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IK_debug.py
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IK_debug.py
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from sympy import *
from time import time
from mpmath import radians
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.launch`
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()
########################################################################################
##
print 'Creating symbols'
# Create symbols
# Joint angles
q1, q2, q3, q4, q5, q6, q7 = symbols('q1:8')
# Link len's
a0, a1, a2, a3, a4, a5, a6 = symbols('a0:7')
# Link offsets
d1, d2, d3, d4, d5, d6, d7 = symbols('d1:8')
# Joint twists
alpha0, alpha1, alpha2, alpha3, alpha4, alpha5, alpha6 = symbols('alpha0:7')
print 'Creating DH parameters'
# Create Modified DH parameters
dhParams = {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, d3: 0, q3: q3,
alpha3: -pi/2., a3: -0.054, d4: 1.5, q4: q4,
alpha4: pi/2, a4: 0, d5: 0, q5: q5,
alpha5: -pi/2., a5: 0, d6: 0, q6: q6,
alpha6: 0, a6: 0, d7: 0.303, q7: 0}
print 'Defining DH transformation matrix'
# Define Modified DH Transformation matrix
def dh_transform(alpha, a, d, q):
dhtMatrix = 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 dhtMatrix
print 'Creating individual transform matrices'
# Create individual transformation matrices
T0_1 = dh_transform(alpha0, a0, d1, q1).subs(dhParams)
T1_2 = dh_transform(alpha1, a1, d2, q2).subs(dhParams)
T2_3 = dh_transform(alpha2, a2, d3, q3).subs(dhParams)
T3_4 = dh_transform(alpha3, a3, d4, q4).subs(dhParams)
T4_5 = dh_transform(alpha4, a4, d5, q5).subs(dhParams)
T5_6 = dh_transform(alpha5, a5, d6, q6).subs(dhParams)
T6_7 = dh_transform(alpha6, a6, d7, q7).subs(dhParams)
T0_7 = (T0_1 * T1_2 * T2_3 * T3_4 * T4_5 * T5_6 * T6_7)
# Extract rotation matrices from the transformation matrices
print 'Creating roll, pitch, and yaw rotation matrices'
# Roll, Pitch, Yaw Symbols
r, p , y = symbols('r p y')
# Roll
rotationX = Matrix([
[1, 0 , 0],
[0, cos(r), -sin(r)],
[0, sin(r), cos(r)]
])
# Pitch
rotationY = Matrix([
[ cos(p), 0, sin(p)],
[ 0, 1, 0],
[ -sin(p), 0, cos(p)]
])
# Yaw
rotationZ = Matrix([
[cos(y), -sin(y), 0],
[sin(y), cos(y), 0],
[ 0, 0, 1]
])
ROT_EE = (rotationX * rotationY * rotationZ)
rotationErr = rotationZ.subs(y, radians(180)) * rotationY.subs(p, radians(-90))
ROT_EE = (ROT_EE * rotationErr)
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])
ROT_EE = ROT_EE.subs({'r': roll, 'p': pitch, 'y': yaw})
EE = Matrix([[px], [py], [pz]])
WC = EE - (0.303) * ROT_EE[:,2]
print 'Calculating theta1'
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))
print 'Calculating theta2'
theta2 = pi/2 - angle_a - atan2(WC[2] - 0.75, sqrt(WC[0] * WC[0] + WC[1] * WC[1]) - 0.35)
print 'Calculating theta3'
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.transpose() * rotationErr
print 'Calculating theta4'
theta4 = atan2(R3_6[2,2], -R3_6[0,2])
print 'Calculating theta5'
theta5 = atan2(sqrt(R3_6[0,2]*R3_6[0,2] + R3_6[2,2]*R3_6[2,2]), R3_6[1,2])
print 'Calculating theta6'
theta6 = atan2(-R3_6[1,1], R3_6[1,0])
print (theta1)
print (theta2)
print (theta3)
print (theta4)
print (theta5)
print (theta6)
##
########################################################################################
########################################################################################
## 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]
FK = T0_7.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
########################################################################################
## 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)
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)
if __name__ == "__main__":
# Change test case number for different scenarios
test_case_number = 1
test_code(test_cases[test_case_number])