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IK_debug.py
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from sympy import *
from time import time
from mpmath import radians
import tf
from sympy.matrices import Matrix
'''
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
print ("\nTest Case is: " test_case)
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()
########################################################################################
##
q1, q2, q3, q4, q5, q6, q7 = symbols('q1:8')
d1, d2, d3, d4, d5, d6, d7 = symbols('d1:8')
a0, a1, a2, a3, a4, a5, a6 = symbols('a0:7')
alpha0, alpha1, alpha2, alpha3, alpha4, alpha5, alpha6 = symbols('alpha0:7')
# Create Modified DH parameters
s = {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}
# Define Modified DH Transformation matrix
def Trans(q, d, a, alpha):
t = 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 t
# Create individual transformation matrices
#
T0_1=Trans(q1 , d1 , a0 , alpha0).subs(s)
T1_2=Trans(q2 , d2 , a1 , alpha1).subs(s)
T2_3=Trans(q3 , d3 , a2 , alpha2).subs(s)
T3_4=Trans(q4 , d4 , a3 , alpha3).subs(s)
T4_5=Trans(q5 , d5 , a4 , alpha4).subs(s)
T5_6=Trans(q6 , d6 , a5 , alpha5).subs(s)
T6_7=Trans(q7 , d7 , a6 , alpha6).subs(s)
T0_3=T0_1*T1_2*T2_3
T0_7=T0_3*T3_4*T4_5*T5_6*T6_7
#
# Extract rotation matrices from the transformation 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]])
ROT_Cor = ROT_z * ROT_y * ROT_x
ROT_corr = ROT_z.subs(y, radians(180)) * ROT_y.subs(p, radians(-90))
ROT_EE = ROT_Cor * ROT_corr
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})
P=Matrix([[px],[py],[pz]])
wc=P-0.303*ROT_EE[:,2]
#Calculating the parameters required to calculate the q2 and q3
a=1.501
c=1.25
b=sqrt((sqrt(wc[0]**2+wc[1]**2)-0.35)**2+(wc[2]-0.75)**2)
angle_x=atan2(wc[2]-0.75,sqrt(wc[0]**2+wc[1]**2)-0.35)
angle_a=acos((b**2+c**2-a**2)/(2*b*c))
angle_b=acos((a**2+c**2-b**2)/(2*a*c))
#Calculating the value of q1, q2 and q3
theta1 = atan2(wc[1],wc[0])
theta2 = pi/2-angle_x-angle_a
theta3 = pi/2-angle_b-0.036
#subsituting the value of q1, q2 and q3 in the roation matrix, so that we can calculate the
# value of q4, q5 and q5
R0_3=T0_3[0:3,0:3]
R0_3=R0_3.subs({q1: theta1, q2: theta2, q3: theta3})
R3_6 = R0_3.inv(method="LU")*ROT_EE
#Finding the value of q4, q5 and q6 from the roation matrix
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])
########################################################################################
## 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!
#wc.subs({q1: theta1, q2: theta2, q3: theta3, q4: theta4, q5: theta5, q6: theta6})
FK=T0_7.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[0,3],FK[1,3],FK[2,3]] # <--- 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 i in range(1,4):
test_case_number = i
test_code(test_cases[test_case_number])