo motor + Ball screw

Leg

DC Servo motor + Harmonic speed reducer

DC Servo motor + Ball screwHead DC motor

Control unit

ArmTMS320LF2407 + Motor DriverLeg

Head

Power Capacity

Arm24V/50AHLeg

Head

SensorUSB cam, Tilt sensor, FSR,

Magnetic sensor, Proximity sensor

Table. 2.2 Degrees-of-freedom of the KUBIR-2

HeadNeck 2 DOF

Eye 1 DOF 2eye = 2DOF

Arm

Left 5 DOF(shoulder 2 + elbow 1 + wrist 1)

Right 5 DOF(shoulder 2 + elbow 1 + wrist 1)

Hand 1 DOF 2hand = 2DOF

Leg

Left 6 DOF(hip 3 + knee 1 + ankle 2)

Right 6 DOF(hip 3 + knee 1 + ankle 2)

Waist 1 DOF

Total 29 DOF

11

2.3

76cm, 9kg

(gripper) 2 (roll-pitch), 1

(pitch), 2 (pitch-yaw) 6

.

(gripper) 4

, .

(gripper)

4 . 4

DC .

4 .

Fig. 2.4 3 .

12

Fig. 2.8 3 dimensional model of the KUBIR-2 arm

13

3 3 3 3

.

(gripper) (kinematics)

(jacobian)

.

, 5 (manipulator)

.

.

3.1

(homogeneous transform)

.

Denavit Hartenberg(D-H)

. 4

.

=

100

0cossin

0sincos

,

zR

=

cossin0

sincos0

001

,xR

=

cos0sin

010

sin0cos

,yR

iiii xaxdzziRotTransTransRotA ,,,,=

14

, , , 4 (parameter).

(length), (twist),

(offset), (angle) .

4 3 1 . ,

, .

Fig. 3.1 D-H coordinate frame assignment for the KUBIR-2 arm

Table 3.1 Link parameter for the KUBIR-2 arm

Link

1 90 0

2 0 0

3 0 0

4 0 90 0

5 0 0

15

.

=

1000

0010

sincos0sin

cossin0cos*

11*

1*

1

*11

*1

*1

1

a

a

A

=

1000

0100

sin0cossin

cos0sincos*22

*2

*2

*22

*2

*2

2

a

a

A

=

1000

0100

sin0cossin

cos0sincos*33

*3

*3

*33

*3

*3

3

a

a

A

=

1000

0010

0cos0sin

0sin0cos*4

*4

*4

*4

4

A

=

1000

100

00cossin

00sincos

5

*5

*5

*5

*5

5d

A

543210

5 AAAAAT =

.

16

=

1000333231

232221

131211

50

z

y

x

prrr

prrr

prrr

T

11 5 1 4 2 3 2 3 1 4 2 3 2 3 1 5{ ( ) ( )}r c c c c c s s c s s c c s s s= + +

12 5 1 4 2 3 2 3 1 4 2 3 2 3 1 5{ ( ) ( )}r s c c c c s s c s s c c s s c= + +

13 1 4 2 3 2 3 1 4 2 3 2 3( ) ( )r c s c c s s c c c c s s= +

21 5 1 4 2 3 2 3 1 4 2 3 2 3 1 5{ ( ) ( )}r c s c c c s s s s s c c s c s= +

22 5 1 4 2 3 2 3 1 4 2 3 2 3 1 5{ ( ) ( )}r s s c c c s s s s s c c s c c= +

23 1 4 2 3 2 3 1 4 2 3 2 3( ) ( )r s s c c s s s c s c c s= + +

31 5 4 2 3 2 3 4 2 3 2 3{ ( ) ( )}r c c s c c s s c c s s= + +

32 5 4 2 3 2 3 4 2 3 2 3{ ( ) ( )}r s c s c c s s c c s s= + +

33 4 2 3 2 3 4 2 3 2 3( ) ( )r c c c s s s s c c s= + +

, p .

5 1 4 2 3 2 3 1 4 2 3 2 3 1 1 2 2 3 3 2 3 3 2{ ( ) ( )} ( )xP d c c s c c s c s c c s s c a a c a c c a s s= + + + + +

5 1 4 2 3 2 3 1 4 2 3 2 3 1 1 2 2 3 3 2 3 3 2{ ( ) ( )} ( )yP d s c s c c s s s c c s s s a a c a c c a s s= + + + + +

5 4 3 2 2 3 4 2 3 2 3 2 2 3 3 2 3 3 2{ ( ) ( )}zP d s c s c s c c c s s a s a s c a c s= + + + +

17

3.2

,

.

5,...,1,10

)()(

)(),...,()(

00

110

=

=

=

nqdqR

qAqAqTnn

nnn

(3. 1)

, .

,

.

.

.

,

Tnnn RRS )()( 000 &&= (3. 2)

. .

0 0n nv d= & (3. 3)

, .

18

5,...,1,)()(,)( === iqqJqRqqJv iTiiivci c

&& (3. 4)

.

.

5,...,1,)(

1

1 =

=

iz

OOzJ

i

inii

(3. 5)

,

.

Fig. 3.1

.

,

.

19

20

21

3.3

Euler-Lagrange , .

5,...,1,)()()( ==++ kqqqqcqqd kkjiijkj

jkj &&&& (3. 6)

. (3. 6)

2 ,

1 Coriolis

,

.

. 5

Euler-Lagrange

.

( ) ( , ) ( )D q q C q q q q + + =&& & & (3. 7)

, 155555 )(,),(,)( RqRqqCRqD & .

.

,

.

22

.

.

.

23

24

, .

:

: ()

:

: ()

: Gripper

: ()

:

Chrostoffel

Coriolis

.

.

25

26

5

.

.

.

27

Euler-Lagrange

.

. .

28

3.4

4

.

.

.

3.4.1

Fig. 3.2 Four-bar-link structure for shoulder joint

4

Fig. 3.2 .

. .

29

. .

,

.

(3. 8)

(3. 8) 1 2 .

(3. 9)

(3. 10)

.

(3. 11)

.

30

(3. 12)

(3. 13)

31

3.4.2

Fig. 3.3 Four-bar-link structure for elbow joint

4 Fig. 3.3

. .

.

. .

,

.

(3. 14)

1 2 .

32

(3. 15)

(3. 16)

.

(3. 17)

.

(3. 18)

(3. 19)

33

3.4.3

Fig. 3.4 Four-bar-link structure for wrist joint

4 Fig. 3.4

. .

.

. .

,

.

(3. 20)

1 2 .

34

(3. 21)

(3. 22)

.

(3. 23)

.

(3. 24)

(3. 25)

35

3.4.4

F .

, ,

,

.

iiii pF sin= (3.26)

i , ip .

)/cos( iii pda= (3.27)22

2 adp ii +=

3,2,1=i , , a

cb, .

3.4.5

. ,

Euler-Lagrange

. (3.26)

36

. ,

5

Euler-Lagrange (3.6)

.

,

.

( ) ( , ) ( )fH d d Q d d d h d LF+ + =&& & & (3.28),

3 1( ) ( ) ( ), ( , ) ( , ) ( ) ( )ij ij i ij j jH d D d R d Q d d C d d H d R d d= = +& & &

. (3.28) L 2

.

37

4 4 4 4

4

, ,

. 10kg (gripper)

. , ,

.

,

.

4.1 4

Fig.

4.1~4.3 .

Fig. 4.1 Torque analysis of the shoulder joint

38

Fig. 4.2 Torque analysis of the elbow joint

Fig. 4.3 Torque analysis of the wrist joint

.

.

39

1111

121211

CosL

CosLMF

=

(4.1)

2121

222222

CosL

CosLMF

=

(4.2)

3131

323233

CosL

CosLMF

=

(4.3)

, .

16.7kgf, 13.2kgf, 11.7kgf .

(4.4) ,

(4.5) .

i

ia Cos

FF

=

(4.4)

A

lF baMotorloadi

=

2)( (4.5)

bl , , A

Table 4.1 .

Table 4.1 Constants of the load torque in each joint

Body name

Lead of ballscrew

bl [mm]

Efficiency of ballscrew

[%]Reduction

Motor

Max. continuous torque

Shoulder 2 mm 90% 1 : 4.3 181Nmm

Elbow 1 mm 90% 1 : 1.75 94.8Nmm

Wrist 1 mm 90% 1 : 1.75 94.8Nmm

40

, (4.5)

Fig. 4.4~4.6 .

,

.

0

20

40

60

80

100

120

140

160

-100 -80 -60 -40 -20 0

q2 (deg)

Torq

ue (

Nm

m)

Fig. 4.4 Load torque of the shoulder joint

0

10

20

30

40

50

60

70

80

90

100

-100 -80 -60 -40 -20 0 20

q3 (deg)

Torq

ue (

Nm

m)

Fig. 4.5 Load torque of the elbow joint

41

0

10

20

30

40

50

60

70

80

-60 -40 -20 0 20 40 60

q4 (deg)

Torq

ue (

Nm

m)

Fig. 4.6 Load torque of the wrist joint

Fig. 4.4~4.6

.

.

42

5 5 5 5

CATIA ANSYS

. ,

.

1kg

10kg 1kg .

5.1

SOLID ,

BEAM .

4

.

Fig. 5.1 .

Fig. 5.1 Finite element model

43

(AL6061) .

Table 5.1 ,

Table 5.2 .

Table 5.1 Material property

Elastic

Modulus()

Tensile

Strength()Poisson's Ratio Density()

AL6061 68.9 225 0.35 2710

Table 5.2 Element type and number

SOLID 104642 283229

BEAM 360 691

5.2

1kg 10kg 1kg

. FEM

Table 5.2 , Fig. 5.2 10kg

.

Table 5.3 Displacement FEM of the KUBIR-2 arm

Weight(kg) Displacement(mm)

1 1.47

2 2.94

3 4.43

4 5.93

5 7.42

6 8.92

7 10.41

8 11.9

9 13.4

10 14.76

44

Fig. 5.2 FEM result of KUBIR-2 arm

45

5.3

(gripper) 1kg 10kg

1kg

. Pic. 5.1 .

Pic. 5.1 Experimental setup of the KUBIR-2 arm for displacement measure

5.4

Table 5.3 ,

.

Table 5.4 .

46

Table 5.4 Experiment result of displacement of the KUBIR-2 arm

Weight(kg) Displacement(mm)

1 3

2 6

3 8

4 11.5

5 13.5

6 16

7 18

8 21

9 23

10 26

Table 5.5 Adjusted displacement by servo motor

Weight(kg)Wrist

(pulse)

Elbow

(pulse)

Shoulder

(pulse)

Displacement of

gripper(mm)

1 46.4 80 566.7 1.53

2 92.7 160.7 1133.3 3.05

3 104.3 180.9 1275 3.42

4 150.6 261.5 1841.7 4.94

5 185.4 322 2266.7 6.08

6 208.6 362.4 2550 6.84

7 231.7 402.7 2833.3 7.59

8 278 483.3 3400 9.1

9 289.6 503.5 3541.7 9.49

10 336 584.18 4108.3 11

47

. Fig. 5.3 .

FEM .

0

2

4

6

8

10

12

14

16

0 5 10 15

Carrying weight (kg)

Dis

pla

cem

ent (m

m)

FEM analysis

Experiment

Fig. 5.3 Comparison result of FEM analysis and experiment

48

6 6 6 6

.

(closed chain)

.

9kg ,

10kg .

. ,

,

,

.

.

ANSYS

,

.

.

FEM

.

49

[1] http://asimo.honda.com/

[2] K. Harada, et al, A Humanoid Robot Carrying a Heavy Object, Proc. IEEE

International Conf. on Robotics and Automation, pp. 1724-1729, 2005.

[3] J.H Kim, S.W Park, I.W Park, and J. H. Oh, Development of a Humanoid

Biped Walking Robot Platform KHR-1 - Initial Design and Its Performance

Evaluation, in Proceedings of 3rd IARP Int.Workshop on Humanoid and Human

Friendly Robotics, pp. 14-21, Tsukuba, Japan, Dec. 2003.

[4] , ,

, 15 2, pp. 523-536, 1991.

[5] , , , , ,

15 2, pp. 515-522, 1991.

[6] , , ,

1 1, pp. 178-181, 1991.

[7] , , , , ,

10 5, pp. 611-617, 1986.

[8] G. Hirzinger, J. Batterfag, M. Fischer, M. Grebenstein, M. Hahnle, H. Liu, I.

Schaefer, and N. Sporer, "A Mechatronics Approach to the Design of Light

Weight Arms and Multi-Singered Hands", ICRA, pp. 46-54, 2000.

[9] , , , KSME 25 ,

1 2 2.1 2.2 2.3

3 3.1 3.2 3.3 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5

4 4.1 4

5 5.1 5.2 5.3 5.4

6