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IK_debug.py
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IK_debug.py
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from mpmath import radians
from sympy import *
from time import time
import math
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()
########################################################################################
##
## Insert IK code here!
theta1 = 0
theta2 = 0
theta3 = 0
theta4 = 0
theta5 = 0
theta6 = 0
# gripper orientation correction as described in lesson
r = symbols('r')
p = symbols('p')
y = symbols('y')
R_x = Matrix([[ 1, 0, 0 ],
[ 0, cos(r), -sin(r) ],
[ 0, sin(r), cos(r) ]])
R_y = Matrix([[ cos(p), 0, sin(p) ],
[ 0, 1, 0 ],
[ -sin(p), 0, cos(p) ]])
R_z = Matrix([[ cos(y), -sin(y), 0 ],
[ sin(y), cos(y), 0 ],
[ 0, 0, 1 ]])
R_corr = R_z.evalf(subs={y: pi}) * R_y.evalf(subs={p: -pi/2})
# Extract end-effector position and orientation from request
# px,py,pz = end-effector position
# roll, pitch, yaw = end-effector orientation
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])
# the orientation of the end effector would be the roll, pitch yaw combined
# with the rotation correction
R_ee = (R_z * R_y * R_x).evalf(subs={r: roll, p: pitch, y: yaw}) * R_corr
# the wrist center would be offset backward from the end effector
eePos = Matrix([[px], [py], [pz]])
wcPos = eePos - 0.303 * R_ee[:, 2]
# symbols for the DH parameters, q stands for theta, note that q[0] here
# is actually q1 and d[0] is actually d1 in the lesson notation
q = symbols('q1:8')
d = symbols('d1:8')
a = symbols('a0:7')
alpha = symbols('alpha0:7')
# constant DH parameters
CONST_DH = {
alpha[0]: 0, a[0]: 0, d[0]: 0.75,
alpha[1]: -pi/2., a[1]: 0.35, d[1]: 0.0, q[1]: q[1] - pi/2.,
alpha[2]: 0, a[2]: 1.25, d[2]: 0.00,
alpha[3]: -pi/2., a[3]: -0.054, d[3]: 1.5,
alpha[4]: pi/2., a[4]: 0, d[4]: 0.0,
alpha[5]: -pi/2., a[5]: 0, d[5]: 0.0,
alpha[6]: 0, a[6]: 0, d[6]: 0.303, q[6]: 0.0
}
### Inverse Position
# theta1 can be obtained by projecting the wrist center to the xy plane and
# calculating the angle between origin-wc vs x-axis
theta1 = atan2(wcPos[1], wcPos[0])
# use the triangle diagram to get theta 2 and theta 3
# side a: distance between link 3 and write center, or sqrt(d[3] ** 2 + a[3] ** 2)
sa = 1.501
# side b: distance between link 2 and wrist center, use world coordinates to calculate dist
dx2Wc = sqrt(wcPos[0] ** 2. + wcPos[1] ** 2.) - 0.35 # offset on xy plane
dz2Wc = wcPos[2] - 0.75 # offset of z
sb = sqrt(dx2Wc ** 2. + dz2Wc ** 2.)
# side c: distance between link 2 and 3, or a[2]
sc = 1.25
# use cosine law to get all three angles for theta 2 and 3
ta = acos((sb ** 2. + sc ** 2. - sa ** 2.) / (2.0 * sb * sc))
tb = acos((sa ** 2. + sc ** 2. - sb ** 2.) / (2.0 * sa * sc))
tc = acos((sa ** 2. + sb ** 2. - sc ** 2.) / (2.0 * sa * sb))
# use the diagram to compute theta 2 and theta 3
# theta2 would be pi/2 minus angle a, then minus the angle of link2-wc vs X1 axis
theta2 = pi/2. - ta - atan2(dz2Wc, dx2Wc)
# theta3 would be the negative of angle b + angle between link3-wc vs X3 (abs(atan2(a[3], d[3]))) minus pi/2
theta3 = - (tb + 0.036 - pi/2.)
### Inverse Orientation
# homogeneous transformation matrices
T = []
for i in range(7):
T.append(Matrix([[ cos(q[i]), -sin(q[i]), 0, a[i] ],
[ sin(q[i]) * cos(alpha[i]), cos(q[i]) * cos(alpha[i]), -sin(alpha[i]), -sin(alpha[i]) * d[i] ],
[ sin(q[i]) * sin(alpha[i]), cos(q[i]) * sin(alpha[i]), cos(alpha[i]), cos(alpha[i]) * d[i] ],
[ 0, 0, 0, 1 ]]))
T[i] = T[i].subs(CONST_DH)
# composition of homogeneous transformations
R0_3 = (T[0] * T[1] * T[2]).evalf(subs={q[0]: theta1, q[1]: theta2, q[2]: theta3})
R3_6 = R0_3[:3,:3].inv('LU') * R_ee
# use the R3_6 matrix elements to get theta 4 through 6
sine5 = sqrt(R3_6[0,2] ** 2. + R3_6[2,2] ** 2.)
theta5 = atan2(sine5, R3_6[1,2])
if sin(theta5) > 0:
theta4 = atan2(R3_6[2,2], -R3_6[0,2])
theta6 = atan2(-R3_6[1,1], R3_6[1,0])
else:
theta4 = atan2(-R3_6[2,2], R3_6[0,2])
theta6 = atan2(R3_6[1,1], -R3_6[1,0])
##
########################################################################################
########################################################################################
## 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!
thetas = {
q[0]: theta1,
q[1]: theta2,
q[2]: theta3,
q[3]: theta4,
q[4]: theta5,
q[5]: theta6
}
T0_EE = T[0].evalf(subs = thetas)
for i in range(1, 7):
T0_EE = T0_EE * T[i].evalf(subs = thetas)
## 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 = wcPos # <--- Load your calculated WC values in this array
your_ee = T0_EE[:3, 3] # <--- 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
for test_case_number in [1, 2, 3]:
print 'Testing case', test_case_number
test_code(test_cases[test_case_number])