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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()
########################################################################################
##
## Insert IK code here!
# Create symbols
q1, q2, q3, q4, q5, q6, q7 = symbols('q1:8') # theta i for joint angles
d1, d2, d3, d4, d5, d6, d7 = symbols('d1:8') # link offset values
a0, a1, a2, a3, a4, a5, a6 = symbols('a0:7') # twist angle
alpha0, alpha1, alpha2, alpha3, alpha4, alpha5, alpha6 = symbols('alpha0:7')
#
# Create Modified DH parameters
DH_params = {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: 1.50, q4: q4,
alpha4: pi/2., a4: 0., d5: 0., q5: q5,
alpha5: -pi/2., a5: 0., d6: 0.303, q6: q6,
alpha6: 0., a6: 0., d7: 0.303, q7: 0.}
#
#
# Define Modified DH Transformation matrix
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
#
#
# Create individual transformation matrices
T0_1 = TF_Matrix(alpha0, a0, d1, q1).subs(DH_params)
print("T0_1",T0_1)
T1_2 = TF_Matrix(alpha1, a1, d2, q2).subs(DH_params)
print("T1_2",T1_2)
T2_3 = TF_Matrix(alpha2, a2, d3, q3).subs(DH_params)
print("T2_3",T2_3)
T3_4 = TF_Matrix(alpha3, a3, d4, q4).subs(DH_params)
print("T3_4",T3_4)
T4_5 = TF_Matrix(alpha4, a4, d5, q5).subs(DH_params)
print("T4_5",T4_5)
T5_6 = TF_Matrix(alpha5, a5, d6, q6).subs(DH_params)
print("T5_6",T5_6)
T6_G = TF_Matrix(alpha6, a6, d7, q7).subs(DH_params)
print("T6_G",T6_G)
T0_G = simplify(T0_1 * T1_2 * T2_3 * T3_4 * T4_5 * T5_6 * T6_G)
print("T0_G",T0_G)
# 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])
# Find Gripper rotation matrix
# Define RPY rotation matrices
r, p, y = symbols('r p y')
#ROLL
ROT_x = Matrix([[1, 0, 0],
[0, cos(r), -sin(r)],
[0, sin(r), cos(r)]])
#PITCH
ROT_y = Matrix([[cos(p), 0, sin(p)],
[0, 1, 0],
[-sin(p), 0, cos(p)]])
#YAW
ROT_z = Matrix([[cos(y), -sin(y), 0],
[sin(y), cos(y), 0],
[0, 0, 1]])
#Rotation composition
ROT_G = ROT_z * ROT_y * ROT_x
# Compensate for rotation discrepancy between DH parameters and Gazebo
#
ROT_error = ROT_z.subs(y, pi) * ROT_y.subs(p, -pi/2)
ROT_G = ROT_G * ROT_error
ROT_G = ROT_G.subs({'r': roll, 'p': pitch, 'y': yaw})
#Matrix for end effector position
G = Matrix([[px],
[py],
[pz]])
#Calculate the Wrist Center based on end effector position and length
WC = G - (0.303) * ROT_G[:,2]
#
# Calculate joint angles using Geometric IK method
#theta 1-3 are calculated using the Wrist Center position
#theta 1
theta1 = atan2(WC[1],WC[0]) #Angle of the first joint calculated using the x-y coordinate of the wrist center setting the z coord to 0
#Determine triangle lengths and angles formed by J2, J3, and the wrist center
sideA = 1.501 #DH parameter d4
sideC = 1.25 #DH parameter a2
sideB = sqrt(pow((sqrt(WC[0]*WC[0]+WC[1]*WC[1])-0.35),2)+pow((WC[2]-0.75),2))
angA = acos((sideB*sideB+sideC*sideC-sideA*sideA)/(2*sideB*sideC))
angB = acos((sideA*sideA+sideC*sideC-sideB*sideB)/(2*sideA*sideC))
angC = acos((sideA*sideA+sideB*sideB-sideC*sideC)/(2*sideA*sideB))
#theta 2
theta2 = pi/2 - angA - atan2(WC[2]-0.75,sqrt(WC[0]*WC[0]+WC[1]*WC[1])-0.35)
#
theta3 = pi/2 - (angB + 0.036) #0.036 adjusts for -0.054m drop in link 4
#
#theta 4-6 are calculated to obtain the desired orientation
#Rotation transform for the spherical wrist is from J3-J6
#first we extract the rotational component of the first 3 joint transforms and evaluate for the specified angles
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})
#Then apply this inversely to the desired end effector orientation to obtain the necessary rotational tranform
#of the spherical wrist
R3_6sym = T3_4[0:3,0:3]*T4_5[0:3,0:3]*T5_6[0:3,0:3]*T6_G[0:3,0:3]
print ("R3_6 Symbolic", R3_6sym)
#R3_6 = R0_3.inv("LU") * ROT_G
R3_6 = transpose(R0_3) * ROT_G
###
# Use the rotation matrix to determine the Euler angles for theta 4, 5, 6
theta4 = atan2(R3_6[2,2], -R3_6[0,2])
theta5 = atan2(sqrt((R3_6[1,0]*R3_6[1,0] + R3_6[1,1]*R3_6[1,1])),R3_6[1,2])
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]
FK = T0_G.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 = [WC[0],WC[1],WC[2]] # <--- Load your calculated WC values in this array
your_ee = [FK[0],FK[1],FK[2]] # <--- 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])
test_code(test_cases[1])
test_code(test_cases[2])
test_code(test_cases[3])