( ) 2006 1
PI
1 1 1.1................................. 1 1.2................................... 1 2 2 2.1...................................... 2 2.1.1.......................... 2 2.1.2.............................. 2 2.2...................................... 2 3 5 3.1................................. 5 3.2................................. 5 3.3................................. 5 3.4.................................. 5 3.5.............................. 6 3.6.................................... 6 3.7................................... 6 4 8 4.1...................................... 8 4.2...................................... 8 4.3.................................. 9 4.4.................................. 10 4.5....................... 10 4.6.............................. 12 4.7................................. 12 4.8.............................. 12 4.9........................... 14 5 16 5.1.............................. 16 5.2.................................. 16 i
5.3.................................. 18 5.4............................ 18 5.5 PI............................... 18 5.6...................................... 19 5.7.................................... 22 5.7.1.............................. 22 5.7.2................. 24 5.7.3................... 25 5.8.................................... 26 5.9............................. 29 5.10................................. 29 5.11............................. 29 6 33 6.1...................................... 33 6.1.1............................... 33 6.1.2............................... 33 6.2................................... 34 6.3........................ 34 6.3.1 URG............................. 34 6.3.2........................ 36 6.4................................... 37 6.4.1 USB................................ 37 6.4.2........................ 38 6.4.3......................... 38 6.4.4............................... 39 6.5................................... 39 6.5.1............................. 39 6.5.2............................. 43 6.6.............................. 43 7 45 46 47 ii
2.1 L B 3 2.2.................................. 3 2.3............................ 4 3.1.................................. 7 4.1.................................. 9 4.2 RSR 9N RSR 12N RSR 15N........... 10 4.3............................... 11 4.4 M-1........................ 13 4.5............................. 14 4.6............................ 15 5.1.............................. 17 5.2................................. 17 5.3 PI ( ). 20 5.4 PI........ 22 5.5 PI PI ( PWM ).............................. 23 5.6............. 25 5.7................................. 27 5.8 ( ) ( )...... 28 5.9 ( ) ( ).................. 30 5.10................................. 31 6.1............................... 33 6.2............................... 35 6.3 URG................................. 36 6.4 USB QV-700N............................... 38 6.5 ( ) ( )..... 39 6.6.............................. 40 6.7.................... 41 6.8 URG........................ 42 iii
6.9............................. 44 iv
1 1.1 [1][2][3] [4][5][6] 1.2 7 2 3 2 4 5 6 7 1
2 2.1 2.1.1 2.1 [7] 2.1.2 2.2 2.2 2.3 2
[a] [b] 147cm 137cm 2.1: L B 15mm 20mm 130cm 2.2: 3
88cm 2.3: 4
3 3.1 M-1 1 3.2 40cm 3.3 ( 2.3) 88cm ( 2.2) 130cm ( 2.1) 110 150cm 150cm 3.4 1 1996 370mm 322mm 420mm 5
2 6 4 3 3.5 3.1 500gf 500gf 3.1: 300 500gf 300 400gf 300gf 3.6 2.2 15mm 20mm 5mm 3.7 [8] [9][10][11] 6
End-effector Arm 3.1: 3.1 1 1 7
4 4.1 4.2 4.1 40cm 110cm 40cm 4 1 2 3 4 1. 1 4.1 [a] 4.1 [b] 2. 1 2 2 1 1 2 2 4.1 [c] 2 1 4.1 [d] 3. 3 4 2 1 2 3 4 1 ( L 1 ) 2 n l l = L 1 +3n (4.1) 8
Belt-holder grasping Timing-belt on First stage Belt-holder grasping Timing-belt on Third stage [d] Belt-holder grasping Timing-belt on Third stage [a] [b] motor [c] Belt-holder grasping Timing-belt on Second stage (1) (2) (3) 4.1: 4.3 1 3 1-2 2-3 3-4 4 1kgf 4.1 4.1: 1-2 2-3 3-4 17.9Nm 11.0Nm 5.4Nm 4.2 (THK ) 4.2 9
4.2: 1 2 3 RSR 15N RSR 12N RSR 9N 63.1Nm 28.9Nm 18.4Nm 350mm 370mm 375mm 417g 270g 147g 4.2: RSR 9N RSR 12N RSR 15N 4.4 ( ) 4 2.0mm ( ) 4.5 4.3 4.3 τ 1,τ 2 4 1 l ng (n =1, 2) 2 0.5kg τ n (n =1, 2) τ g 10
l1g l1 l l2 l2g Robot τ1 τ2 M1 Mj2 M2 4.3: 4.3: 1 1100mm(l 1 ) 1.5kg(M 1 ) 2-0.3kg(M j2 ) 2+ (0.5kg) 100mm(l 2 ) 0.7kg(M 2 ) τ w τ n = τ ng + τ nw (n =1, 2) (4.2) τ ng (n =1, 2) τ 1g = {M 1 l 1g + M j2 l 1 + M 2 (l 1 + l 2g )} g (4.3) τ 2g = M 2 l 2g g (4.4) τ nw (n =1, 2) τ nw = I n ω n (n =1, 2) (4.5) I n (n =1, 2) I 1 4.3 2 1 l1 M l1 1 I 1 = x 2 +l 2 M 2 dx + x 2 dx + M j2 l1 2 (4.6) 0 l 1 l 1 l 2 l2 M 2 I 2 = x 2 dx (4.7) l 2 0 τ 1 =21.9Nm, τ 2 =1.96Nm 0.5m/sec 2 1.424kg 0.37Nm 11
4.6 4.4 Maxon 4.4: 1 24V20W 300 28.8Nm 2 24V2.5W 400 2.27Nm 24V20W 19 0.44Nm 4.7 4.8 4.4 M-1 4.5 4.5 4.6 M-1 160cm 12
4.4: M-1 4.5: 388mm 1218mm 225deg 270deg DC 3 25cm/sec 500g 2.8kg 13
4.5: 4.9 14
4.6: 15
5 5.1 5.1 PWM 8 3 5.2 5.2 x : x y : y z : z x v : x y v : y L 0 : L h : L 1 : L 2 : θ a : θ b : θ 1 : θ 2 : θ v : 16
5.1: Z Y θ 1 L 0 (x v, y v ) L h L 1 θ b θ 2 L 2 (x,y,z) θ a, θ v X 5.2: 17
5.3 (x, y, z) (θ a,θ b ) (θ 1,θ 2 ) (L 1 ) (x v,y v,θ v ) x = x v + {L 0 L 1 cos θ 1 + L 2 cos (θ 1 + θ 2 )} cos θ v (5.1) y = y v + {L 0 L 1 cos θ 1 + L 2 cos (θ 1 + θ 2 )} sin θ v (5.2) z = L h + L 1 sin θ 1 + L 2 sin (θ 1 + θ 2 ) (5.3) θ a = θ v (5.4) θ b = θ 1 + θ 2 π (5.5) 5.4 (x, z, θ b ) (θ 1,θ 2 ) (L 1 ) θ 1 = arctan x + L 2 cos θ b + π (5.6) z L 2 sin θ b 2 θ 2 = θ b arctan x + L 2 cos θ b + π (5.7) z L 2 sin θ b 2 L 1 = (x + L 2 cos θ b ) 2 +(z L 2 sin θ b ) 2 (5.8) 5.5 PI PI [12] PI ) ( ) τ ref = K P (θ ref θ + K I θ ref θ dt (5.9) τ ref : [Nm] θ ref : [deg] 18
θ : [deg] K P : K I : PWM 0 PWM PWM δ = 1 V 0 ( R τ ref K τ + K e ω ) (5.10) δ : PWM /255 V 0 : [V ] R : [Ω] τ ref : [Nm] K τ : [Nm/A] K e : [V/rpm] ω : [rpm] PWM PI 5.3 5 200 100 50 0 5 800mm 400mm 200mm 0mm 5.6 19
200 Reference angle Actual angle 150 angle [deg] 100 50 0 0 5 10 15 20 time [sec] 800 700 Reference length Actual length length [mm] 600 500 400 300 200 100 0 0 5 10 15 20 time [sec] 200 Reference angle Actual angle 150 angle [deg] 100 50 0 0 5 10 15 20 time [sec] 5.3: PI ( ) 20
5.4 θ 1 l 1 τ ref θ 1 = K Pθ1 ( θ ref 1 θ 1 ) + K Iθ1 ( θ ref 1 θ 1 ) dt + mg l 1 2 cos θ 1 (5.11) τ ref θ 1 : [Nm] θ ref 1 : [deg] θ 1 : [deg] K Pθ1 : K Iθ1 : m : [kg] g : [m/sec 2 ] l 1 : [m] θ 1 τ ref l 1 = K Pl1 ( l ref 1 l 1 ) + K Il1 ( l ref 1 l 1 ) dt + mg sin θ 1 (5.12) τ ref l 1 : [Nm] l ref 1 : [mm] l 1 : [mm] K Pl1 : K Il1 : PI 5.5 PWM 21
5.4: PI 5.5 20 5.5 PI I PI 5.5 PWM 5.7 5.7.1 (x, z, θ b ) PI (θ b ) (x, z, θ b ) 60mm 22
l 1 [mm] 800 600 400 200 0 0 5 10 15 20 25 30 35 40 45 time [sec] θ 1 [deg] 7.5 7.0 6.5 6.0 5.5 without gravity compensation with gravity compensation 5.0 4.5 4.0 3.5 3.0 0 5 10 15 20 25 30 35 40 45 time [sec] PWM duty [y/255] 40 without gravity compensation 30 20 with gravity compensation 10 0 0 5 10 15 20 25 30 35 40 45 time [sec] 5.5: PI PI ( PWM ) 23
(x, z, θ b ) (θ 1,θ 2,l) 5.7.2 W t [Nm] v t 5.13 W a [Nm] v a 5.14 v t = W tl 3 3EI v a = W al 4 8EI (5.13) (5.14) l : [m] E : [Pa] I : 10mm - 5.6 θ 1 l 1 x y x 10cm f(x, y) =e x2 +y 2 5.15 (a,b,c,d) f(θ 1,l 1 )=ae b((θ 1 c) 2 +(l 1 d) 2 ) (5.15) 24
a*exp(b*((x-c)*(x-c)+(y-d)*(y-d))) gaps caused by deflection gap [mm] 80 70 60 50 40 30 20 10-10 0 θ 1 [deg] 220 200 180 160 140 800 l 1 [mm] 700 600 500 400 300 200 100 0 120 100 5.6: 5.6 a =70, b = 0.00035, c = 173, d = 800 (x, z, θ b ) 5.7.3 5.7 1. (x, z, θ b ) (θ 1,l 1,θ 2 ) 2. θ 1 l 1 ( x, z, θ b ) 3. (x, z, θ b ) ( x, z, θ b ) 4. (x + x, z + z,θ + θ b ) 25
(θ 1,l 1,θ 2 ) 5. θ 1 l 1 ( x, z, θ b ) 6. (x + x, z + z,θ + θ b ) ( x, z, θ b ) (x, z, θ b ) 1mm (θ 1,l 1,θ 2 ) 1mm (x + x, z + z,θ + θ b ) 1mm 4 6 5.8 3mm 5.8 5.5 5.9 5.9 5.9 PWM 26
No Yes 5.7: 27
5.8: ( ) ( ) 28
0.3 5.9 3 ( ) ( ) 0( ) PWM 5.8 PWM 0 5.10 5.10 PC PI 5.9 5.11 PI 29
PWM duty [y/255], Angular Velocity [deg/sec] 60 Load Value 0.024 50 0.02 40 0.016 30 0.012 20 0.008 10 0.004 0 0-10 -0.004 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [sec] PWM duty [y/255], Angular Velocity [deg/sec] 60 Load Value 0.024 50 0.02 40 0.016 30 0.012 20 0.008 10 0.004 0 0-10 -0.004 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [sec] 5.9: ( ) ( ) 30
5.10: 31
2 5.10 PC PC PC 32
6 6.1 6.1.1 6.1 6.1.2 6.2 6.1: 33
15 20cm 1. 2. 20mm 3. 5.8 6.2 PC PC LxSystem[13] 6.3 6.3.1 URG 6.3 URG-X002S( URG ) URG 6.1 URG 34
6.2: 35
6.3: URG [rad] [mm] (x, y) θ URG (x p,y p ) x p = r cos(φ + θ)+x + L cos θ (6.1) y p = r sin(φ + θ)+y + L sin θ (6.2) x p : x y p : y r : φ : x : x y : y θ : L : URG 6.3.2 36
6.1: URG URG-X002S 20 4000mm, 240 20 1000mm 10mm, 1000 4000mm 1% 0.36 100ms/scan 170g 50mm 50mm 70mm URG n (x i,y i ) y = ax + b a,b a = b = n n n n x i y i x i y i i=1 i=1 i=1 ( n n ) n x 2 i 2 (6.3) x i i=1 i=1 n n n x 2 n i y i x i y i x i i=1 i=1 i=1 i=1 ( n n ) n x 2 2 (6.4) i x i i=1 i=1 (x r,y r ) d d = (ax r y r + b) 2 1+a 2 (6.5) URG 6.4 6.4.1 USB cm 37
6.4: USB QV-700N 6.4 Logicool USB QV-700N PC 6.4.2 Camera Calibration Toolbox for Matlab[15] 6.4.3 USB RGB 5 5 6.5 38
6.5: ( ) ( ) 6.4.4 6.6 (u, v) ( u, v) U V 1 θu θv URG L (x obj,y obj,z obj ) x obj = L (6.6) y obj = L tan( θ v v) (6.7) z obj = L tan( θ u u) (6.8) 6.5 6.5.1 L 3 4 39
Y Z Projected Surface Object Projected Surface Object v θv* v Yobj u θu* u Zobj X X Xobj Xobj Top View Side View 6.6: 1. L 3 2. URG 3. URG 4. 5. 6. 7. 8. 5 6 9. 10. L 4 6.7 URG 6.8 40
1 5 9 2 6 10 3 7 11 4 8 12 図 6.7: エレベータによるフロア移動実験の様子 41
y [mm] 4000 2000 0-2000 -4000-6000 3L302-1 3rd Floor Elevator -8000-5000 0 5000 10000 15000 20000 25000 30000 x [mm] y [mm] 4000 2000 0-2000 -4000-6000 3L402 4th Floor Elevator -8000-5000 0 5000 10000 15000 20000 25000 30000 x [mm] 42 6.8: URG
6.5.2 6.9 6.1.2 6.6 5 43
1 5 9 2 6 10 3 7 11 4 8 12 図 6.9: 引き出し操作実験の様子 44
7 PI 3mm PC 45
46
[1] NEC PaPeRo, http://www.incx.nec.co.jp/robot/20-03papero/index.html [2] ApriAlpha, http://www.toshiba.co.jp/about/- press/2003 03/pr j2001.htm [3] PFU MARON-1, http://www.pfu.fujitsu.com/maron/characteristic.html [4], 13. [5] T.Tomizawa, A.Ohya, S.Yuta : Book Browsing System using an Autonomous Mobile Robot Teleoperated via the Internet, Proceedings of IROS 02. [6], 15. [7],,, 03, 2A1-1F-B6 (2003-05) [8], 9. [9], 11. [10], 12. [11], 14. [12] PID, (1992) [13] 15 47
[14] H.Kawata, W.Santosh, T.Mori, A.Ohya, S.Yuta : Development of Ultra-Small Lightweight Optical Range Sensor System, Proceedings of IROS 05. [15] Camera Calibration Toolbox for Matlab : http://www.vision.caltech.edu/bouguetj/calib doc/index.html 48