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inverse_dynamics.py
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inverse_dynamics.py
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from math import sin,cos
from numpy import array,mat,ravel
import sys
from termcolor import colored, cprint
####################---------Inverse Dynamics of RRR
# text = colored('Hello, World!', 'red', attrs=['reverse', 'blink'])
# print(text)
# print(colored('Hello, World!', 'green', 'on_red'))
L1=0.18
L2=0.18
L3=0.05
M1=1.5
M2=1.5
M3=1.0
spec=[L1, L2, L3, M1, M2, M3]
def TorqueCalc(x):
global spec
theta1dd,theta2dd,theta3dd = 3,-11,-1
qdd = mat([ [theta1dd], [theta2dd], [theta3dd] ])
L1 = spec[0]
L2 = spec[1]
L3 = spec[2]
M1 = spec[3]
M2 = spec[4]
M3 = spec[5]
g = 9.8
#print('hehe :',x[0])
############################-------INERTIAL TERM---------#################
I11 = (
(M1+M2+M3)*L1**2 +
(M2+M3)*L2**2 +
M3*L3**2 +
2*(M2+M3)*L1*L2*cos(x[5]) +
2*M3*L2*L3*cos(x[6]) +
2*M3*L3*L1*cos(x[5]+ x[6])
)
I12 = (
(M2+M3)*L2**2 +
(M2+M3)*L1*L2*cos(x[5]) +
M3*L3**2 +
2*M3*L2*L3*cos(x[6]) +
M3*L3*L1*cos(x[5]+ x[6])
)
I13 = (
M3*L3**2 +
M3*L2*L3*cos(x[6]) +
M3*L3*L1*cos(x[5]+ x[6])
)
I21 = (
(M2+M3)*L2**2 +
(M2+M3)*L1*L2*cos(x[5]) +
M3*L3**2 +
2*M3*L2*L3*cos(x[6]) +
M3*L3*L1*cos(x[5]+ x[6])
)
I22 = (
(M2+M3)*L2**2 +
M3*L3**2 +
2*M2*L2*L3*cos(x[6])
)
I23 = (
M3*L3**2 +
M3*L2*L3*cos(x[6])
)
I31 = (
M3*L3**2 +
M3*L2*L3*cos(x[6]) +
M3*L3*L1*cos(x[5]+ x[6])
)
I32 = M3*L3**2 + M3*L2*L3*cos(x[6])
I33 = M3*L3**2
I = mat([ [I11, I12, I13],
[I21, I22, I23],
[I31, I32, I33] ])
############################-------INERTIAL TERM---------#################
############################-------CORIOLIS TERM---------#################
c1 = (
-(2*(M2+M3)*L1*L2*sin(x[5]) + 2*M3*L3*L1*sin(x[5] + x[6]))*x[7]*x[8] -
(2*M3*L2*L3*sin(x[6]) + 2*M3*L3*L1*sin(x[5] + x[6]))*x[8]*x[9] -
(2*M3*L2*L3*sin(x[6]) + 2*M3*L3*L1*sin(x[5] + x[6]))*x[9]*x[7] -
((M2+M3)*L1*L2*sin(x[5]) + M3*L3*L1*sin(x[5] + x[6]))*(x[8])**2 -
(M3*L2*L3*sin(x[6]) + M3*L3*L1*sin(x[5] + x[6]))*(x[9])**2
)
c2 = (
-((M2+M3)*L1*L2*sin(x[5]) +
M3*L3*L1*sin(x[5] +
x[6])*x[7]*x[8]) -
(2*M3*L2*L3*sin(x[6])*x[8]*x[9]) -
(2*M3*L2*L3*sin(x[6]) +
M3*L3*L1*sin(x[5] + x[6]))*x[7]*x[9] -
(M3*L2*L3*sin(x[6])*(x[9])**2)
)
c3 = (
-M3*L2*L3*sin(x[6])*x[8]*x[9] -
(M3*L2*L3*sin(x[6]) +
M3*L3*L1*sin(x[5] +
x[6]))*x[7]*x[8] -
M3*L3*L1*sin(x[5] + x[6])*x[7]*x[8]
)
C = mat([ [c1],
[c2],
[c3] ])
############################-------CORIOLIS TERM---------#################
#############################-------GRAVITY TERM---------#################
g1 = (
-(M1+M2+M3)*g*L1*sin(x[4]) -
(M2+M3)*g*L2*sin(x[4] + x[5]) -
M3*g*L3*sin(x[4] + x[5] + x[6])
)
g2 = (
-(M2+M3)*g*L2*sin(x[4] + x[5]) -
M3*g*L3*sin(x[4] + x[5] + x[6])
)
g3 = -M3*g*L3*sin(x[4] + x[5] + x[6])
G = mat([ [g1],
[g2],
[g3] ])
#############################-------GRAVITY TERM---------#################
Torques = I*qdd + C + G
return Torques
x = array([0,1,0,0,0,0,0,0,0,0])
values = TorqueCalc(x)
print('Torques :',ravel(values))
th1,th2,th3 = 0,0,0
x1=L1*sin(th1)
y1=L1*cos(th1)
x2=L1*sin(th1)+L2*sin(th1+th2)
y2=L1*cos(th1)+L2*cos(th1+th2)
x3=L1*sin(th1)+L2*sin(th1+th2)+L3*sin(th1+th2+th3)
y3=L1*cos(th1)+L2*cos(th1+th2)+L3*cos(th1+th2+th3)