Oct-23-2017, 12:14 PM
from sympy import *
from time import time
from mpmath import radians
from math import *
import tf
'''
Format of test case is [ [[EE position],[EE orientation as quaternions]],[WC location],[joint angles]]
You can generate additional test cases by setting up your kuka project and running
From here you can adjust the joint angles to find thetas, use the gripper to extract positions and orientation (in quaternion xyzw) and lastly use link 5
to find the position of the wrist center. These newly generated test cases can be added to the test_cases dictionary.
'''
test_cases = {1:[[[2.16135,-1.42635,1.55109],
[0.708611,0.186356,-0.157931,0.661967]],
[1.89451,-1.44302,1.69366],
[-0.65,0.45,-0.36,0.95,0.79,0.49]],
2:[[[-0.56754,0.93663,3.0038],
[0.62073, 0.48318,0.38759,0.480629]],
[-0.638,0.64198,2.9988],
[-0.79,-0.11,-2.33,1.94,1.14,-3.68]],
3:[[[-1.3863,0.02074,0.90986],
[0.01735,-0.2179,0.9025,0.371016]],
[-1.1669,-0.17989,0.85137],
[-2.99,-0.12,0.94,4.06,1.29,-4.12]],
4:,
5:}
def test_code(test_case):
## Set up code
## Do not modify!
x = 0
class Position:
def __init__(self,EE_pos):
self.x = EE_pos[0]
self.y = EE_pos[1]
self.z = EE_pos[2]
class Orientation:
def __init__(self,EE_ori):
self.x = EE_ori[0]
self.y = EE_ori[1]
self.z = EE_ori[2]
self.w = EE_ori[3]
position = Position(test_case[0][0])
orientation = Orientation(test_case[0][1])
class Combine:
def __init__(self,position,orientation):
self.position = position
self.orientation = orientation
comb = Combine(position,orientation)
class Pose:
def __init__(self,comb):
self.poses = [comb]
req = Pose(comb)
start_time = time()
########################################################################################
##
## Insert IK code here!
# FK/IK Code begins
d1, d2, d3, d4, d5, d6, d7 = symbols('d1:8') # Link Offset
a0, a1, a2, a3, a4, a5, a6 = symbols('a0:7') # Link Lengths
alpha0, alpha1, alpha2, alpha3, alpha4, alpha5, alpha6 = symbols('alpha0:7') # Twist angles
q1, q2, q3, q4, q5, q6, q7 = symbols('q1:8') # joint angle
DH_Table = { alpha0: 0, a0: 0, d1: 0.75, q1: q1,
alpha1: -pi/2., a1: 0.35, d2: 0, q2: -pi/2. + q2,
alpha2: 0, a2: 1.25, d1: 0, q3: q3,
alpha3: -pi/2., a3: -0.054, d1: 1.5, q4: q4,
alpha4: pi/2., a4: 0, d1: 0, q5: q5,
alpha5: -pi/2., a5: 0, d1: 0, q6: q6,
alpha6: 0, a6: 0, d1: 0.303, q7: 0 }
def TF_Matrix(alpha, a, d, q):
TF = Matrix([[ cos(q), -sin(q), 0, a],
[sin(q)*cos(alpha), cos(q)*cos(alpha), -sin(alpha), -sin(alpha)*d],
[sin(q)*sin(alpha), cos(q)*sin(alpha), cos(alpha), cos(alpha)*d],
[ 0, 0, 0, 1]])
return TF
T0_1 = TF_Matrix(alpha0, a0, d1, q1).subs(DH_Table)
T1_2 = TF_Matrix(alpha1, a1, d2, q2).subs(DH_Table)
T2_3 = TF_Matrix(alpha2, a2, d3, q3).subs(DH_Table)
T3_4 = TF_Matrix(alpha3, a3, d4, q4).subs(DH_Table)
T4_5 = TF_Matrix(alpha4, a4, d5, q5).subs(DH_Table)
T5_6 = TF_Matrix(alpha5, a5, d6, q6).subs(DH_Table)
T6_EE = TF_Matrix(alpha6, a6, d7, q7).subs(DH_Table)
T0_EE = T0_1 * T1_2 * T2_3 * T3_4 * T4_5 * T5_6 * T6_EE
px = req.poses[x].position.x
py = req.poses[x].position.y
pz = req.poses[x].position.z
(roll, pitch, yaw) = tf.transformations.euler_from_quaternion(
[req.poses[x].orientation.x, req.poses[x].orientation.y,
req.poses[x].orientation.z, req.poses[x].orientation.w])
r, p, y = symbols('r p y')
ROT_x = Matrix([[1, 0, 0],
[0, cos®, -sin®],
[0, sin®, cos®]])
ROT_y = Matrix([[ cos(p), 0, sin(p)],
[ 0, 1, 0],
[-sin(p), 0, cos(p)]])
ROT_z = Matrix([[cos(y), -sin(y), 0],
[sin(y), cos(y), 0],
[ 0, 0, 1]])
ROT_EE = ROT_z * ROT_y * ROT_x
Rot_Error = ROT_z.subs(y, radians(180)) * ROT_y.subs(p, radians(-90))
ROT_EE = ROT_EE * Rot_Error
ROT_EE = ROT_EE.subs({'r':roll, 'p': pitch, 'y': yaw})
EE = Matrix([[px],
[py],
[pz]])
WC = EE - (0.303) * ROT_EE[:,2]
theta1 = atan2(WC[1], WC[0])
side_a = 1.501
side_b = sqrt(pow((sqrt(WC[0] * WC[0] + WC[1] * WC[1]) - 0.35), 2) + pow((WC[2] - 0.75), 2))
side_c = 1.25
angle_a = acos((side_b * side_b + side_c * side_c - side_a * side_a)/(2 * side_b * side_c))
angle_b = acos((side_a * side_a + side_c * side_c - side_b * side_b)/(2 * side_a * side_c))
angle_c = acos((side_a * side_a * + side_b * side_b - side_c * side_c)/(2 * side_a * side_b))
theta2 = pi/2 - angle_a - atan2(WC[2] - 0.75, sqrt(WC[0] * WC[0] + WC[1] * WC[1]) - 0.35)
theta3 = pi/2 - (angle_b + 0.036)
R0_3 = T0_1[0:3, 0:3] * T1_2[0:3, 0:3] * T2_3[0:3, 0:3]
R0_3 = R0_3.evalf(subs={q1:theta1, q2:theta2, q3:theta3})
R3_6 = R0_3.inv("LU") * ROT_EE
theta4 = atan2(R3_6[2,2], -R3_6[0,2])
theta5 = atan2(sqrt(R3_6[0,2] * R3_6[0,2] + R3_6[2,2] * R3_6[2,2]), R3_6[1,2])
theta6 = atan2(-R3_6[1,1], R3_6[1,0])
# FK/IK Code Ends
# theta1 = 0
# theta2 = 0
# theta3 = 0
# theta4 = 0
# theta5 = 0
# theta6 = 0
##
########################################################################################
########################################################################################
## For additional debugging add your forward kinematics here. Use your previously calculated thetas
## as the input and output the position of your end effector as your_ee = [x,y,z]
## (OPTIONAL) YOUR CODE HERE!
FK = T0_EE.evalf(subs={q1: theta1, q2: theta2, q3: theta3, q4: theta4, q5: theta5, q6: theta6})
## End your code input for forward kinematics here!
########################################################################################
## For error analysis please set the following variables of your WC location and EE location in the format of [x,y,z]
# your_wc = [1,1,1] # <--- Load your calculated WC values in this array
# your_ee = [1,1,1] # <--- Load your calculated end effector value from your forward kinematics
your_wc = [WC[0],WC[1],WC[2]]
your_ee = [FK[0,3],FK[1,3],FK[2,3]]
########################################################################################
## Error analysis
print ("\nTotal run time to calculate joint angles from pose is %04.4f seconds" % (time()-start_time))
# Find WC error
if not(sum(your_wc)==3):
wc_x_e = abs(your_wc[0]-test_case[1][0])
wc_y_e = abs(your_wc[1]-test_case[1][1])
wc_z_e = abs(your_wc[2]-test_case[1][2])
wc_offset = sqrt(wc_x_e**2 + wc_y_e**2 + wc_z_e**2)
print ("\nWrist error for x position is: %04.8f" % wc_x_e)
print ("Wrist error for y position is: %04.8f" % wc_y_e)
print ("Wrist error for z position is: %04.8f" % wc_z_e)
print ("Overall wrist offset is: %04.8f units" % wc_offset)
# Find theta errors
t_1_e = abs(theta1-test_case[2][0])
t_2_e = abs(theta2-test_case[2][1])
t_3_e = abs(theta3-test_case[2][2])
t_4_e = abs(theta4-test_case[2][3])
t_5_e = abs(theta5-test_case[2][4])
t_6_e = abs(theta6-test_case[2][5])
print ("\nTheta 1 error is: %04.8f" % t_1_e)
print ("Theta 2 error is: %04.8f" % t_2_e)
print ("Theta 3 error is: %04.8f" % t_3_e)
print ("Theta 4 error is: %04.8f" % t_4_e)
print ("Theta 5 error is: %04.8f" % t_5_e)
print ("Theta 6 error is: %04.8f" % t_6_e)
print ("\n**These theta errors may not be a correct representation of your code, due to the fact \
\nthat the arm can have muliple positions. It is best to add your forward kinmeatics to \
\nconfirm whether your code is working or not**")
print (" ")
# Find FK EE error
if not(sum(your_ee)==3):
ee_x_e = abs(your_ee[0]-test_case[0][0][0])
ee_y_e = abs(your_ee[1]-test_case[0][0][1])
ee_z_e = abs(your_ee[2]-test_case[0][0][2])
ee_offset = sqrt(ee_x_e**2 + ee_y_e**2 + ee_z_e**2)
# ee_x_e = math.fabs(ee_x_e)
# print ("\nEnd effector error for x position is: %04.8f" % ee_x_e)
# print ("End effector error for y position is: %04.8f" % ee_y_e)
# print ("End effector error for z position is: %04.8f" % ee_z_e)
# print ("Overall end effector offset is: %04.8f units \n" % ee_offset)
print ("\nEnd effector error for x position is: %r" % ee_x_e)
print ("End effector error for y position is: %r" % ee_y_e)
print ("End effector error for z position is: %r" % ee_z_e)
print ("Overall end effector offset is: %r units \n" % ee_offset)
if __name__ == "__main__":
# Change test case number for different scenarios
test_case_number = 1
test_code(test_cases[test_case_number])
Error:
Traceback (most recent call last):
File "IK_debug.py", line 236, in <module>
test_code(test_cases[test_case_number])
File "IK_debug.py", line 90, in test_code
T0_1 = TF_Matrix(alpha0, a0, d1, q1).subs(DH_Table)
File "IK_debug.py", line 84, in TF_Matrix
TF = Matrix([[ cos(q), -sin(q), 0, a],
File "/home/robond/.local/lib/python2.7/site-packages/sympy/core/expr.py", line 226, in __float__
raise TypeError("can't convert expression to floa
from time import time
from mpmath import radians
from math import *
import tf
'''
Format of test case is [ [[EE position],[EE orientation as quaternions]],[WC location],[joint angles]]
You can generate additional test cases by setting up your kuka project and running
$ roslaunch kuka_arm forward_kinematics.launchFrom here you can adjust the joint angles to find thetas, use the gripper to extract positions and orientation (in quaternion xyzw) and lastly use link 5
to find the position of the wrist center. These newly generated test cases can be added to the test_cases dictionary.
'''
test_cases = {1:[[[2.16135,-1.42635,1.55109],
[0.708611,0.186356,-0.157931,0.661967]],
[1.89451,-1.44302,1.69366],
[-0.65,0.45,-0.36,0.95,0.79,0.49]],
2:[[[-0.56754,0.93663,3.0038],
[0.62073, 0.48318,0.38759,0.480629]],
[-0.638,0.64198,2.9988],
[-0.79,-0.11,-2.33,1.94,1.14,-3.68]],
3:[[[-1.3863,0.02074,0.90986],
[0.01735,-0.2179,0.9025,0.371016]],
[-1.1669,-0.17989,0.85137],
[-2.99,-0.12,0.94,4.06,1.29,-4.12]],
4:,
5:}
def test_code(test_case):
## Set up code
## Do not modify!
x = 0
class Position:
def __init__(self,EE_pos):
self.x = EE_pos[0]
self.y = EE_pos[1]
self.z = EE_pos[2]
class Orientation:
def __init__(self,EE_ori):
self.x = EE_ori[0]
self.y = EE_ori[1]
self.z = EE_ori[2]
self.w = EE_ori[3]
position = Position(test_case[0][0])
orientation = Orientation(test_case[0][1])
class Combine:
def __init__(self,position,orientation):
self.position = position
self.orientation = orientation
comb = Combine(position,orientation)
class Pose:
def __init__(self,comb):
self.poses = [comb]
req = Pose(comb)
start_time = time()
########################################################################################
##
## Insert IK code here!
# FK/IK Code begins
d1, d2, d3, d4, d5, d6, d7 = symbols('d1:8') # Link Offset
a0, a1, a2, a3, a4, a5, a6 = symbols('a0:7') # Link Lengths
alpha0, alpha1, alpha2, alpha3, alpha4, alpha5, alpha6 = symbols('alpha0:7') # Twist angles
q1, q2, q3, q4, q5, q6, q7 = symbols('q1:8') # joint angle
DH_Table = { alpha0: 0, a0: 0, d1: 0.75, q1: q1,
alpha1: -pi/2., a1: 0.35, d2: 0, q2: -pi/2. + q2,
alpha2: 0, a2: 1.25, d1: 0, q3: q3,
alpha3: -pi/2., a3: -0.054, d1: 1.5, q4: q4,
alpha4: pi/2., a4: 0, d1: 0, q5: q5,
alpha5: -pi/2., a5: 0, d1: 0, q6: q6,
alpha6: 0, a6: 0, d1: 0.303, q7: 0 }
def TF_Matrix(alpha, a, d, q):
TF = Matrix([[ cos(q), -sin(q), 0, a],
[sin(q)*cos(alpha), cos(q)*cos(alpha), -sin(alpha), -sin(alpha)*d],
[sin(q)*sin(alpha), cos(q)*sin(alpha), cos(alpha), cos(alpha)*d],
[ 0, 0, 0, 1]])
return TF
T0_1 = TF_Matrix(alpha0, a0, d1, q1).subs(DH_Table)
T1_2 = TF_Matrix(alpha1, a1, d2, q2).subs(DH_Table)
T2_3 = TF_Matrix(alpha2, a2, d3, q3).subs(DH_Table)
T3_4 = TF_Matrix(alpha3, a3, d4, q4).subs(DH_Table)
T4_5 = TF_Matrix(alpha4, a4, d5, q5).subs(DH_Table)
T5_6 = TF_Matrix(alpha5, a5, d6, q6).subs(DH_Table)
T6_EE = TF_Matrix(alpha6, a6, d7, q7).subs(DH_Table)
T0_EE = T0_1 * T1_2 * T2_3 * T3_4 * T4_5 * T5_6 * T6_EE
px = req.poses[x].position.x
py = req.poses[x].position.y
pz = req.poses[x].position.z
(roll, pitch, yaw) = tf.transformations.euler_from_quaternion(
[req.poses[x].orientation.x, req.poses[x].orientation.y,
req.poses[x].orientation.z, req.poses[x].orientation.w])
r, p, y = symbols('r p y')
ROT_x = Matrix([[1, 0, 0],
[0, cos®, -sin®],
[0, sin®, cos®]])
ROT_y = Matrix([[ cos(p), 0, sin(p)],
[ 0, 1, 0],
[-sin(p), 0, cos(p)]])
ROT_z = Matrix([[cos(y), -sin(y), 0],
[sin(y), cos(y), 0],
[ 0, 0, 1]])
ROT_EE = ROT_z * ROT_y * ROT_x
Rot_Error = ROT_z.subs(y, radians(180)) * ROT_y.subs(p, radians(-90))
ROT_EE = ROT_EE * Rot_Error
ROT_EE = ROT_EE.subs({'r':roll, 'p': pitch, 'y': yaw})
EE = Matrix([[px],
[py],
[pz]])
WC = EE - (0.303) * ROT_EE[:,2]
theta1 = atan2(WC[1], WC[0])
side_a = 1.501
side_b = sqrt(pow((sqrt(WC[0] * WC[0] + WC[1] * WC[1]) - 0.35), 2) + pow((WC[2] - 0.75), 2))
side_c = 1.25
angle_a = acos((side_b * side_b + side_c * side_c - side_a * side_a)/(2 * side_b * side_c))
angle_b = acos((side_a * side_a + side_c * side_c - side_b * side_b)/(2 * side_a * side_c))
angle_c = acos((side_a * side_a * + side_b * side_b - side_c * side_c)/(2 * side_a * side_b))
theta2 = pi/2 - angle_a - atan2(WC[2] - 0.75, sqrt(WC[0] * WC[0] + WC[1] * WC[1]) - 0.35)
theta3 = pi/2 - (angle_b + 0.036)
R0_3 = T0_1[0:3, 0:3] * T1_2[0:3, 0:3] * T2_3[0:3, 0:3]
R0_3 = R0_3.evalf(subs={q1:theta1, q2:theta2, q3:theta3})
R3_6 = R0_3.inv("LU") * ROT_EE
theta4 = atan2(R3_6[2,2], -R3_6[0,2])
theta5 = atan2(sqrt(R3_6[0,2] * R3_6[0,2] + R3_6[2,2] * R3_6[2,2]), R3_6[1,2])
theta6 = atan2(-R3_6[1,1], R3_6[1,0])
# FK/IK Code Ends
# theta1 = 0
# theta2 = 0
# theta3 = 0
# theta4 = 0
# theta5 = 0
# theta6 = 0
##
########################################################################################
########################################################################################
## For additional debugging add your forward kinematics here. Use your previously calculated thetas
## as the input and output the position of your end effector as your_ee = [x,y,z]
## (OPTIONAL) YOUR CODE HERE!
FK = T0_EE.evalf(subs={q1: theta1, q2: theta2, q3: theta3, q4: theta4, q5: theta5, q6: theta6})
## End your code input for forward kinematics here!
########################################################################################
## For error analysis please set the following variables of your WC location and EE location in the format of [x,y,z]
# your_wc = [1,1,1] # <--- Load your calculated WC values in this array
# your_ee = [1,1,1] # <--- Load your calculated end effector value from your forward kinematics
your_wc = [WC[0],WC[1],WC[2]]
your_ee = [FK[0,3],FK[1,3],FK[2,3]]
########################################################################################
## Error analysis
print ("\nTotal run time to calculate joint angles from pose is %04.4f seconds" % (time()-start_time))
# Find WC error
if not(sum(your_wc)==3):
wc_x_e = abs(your_wc[0]-test_case[1][0])
wc_y_e = abs(your_wc[1]-test_case[1][1])
wc_z_e = abs(your_wc[2]-test_case[1][2])
wc_offset = sqrt(wc_x_e**2 + wc_y_e**2 + wc_z_e**2)
print ("\nWrist error for x position is: %04.8f" % wc_x_e)
print ("Wrist error for y position is: %04.8f" % wc_y_e)
print ("Wrist error for z position is: %04.8f" % wc_z_e)
print ("Overall wrist offset is: %04.8f units" % wc_offset)
# Find theta errors
t_1_e = abs(theta1-test_case[2][0])
t_2_e = abs(theta2-test_case[2][1])
t_3_e = abs(theta3-test_case[2][2])
t_4_e = abs(theta4-test_case[2][3])
t_5_e = abs(theta5-test_case[2][4])
t_6_e = abs(theta6-test_case[2][5])
print ("\nTheta 1 error is: %04.8f" % t_1_e)
print ("Theta 2 error is: %04.8f" % t_2_e)
print ("Theta 3 error is: %04.8f" % t_3_e)
print ("Theta 4 error is: %04.8f" % t_4_e)
print ("Theta 5 error is: %04.8f" % t_5_e)
print ("Theta 6 error is: %04.8f" % t_6_e)
print ("\n**These theta errors may not be a correct representation of your code, due to the fact \
\nthat the arm can have muliple positions. It is best to add your forward kinmeatics to \
\nconfirm whether your code is working or not**")
print (" ")
# Find FK EE error
if not(sum(your_ee)==3):
ee_x_e = abs(your_ee[0]-test_case[0][0][0])
ee_y_e = abs(your_ee[1]-test_case[0][0][1])
ee_z_e = abs(your_ee[2]-test_case[0][0][2])
ee_offset = sqrt(ee_x_e**2 + ee_y_e**2 + ee_z_e**2)
# ee_x_e = math.fabs(ee_x_e)
# print ("\nEnd effector error for x position is: %04.8f" % ee_x_e)
# print ("End effector error for y position is: %04.8f" % ee_y_e)
# print ("End effector error for z position is: %04.8f" % ee_z_e)
# print ("Overall end effector offset is: %04.8f units \n" % ee_offset)
print ("\nEnd effector error for x position is: %r" % ee_x_e)
print ("End effector error for y position is: %r" % ee_y_e)
print ("End effector error for z position is: %r" % ee_z_e)
print ("Overall end effector offset is: %r units \n" % ee_offset)
if __name__ == "__main__":
# Change test case number for different scenarios
test_case_number = 1
test_code(test_cases[test_case_number])
Error:
Traceback (most recent call last):
File "IK_debug.py", line 236, in <module>
test_code(test_cases[test_case_number])
File "IK_debug.py", line 90, in test_code
T0_1 = TF_Matrix(alpha0, a0, d1, q1).subs(DH_Table)
File "IK_debug.py", line 84, in TF_Matrix
TF = Matrix([[ cos(q), -sin(q), 0, a],
File "/home/robond/.local/lib/python2.7/site-packages/sympy/core/expr.py", line 226, in __float__
raise TypeError("can't convert expression to floa