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- なおみ つちかね
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1 MI/CS :27 NAO Next Gen *1 ( 1A) ( 1B) 1 (A) NAO Next Gen ; (B) Webots for NAO : MI robot-simulation@ml.numericalbrain.org *1 1
2 NAO Denavit-Hartenberg (DH) : NAO :
3 : : : : 52 9 : A Python 55 B Webots for NAO 57 C 58 D NAO 59 3
4 1 1.1 M J MI/CS MI CS Webots for NAO JED Webots for NAO Webots JED 2,3 4,5,6 7 4
5 NAO V3.3 Next Gen V4 V ( ) Webots for NAO: V4 ( 1500 ) V3.3 NAO Webots for NAO NAO 2 Webots for NAO Python NAO Python C Python Python A 5
6 *2 Code Academy Python * Reza N. Jazer. Theory of Applied Robotics: Kinematics, Dynamics, and Control (2nd edition). Springer ,3 Jazer NAO Programming Guide: NAOqi modules APIs: Open Dynamics Engine (ODE) C HRP,. ( 2) ,, *2 *3 6
7 ,, NAO (Revolute joints) (Translate joints) ( ) (Dynamics) (Forward dynamics)( ) (Inverse dynamics)( ) Webot for NAO NAO
8 J1 JED 1, JED JED
9 2 2.1 Python csh (JED ) ~tyam/lectures/robot/environment.csh bash ~tyam/lectures/robot/environment.bash [tyam@blue13]$ source ~tyam/lectures/robot/environment.csh (csh ) [tyam@blue13]$ source ~tyam/lectures/robot/environment.bash (bash ) echo $SHELL [tyam@blue13]$ echo $SHELL /bin/tcsh 2.2 Webots for NAO NAO webots & [tyam@blue13]$ webots & 3 Step 2: Enter license informaiton in the Webots preferences preferences 4 Password: Network Proxy HTTP proxy: proxy.jed.uec.ac.jp:8080 OK 5 6 OK 7 System below the minimal requirements JED PC 9
10 3 Webots for NAO 4 warning OK 2.3 webotstest.py 1 webottest.py 1 #!/usr/bin/python 2 3 import sys 4 from naoqi import ALProxy 5 6 postureproxy = ALProxy("ALRobotPosture", "localhost", 9559) 10
![5 Proxy 6 7 8 postureproxy.gotoposture("standinit", 1.0) [tyam@blue13]$ chmod a+x./webotstest.](/docs-images/48/24423697/images/11-0.png "py [tyam@blue13]$./webotstest.py NAO 1 print postureproxy.getposturelist() NAO postureproxy.")
11 5 Proxy postureproxy.gotoposture("standinit", 1.0) [tyam@blue13]$ chmod a+x./webotstest.py [tyam@blue13]$./webotstest.py NAO 1 print postureproxy.getposturelist() NAO postureproxy.gotoposture "StandInit" 11
12 7 Webots for NAO Warning PC 12
13 (Link) (Joint) (degree of freedom, DOF) (Manipulator) (Base link) (End-effector) (Actuator) (Sensor) (Controller) NAO NAO 60cm 25 2 D NAO Intel Atom Linux Wifi ssh 13
14 4 (Forward kinematics) (Global frame) G r = (X, Y, Z) (Local frame) L r = (x, y, z) 8 X Y, Z X Y, Z 8 ( ) ( ) 4.2 (Joint rotation) 3 P G r, L r G r = L r Z α : G r = Q L Z,α r (1) 14
15 X G r = Y, Z x cos α sin α 0 L r = y, Q Z,α = sin α cos α 0 (2) z Y β X γ G r = Q L Y,β r (3) G r = Q L X,γ r (4) cos β 0 sin β Q Y,β = (5) sin β 0 cos β Q X,γ = 0 cos γ sin γ (6) 0 sin γ cos γ 9 Z (A) (B) Z L r = Q 1 Z,α r (7) L r = Q 1 Y,β r (8) L r = Q 1 X,γ r (9) Q 1, Q 2,, Q n G r = G Q L L r (10) 15
16 G Q L = Q n Q 2 Q 1 (11) G Q L 1 L r = 2 X 30 Y 45 X 3 Y G r X Y = Q Y,45 Q L X,30 r = = (12) G r Y X = Q X,30 Q L Y,45 r = = (13) X (Roll) Y (Pitch) Z (Yaw) - - G Q L = Q Z,γ Q Y,β Q X,α cos β cos γ cos α sin γ + cos γ sin α sin β sin α sin γ + cos α cos γ sin β = cos β sin γ cos α cos γ + sin α sin β sin γ cos γ sin α + cos α sin β sin γ (14) sin]β cos β sin α cos α cos β ( ) α = tan 1 r32 r 33 β = sin 1 (r 31 ) ( ) γ = tan 1 r21 ( cos β 0) r 11 (15) 16
17 4.4 3 L r G d G R L : G r = G R L L r + G d (16) G R L 3 3 G r, L r, G d : G r = G T L L r (17) r 11 r 12 r 13 X 0 G T L = r 21 r 22 r 23 Y 0 r 31 r 32 r 33 Z ( G ) R = G L d 0 1 X x X 0 G r = Y Z, L r = y z, G d = Y 0 Z (18) G T L (Homogeneous transformation matrix)
18 4.7 Denavit-Hartenberg (DH) 10 10(A) X Y *4 N ( (Manipulator) ) i, i + 1 B i, B i+1 0 i + 1 l i+1 θ i+1 B i+1 i+1 r B i Z cos θ i+1 sin θ i+1 0 l i+1 cos θ i+1 i T i+1 = sin θ i+1 cos θ i+1 0 l i+1 sin θ i (19) i r = i T i+1 i+1 r (20) i X α i+1 cos θ i+1 sin θ i+1 cos α i+1 sin θ i+1 sin α i+1 l i+1 cos θ i+1 i T i+1 = sin θ i+1 cos θ i+1 cos α i+1 cos θ i sin α i+1 l i+1 sin θ i+1 0 sin α i+1 cos α i+1 0 (21) ( ) *5 *4 Z *5 1 18
19 B i i r i 1 T i i 1 r = i 1 T i i r (22) B i+1 B i+1 r B i 1 i 1 r = i 1 T i i T i+1 i r (23) j i i r = i T i+1 i+1 T i+2 j 1 T j j r (24) 1. z i i x i z i 1, z i 3. y i y i = z i x i Denavit-Hartenberg (DH ) *6 10(B) 2 B i B i 1 cos θ 2 sin θ 2 0 l2 cos θ 2 1 T 2 = sin θ 2 cos θ 2 0 l2 sin θ cos θ 1 sin θ 1 0 l1 cos θ 1 0 T 1 = sin θ 1 cos θ 1 0 l1 sin θ cos(θ 1 + θ 2 ) sin(θ 1 + θ 2 ) 0 l 1 cos θ 1 + l 2 cos(θ 1 + θ 2 ) 0 T 2 = sin(θ 1 + θ 2 ) cos(θ 1 + θ 2 ) 0 l 1 sin θ 1 + l 2 sin(θ 1 + θ 2 ) (26) (25) 4.8 1: 3 10(B) 1 3 *6 19
20 3 B 3 θ 3 l 3 2 T 3 0 T 3 0 B 3 3 r = r 2 T 3 0 T 3 0 r 4.9 NAO NAO 2 *7 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 from naoqi import ALProxy 6 7 HOST = "localhost" 8 PORT = def main(): 2 skel.py 11 motionproxy = ALProxy("ALMotion", HOST, PORT) motionproxy.wakeup() """ """ motionproxy.rest() if name == " main ": 22 main() *7 ~tyam/lectures/robot-simulation/code/ 20
21 Webots for NAO NAO PC NAO ALProxy localhost * NAO ALMotion 11 motionproxy = ALProxy("ALMotion", HOST, PORT) NAO wakeup() NAO rest() webotstest.py StandInit 3 webotstest.py 1 #!/usr/bin/python 2 3 import sys 4 from naoqi import ALProxy 5 6 postureproxy = ALProxy("ALRobotPosture", "localhost", 9559) 7 8 postureproxy.gotoposture("standinit", 1.0) ALMotion ALRobotPosture 1 motionproxy postureproxy NAO StandZero 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 from naoqi import ALProxy 6 import time 7 import math 8 9 HOST = "localhost" 10 PORT = naosaysno.py *8 PC IP
22 12 def main(): 13 motionproxy = ALProxy("ALMotion", HOST, PORT) motionproxy.wakeup() postureproxy = ALProxy("ALRobotPosture", "localhost", 9559) 18 postureproxy.gotoposture("standzero", 1.0) motionproxy.setangles("headyaw", -90.0*(2*math.pi/360.0), 1.0) 21 time.sleep(1.0) 22 motionproxy.setangles("headyaw", 90.0*(2*math.pi/360.0), 1.0) 23 time.sleep(1.0) 24 motionproxy.setangles("headyaw", 0, 1.0) 25 time.sleep(1.0) motionproxy.rest() if name == " main ": 30 main() wakeup() postureproxy StandZero HeadYaw setangles() 20 motionproxy.setangles("headyaw", -90.0*(2*math.pi/360.0), 1.0) -90.0*(2*math.pi/360.0) ( ) NAO 1 time.sleep(1.0) rest() HeadYaw NAO 5 getjointangles.py 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 from naoqi import ALProxy 6 import math 7 8 HOST = "localhost" 9 PORT =
23 10 11 def main(): 12 motionproxy = ALProxy("ALMotion", HOST, PORT) motionproxy.wakeup() bodynames = motionproxy.getbodynames("body") targetanglesinrad = motionproxy.getangles("body", False) 19 targetanglesindeg = [ x * (360.0/2*math.pi) for x in targetanglesinrad ] for i in range(len(bodynames)): 22 print bodynames[i] + " = " + str(targetanglesindeg[i]) motionproxy.rest() if name == " main ": 27 main() getbodynames("body") getangles("body", False) (Radian) 19 targetanglesindeg = [ x * (360.0/2*math.pi) for x in targetanglesinrad ] (Degree) *9 for setangles 6 brave.py 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 from naoqi import ALProxy 6 import time 7 import math 8 9 HOST = "localhost" 10 PORT = def main(): *9 Python Scheme Javascript map Lisp mapcar Ruby collect 23
24 13 motionproxy = ALProxy("ALMotion", HOST, PORT) motionproxy.wakeup() postureproxy = ALProxy("ALRobotPosture", "localhost", 9559) 19 postureproxy.gotoposture("standzero", 1.0) names = ["RShoulderRoll", "RElbowRoll", "RWristYaw"] 22 anglesindeg = [15.0, 80.0, 90.0] 23 anglesinrad = [ x * (2*math.pi/360.0) for x in anglesindeg ] 24 motionproxy.setangles(names, anglesinrad, 1.0) 25 time.sleep(2.0) motionproxy.rest() if name == " main ": 30 main() : NAO (NAO ) 11 ( ) 24
25 StandZero Z X Y 0 T T 2 1 r = T 1, 1 T 2 0 r = 0 T 1 1 T 1 2 r (27) D HandOffsetX 20mm ShoulderOffsetY 25
26 Python numpy ( ) cos(π/2) sin(π/2) A = sin(π/2) cos(π/2) (28) x = (1, 1) y = Ax = ( 1, 1) 1 #!/usr/local/bin/python 2 3 import numpy as np 4 import math 5 6 def main(): 7 8 PI = math.pi 7 rotatematrix.py 9 A = np.array([[math.cos(0.5*pi), -math.sin(0.5*pi)], 10 [math.sin(0.5*pi), math.cos(0.5*pi)]]) 11 x = np.array([[1.0], 12 [1.0]]) 13 y = np.dot(a, x) print y if name == " main ": 18 main() numpy import np np.array ( N 1 ) np.dot 0 T 1 1 T 2 26
27 5 (Inverse kinematics) ( ) (B) 2 0 T 2 = 0 T 1 1 T 2 cos(θ 1 + θ 2 ) sin(θ 1 + θ 2 ) 0 l 1 cos θ 1 + l 2 cos(θ 1 + θ 2 ) = sin(θ 1 + θ 2 ) cos(θ 1 + θ 2 ) 0 l 1 sin θ 1 + l 2 sin(θ 1 + θ 2 ) ( ) ( ) X l1 cos θ = 1 + l 2 cos(θ 1 + θ 2 ) Y l 1 sin θ 1 + l 2 sin(θ 1 + θ 2 ) (29) (30) X 2 + Y 2 = l l l 1 l 2 cos θ 2 (31) cos θ 2 = X2 + Y 2 l 2 1 l 2 2 2l 1 l 2 (32) 27
28 θ 2 = cos 1 X2 + Y 2 l 2 1 l 2 2 2l 1 l 2 (33) cos 1 (x) ( x 1 acos,asin ) tan 2 θ 2 = 1 cos θ 1 + cos θ (34) θ 2 = ±atan2 (l 1 + l 2 ) 2 (X 2 + Y 2 ) (X 2 + Y 2 ) (l 1 + l 2 ) 2 (35) θ 2 > 0 θ 1 = atan2 Y X + atan2 l 2 sin θ 2 l 1 + l 2 cos θ 2 (36) θ 2 < 0 θ 1 = atan2 Y X atan2 l 2 sin θ 2 l 1 + l 2 cos θ 2 (37) : acos,asin acos, asin asin(x) = x + 1 x x acos(x) = π (38) 2 asin(x) x 1 x 1 x 1 acos(x) cos θ = x cos 2 θ + sin 2 θ = x 2 + sin 2 θ = 1 ( ) θ = asin 1 x 2 ( ) (39) 1 x 2 1 cos 1 (x) C acos (3) glibc double glibc/sysdeps/ieee754/dbl-64/e acos.c float flt-32/e acosf.c 28
29 5.2 2 ( ) T q T = T(q) (40) q q = q δq (41) T = T (q ) (42) δt = T T (43) T δq J = T q T (q) = T (q + δq) = T (q ) + T q δq + O ( δq 2) (44) δt = T δq = Jδq (45) q J δq = J 1 δt (46) q = q + δq = q + J 1 δt (47) q (0) i q (i+1) = q (i) + J 1 ( q (i)) δt ( q (i)) (48) (Newton-Raphson Method) 2 ( ) ( ) X l1 cos θ = 1 + l 2 cos(θ 1 + θ 2 ) (49) Y l 1 sin θ 1 + l 2 sin(θ 1 + θ 2 ) 29
30 ( ) θ1 q = θ 2 ( ) (50) X T = Y J(q) J(q) = ( Ti = = ) q j ( X θ 1 Y θ 1 X θ 2 Y θ 2 ) ( l1 sin θ 1 l 2 sin(θ 1 + θ 2 ) l 2 sin(θ 1 + θ 2 ) l 1 cos θ 1 + l 2 cos(θ 1 + θ 2 ) l 2 cos(θ 1 + θ 2 ) ( ) J 1 1 l = 2 cos(θ 1 + θ 2 ) l 2 sin(θ 1 + θ 2 ) l 1 l 2 sin θ 2 l 1 cos θ 1 + l 2 cos(θ 1 + θ 2 ) l 1 sin θ 1 + l 2 sin(θ 1 + θ 2 ) ( θ1 θ 2 ) (i+1) = ( θ1 θ 2 ) (i) + J 1 [ (X Y ) ( ) ] (i) X Y ) (51) (52) (53) l 1 = l 2 = 1 (54) T q (0) = T = ( ) X = Y ( ) 1 1 ( ) (0) ( ) θ1 π/3 = θ 2 π/3 (55) (56) δt = ( 1 1) ( ) ( cos π/3 + cos(π/3 π/3) 1 = sin π/3 + sin(π/3 π/3) 1) ( 3 ) ( ) = (57) ( ) 1 J = ( ) (58) J 1 2 =
31 1 : 2 : 3 : 4 : ( ) (1) ( ) (0) θ1 θ1 = θ 2 θ 2 ( ) π/3 = = + J 1 δt + π/3 ( ( ) ( ) ). ( ) 1 J = ( 1 ) δt = ( ) q (1) = ( ) J = ( ) δt = ( ) q (2) = ( ) J = ( ) δt = ( ) q (3) = ( ) J = ( ) δt = ( ) q (4) = (59) (60) (61) (62) (63)
32 ( π/2 ) q (4) q = π/2 5.3 θ 1 ( θ 2 ) X( Y ) * 10 numpy numpy.linalg.inv() 2 8 inverse.py 1 #!/usr/bin/python 2 3 import numpy as np 4 import math 5 6 L1 = L2 = Epsilon = 1.0e def X(theta1, theta2): 11 return L1*math.cos(theta1) + L2*math.cos(theta1+theta2) def Y(theta1, theta2): 14 return L1*math.sin(theta1) + L2*math.sin(theta1+theta2) def Jacobian(q): 17 theta1 = q[0] 18 theta2 = q[1] 19 dxdtheta1 = (X(theta1+Epsilon, theta2)-x(theta1, theta2))/epsilon 20 dxdtheta2 = (X(theta1, theta2+epsilon)-x(theta1, theta2))/epsilon 21 dydtheta1 = (Y(theta1+Epsilon, theta2)-y(theta1, theta2))/epsilon 22 dydtheta2 = (Y(theta1, theta2+epsilon)-y(theta1, theta2))/epsilon 23 return np.array([[dxdtheta1, dxdtheta2], [dydtheta1, dydtheta2]]) def distance(u, v): 26 return math.sqrt((u[0]-v[0])*(u[0]-v[0])+(u[1]-v[1])*(u[1]-v[1])) def Tstar(q): 29 return np.array([[x(q[0],q[1])], [Y(q[0],q[1])]]) *10 32
33 30 31 def main(): 32 T = np.array([[1.0], [1.0]]) 33 q = np.array([[np.pi/3.0], [-np.pi/3.0]]) while distance(t, Tstar(q)) > Epsilon: 36 th1 = q[0] 37 th2 = q[1] 38 deltat = T - Tstar(q) 39 J = Jacobian(q) 40 Jinv = np.linalg.inv(j) 41 q += np.dot(jinv, deltat) 42 print q if name == " main ": 45 main() 5.4 ( 2 (2, 2)) ( ) (45): δt = Jδq (45) * 11 *11 J 33
34 5.4.1 ( ) 2/2 θ 1 = π/4, θ 2 = 0 2 2/2 ( ) J 1 1 l = 2 cos(θ 1 + θ 2 ) l 2 sin(θ 1 + θ 2 ) l 1 l 2 sin θ 2 l 1 cos θ 1 + l 2 cos(θ 1 + θ 2 ) l 1 sin θ 1 + l 2 sin(θ 1 + θ 2 ) (64) l 1 l 2 sin θ 2 (Singular configuration) : 5.5 3: 13 Nao ( ) Nao (StandInit ) ( Crouch ) StandInit (x, y, z) (x, y, z ) x = x y = y StandInit z 560 mm 450 mm = 110 mm 10 p 0, p 10 getangles() setangles() 13 StandZero θ 1 = 90 Nao θ 1 = 0 90 StandZero 34
35 13 Nao 35
36 6 IS 1 ( * 12 ) DH postureproxy.applyposture("lyingback") *
37 7 7.1 C NAO 2m 15cm NAO 2m * 13 NAO 9 walkstraight.py 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 from naoqi import ALProxy 6 import time HOST = "localhost" 9 PORT = def main(): 12 motionproxy = ALProxy("ALMotion", HOST, PORT) postureproxy = ALProxy("ALRobotPosture", HOST, PORT) 15 postureproxy.gotoposture("standinit", 1.0) motionproxy.moveto(2.0, 0, 0) # X 2m Y 0m if name == " main ": 20 main() * 14 ( (ground reaction force)) * 15 ( (error)) (control) *13 *14 *15 JED 37
38 (Block diagram) 14 Python NAO NAO NAO Python PID PID t e(t) Q(t) PID (PID control) Q(t) = k P e(t) + k I t 0 e(t)dt + k D de dt (65) P (Proportional) I (Integral) D (Derivative) k P, k I, k D P I D P 0 0 P (PI ) t e(t) t + t e(t + t) e(t) + de t (66) dt 38
39 P (PD ) : DC NAO setanglees() NAO DC 15(A) 15 DC (A) (B) 0 θ d (t) = θ d u(t) θ d u(t) u(t) = { 1 t > 0 0 θ(t) ˆθ(s) = (ˆθd Ĝ(s)Ĥ(s) (s) ˆθ(s) ) (67) (68) ˆθ(s) = Ĝ(s)Ĥ(s) 1 + Ĝ(s)Ĥ(s) ˆθd (s) (69) Ĝ(s) Ĥ(s) P Ĝ(s) = k p Ĥ(s) Ĥ(s) = K s(t s + 1) (70) * 16 K, T ˆθ d (s) = θ d /s *16 (1999). MATLAB. 39
40 ˆθ(s) = = k p K s(t s+1) θ d K 1 + k p s s(t s+1) k p K s(t s + 1) + k p K θ d k p K θ d s = s(t s 2 + s + k p K) 1 = θ d k p K s(s a)(s b) (71) a, b 2 T s 2 + s + k p K = 0 a, b = 1 ± 1 4T Kk p 2T (72) θ d (t) = θ d Θ(t) θ(t) (α, β, γ ) 1 ˆθ(s) = θ d k p K s(s a)(s b) ( α = θ d k p K s + β s a + γ ) (73) s b θ(t) = k p Kθ d ( αu(t) + βe at + γe bt) (74) 1. k p < 1/(4T K) 1 4T Kk p 1 a, b θ(t) k p Kαθ d u(t) θ d ( α = 1/(k p K)) (75) k p 2. k p > 1/(4T K) 1 4T Kk p ωi ( θ(t) = k p Kθ d αu(t) + βe ( 1/(2T )+iω/(2t ))t ( 1/(2T ) iω/(2t + γe ))t) ( (76) = k p Kθ d αu(t) + βe t/(2t ) e iωt/(2t ) + γe t/(2t ) iωt/(2t e )) θ(t) 40
41 7.3 4: P 1 1 τ dy dt = y(t) + z(t) (77) τ t z(t) y(t) 1 τ 1 ( 16) H(t) z(t) y(t) time (s) 16 z(t)( ) y(t)( ) (s) τ = 0.1 (s) z(t), y(t) ẑ(s), ŷ(s) ( ) Ĥ(s) = 1/(sτ + 1) ŷ(s) = 1 (78) sτ + 1ẑ(s) 17 PID 41
42 17 PI e(t) = x(t) y(t) t z(t) = k P e(t) + k I e(t)dt (79) x(t) ( ) Ĝ(s) = K P + K I /s 17 0 ẑ(s) = k P ê(s) + K I ê(s) (80) s ŷ(s) = G(s)H(s) (ˆx(s) ŷ(s)) = G(s)H(s) 1 + G(s)H(s) ˆx(s) (81) G(s)H(s) 1+G(s)H(s) ˆx(s) ŷ(s) G(s)H(s) 1 + G(s)H(s) = (K P + K I /s)(1/(sτ + 1)) 1 + (K P + K I /s)(1/(sτ + 1)) K P + K I /s = (sτ + 1) + (K P + K I /s) K P = (sτ + 1) + (K P + K I /s) + K I /s (sτ + 1) + (K P + K I /s) K P s K I = s 2 + τ + (1 + K P )s + K I s 2 τ + (1 + K P )s + K I ) (82) P G(s)H(s) 1 + G(s)H(s) = K P sτ K P (83) x(t) t = 0 a x(t) = au(t) * 17 (84) u(t) u(t) = { 1 t 0 0 (85) *17 au 42
43 ˆx(s) ( ) ˆx(s) = a 1 s (86) K P ŷ(s) = a s 2 + a τ + (1 + K P )s + K I s (s 2 τ + (1 + K P )s + K I )) K I (87) P K P ŷ(s) = a s(sτ K P ) (88) ( (85)) y(t) P P K P ŷ(s) = a s(sτ K P ) = ak P 1 τ s(s + (1 + K P )/τ)) = ak ( ) P 1 1 τ (1 + K p )/τ s 1 s + (1 + K P )/τ = ak ( ) P 1 (1 + K p ) s 1 s + (1 + K P )/τ (L 1 [1/(s + a)] = e at ) y(t) = ak P (u(t) ) + e 1+K p τ t (1 + K p ) = ak P (1 + K p ) u(t) + ak P (1 + K p ) e 1+Kp τ t (89) (90) 2 y(t) ak P (1 + K p ) (91) a P K P /(1 + K P ) 1 P K P ( ) (a): pid.py 1 PID Ki=0, Kd=0 Kp gnuplot K P 43
44 10 pi.py 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import math 5 6 def main(): 7 8 Dt = # \Delta t = 1 ms 9 Tau = 0.1 # \tau = 100 ms 10 Kp = 1.0 # proportional control gain parameter 11 Ki = 0.0 # integral control gain parameter 12 Kd = 0.0 # difference control gain parameter y = 0 # output 15 e = 0 # error 16 ei = 0 # integral of error 17 e_prev = 0 # old value of error 18 x = 1.0 # desired output for i in range(1000): 21 t = Dt*i # time 22 print str(t) + " " + str(y) 23 e_prev = e 24 e = x - y # error 25 ei += Dt*(e + e_prev)/2.0 # integral of error with averaging 26 ed = (e - e_prev)/dt # difference of error 27 dy = (Dt/Tau)*(-y + (Kp*e + Ki*ei + Kd*ed)) # compute difference, PID control 28 y += dy # forward Euler method if name == " main ": 31 main() PI PI (b): pi.py Ki Ki gnuplot K I (c): 44
45 P (b) P 2 1/s x(t) = a τ dy dt = y(t) + a (92) y(t) = a PID (d): (d) Kd 7.4 NAO 2 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 from naoqi import ALProxy 6 import time HOST = "localhost" 9 PORT = def main(): 11 balldetection 12 motionproxy = ALProxy("ALMotion", HOST, PORT) postureproxy = ALProxy("ALRobotPosture", HOST, PORT) 15 postureproxy.gotoposture("standinit", 1.0) memoryproxy = ALProxy("ALMemory", HOST, PORT) 18 45
46 19 redballdetectionproxy = ALProxy("ALRedBallDetection", HOST, PORT) 20 redballdetectionproxy.subscribe("foo") videodeviceproxy = ALProxy("ALVideoDevice", HOST, PORT) 23 videodeviceproxy.subscribe("bar", 0, 0, 5) j = 0 26 for i in range(60): 27 ballinfo = memoryproxy.getdata("redballdetected") 28 videodeviceproxy.setactivecamera(j) 29 j = (j+1)%2 30 if ballinfo!= None: 31 print ballinfo[1] 32 time.sleep(1.0) redballdetectionproxy.unsubscribe("foo") 35 videodeviceproxy.unsubscribe("bar") time.sleep(1.0) motionproxy.rest() if name == " main ": 42 main() 2 1 * 18 [ X, Y, X, X ] 18 ( ) B turnmotion.py 1 #!/usr/local/bin/python *
![18 2 # -*- coding: utf-8 -*- 3 4 import sys 5 import math 6 import time 7 8 def turnleftpose(angleindeg): 9 poselist = [[["RAnkleRoll", "LAnkleRoll", "RHipRoll", "LHipRoll"], 10 [-5.0, -5.0, 5.](/docs-images/48/24423697/images/47-0.png "0, 5.0]], 11 [[\"RAnkleRoll\", \"LAnkleRoll\"], 12 [-10.0, -10.0]], 13 [[\"LHipYawPitch\"], 14 [-angleindeg]], 15 [[\"RAnkleRoll\", \"LAnkleRoll\", \"RHipRoll\", \"LHipRoll\"], 16 [0.0, 0.")
47 18 2 # -*- coding: utf-8 -*- 3 4 import sys 5 import math 6 import time 7 8 def turnleftpose(angleindeg): 9 poselist = [[["RAnkleRoll", "LAnkleRoll", "RHipRoll", "LHipRoll"], 10 [-5.0, -5.0, 5.0, 5.0]], 11 [["RAnkleRoll", "LAnkleRoll"], 12 [-10.0, -10.0]], 13 [["LHipYawPitch"], 14 [-angleindeg]], 15 [["RAnkleRoll", "LAnkleRoll", "RHipRoll", "LHipRoll"], 16 [0.0, 0.0, 0.0, 0.0]], 17 [["RAnkleRoll", "LAnkleRoll", "RHipRoll", "LHipRoll"], 18 [5.0, 5.0, -5.0, -5.0]], 19 [["RAnkleRoll", "LAnkleRoll"], 20 [10.0, 10.0]], 21 [["LHipYawPitch"], 22 [0.0]], 23 [["RAnkleRoll", "LAnkleRoll", "RHipRoll", "LHipRoll"], 24 [0.0, 0.0, 0.0, 0.0]]] 25 return poselist def turnrightpose(angleindeg): 28 poselist = [[["LAnkleRoll", "RAnkleRoll", "LHipRoll", "RHipRoll"], 29 [5.0, 5.0, -5.0, -5.0]], 30 [["LAnkleRoll", "RAnkleRoll"], 31 [10.0, 10.0]], 47
48 32 [["LHipYawPitch"], # only LHipYawPitch is movable 33 [-angleindeg]], 34 [["LAnkleRoll", "RAnkleRoll", "LHipRoll", "RHipRoll"], 35 [0.0, 0.0, 0.0, 0.0]], 36 [["LAnkleRoll", "RAnkleRoll", "LHipRoll", "RHipRoll"], 37 [-5.0, -5.0, 5.0, 5.0]], 38 [["LAnkleRoll", "RAnkleRoll"], 39 [-10.0, -10.0]], 40 [["LHipYawPitch"], 41 [0.0]], 42 [["LAnkleRoll", "RAnkleRoll", "LHipRoll", "RHipRoll"], 43 [0.0, 0.0, 0.0, 0.0]]] 44 return poselist def turnbysetangles(motionproxy, direction, angleindeg): 47 if direction == "Left": 48 poselist = turnleftpose(angleindeg) 49 else: 50 poselist = turnrightpose(angleindeg) for pose in poselist: 53 names = pose[0] 54 anglesindeg = pose[1] 55 anglesinrad = [ x * (2*math.pi/360.0) for x in anglesindeg ] 56 motionproxy.setangles(names, anglesinrad, 1.0) 57 time.sleep(0.1) 58 time.sleep(1.0) 13 turn.py 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 from naoqi import ALProxy 6 import time 7 import math 8 import turnmotion 9 10 HOST = "localhost" #"localhost" 11 PORT = def main(): 14 motionproxy = ALProxy("ALMotion", HOST, PORT) motionproxy.wakeup() 48
49 17 18 postureproxy = ALProxy("ALRobotPosture", HOST, 9559) postureproxy.gotoposture("standinit", 1.0) turnangleindeg = for i in range(10): 24 turnmotion.turnbysetangles(motionproxy, "Left", turnangleindeg) 25 for i in range(10): 26 turnmotion.turnbysetangles(motionproxy, "Right", turnangleindeg) time.sleep(3.0) motionproxy.rest() if name == " main ": 33 main() NAO 14 turntoball.py 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 from naoqi import ALProxy 6 import time 7 import math 8 import turnmotion 9 10 HOST = "localhost" 11 PORT = def main(): 14 motionproxy = ALProxy("ALMotion", HOST, PORT) 15 motionproxy.wakeup() postureproxy = ALProxy("ALRobotPosture", HOST, 9559) 18 postureproxy.gotoposture("standinit", 1.0) memoryproxy = ALProxy("ALMemory", HOST, PORT) 21 49
50 22 redballdetectionproxy = ALProxy("ALRedBallDetection", HOST, PORT) 23 redballdetectionproxy.subscribe("foo") videodeviceproxy = ALProxy("ALVideoDevice", HOST, PORT) 26 videodeviceproxy.subscribe("bar", 0, 0, 5) error = 0.3 # artibrary number 29 Kp = 0.5 # gain parameter 30 for i in range(30): 31 if abs(error) == 0.0: 32 break 33 for j in range(2): 34 videodeviceproxy.setactivecamera(j) 35 ballinfo = memoryproxy.getdata("redballdetected") 36 if ballinfo!= None: 37 error = ballinfo[1][0] 38 print error 39 if float(error) > 0: 40 turnmotion.turnbysetangles(motionproxy, "Left", Kp*float(error 41 else: )*(180.0/math.pi)) 42 turnmotion.turnbysetangles(motionproxy, "Right", Kp*abs(float(error ))*(180.0/math.pi)) 43 time.sleep(1.0) redballdetectionproxy.unsubscribe("foo") 46 videodeviceproxy.unsubscribe("bar") 47 motionproxy.rest() if name == " main ": 50 main() :
51 7.8.2 NAO 2m 15cm 10cm ( ) 51
52 8 : NAO NAO 15cm 52
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55 A Python Hello world 15 its.py 1 #!/usr/local/bin/python 2 # -*- coding: utf-8 -*- 3 4 import sys 5 import time 6 7 def main(): 8 print "And now for something completely different..." 9 time.sleep(3.0) 10 for i in ["Graham Chapman", "John Cleese", "Terry Gilliam", 11 "Eric Idle", "Terry Jones", "Michael Palin"]: 12 print i if name == " main ": 15 main() ( UTF8) C #include<stdio.h> 5. 5 time * main C main Python (:) * And now for something complete different... * 22 C (;) C {} Python 9. 9 time sleep C sleep 3 *20 C *21 *22 Monty Python s Flying Circus ( ) The Olympic Hide-and-Seek Final YouTube ( ) 55
56 for C Python [] (:) import false main() for C range() 0 ( 1) 1 % python 2 Python (v2.7.5:ab05e7dd2788, May , 13:18:45) 3 [GCC (Apple Inc. build 5666) (dot 3)] on darwin 4 Type "help", "copyright", "credits" or "license" for more information. 5 >>> range(10) 6 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] 7 >>> for i in range(10): 8... print i 9... ^D >>> 1 # # (C //) 2 """ 3 """ """ (C /*... */) 4 """ (/* foo */ """ foo """ ) 5 """ 56
57 B Webots for NAO View Ctrl Shift Webots Console 1 [naoqisim] [INFO ] NAOqi is ready... 2 [naoqisim] [INFO ] entSyncPlugin: End decrease stiffness 57
58 C ~tyam/lectures/robot/nao-control.wbt Webots for NAO File Open File... nao-control.wbt * 23 15cm NAO 2m NAO *23 SceneTree ( SpherecalSkyDome) Add a new object Add a node PROTO objects robocup spl Ball (Solid) Add (0,0,0) SceneTree Ball 58
59 D NAO NAO NAO Technical overview * *24 robots.html 59
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Excel ではじめる数値解析 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
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基礎から学ぶトラヒック理論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
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