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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()
########################################################################################
##
## Insert IK code here!
### Your FK code here
# Create symbols
q1, q2, q3, q4, q5, q6, q7 = symbols('q1:8') #theta_i
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
dh = {alpha0: 0, a0: 0, d1: 0.75,
alpha1: -pi/2., a1: 0.35, d2: 0, q2:q2-pi/2,
alpha2: 0, a2: 1.25, d3: 0,
alpha3: -pi/2., a3: -0.054, d4: 1.5,
alpha4: pi/2., a4: 0, d5: 0,
alpha5: -pi/2., a5: 0, d6: 0,
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)
T1_2 = TF_matrix(alpha1, a1, d2, q2).subs(dh)
T2_3 = TF_matrix(alpha2, a2, d3, q3).subs(dh)
T3_4 = TF_matrix(alpha3, a3, d4, q4).subs(dh)
T4_5 = TF_matrix(alpha4, a4, d5, q5).subs(dh)
T5_6 = TF_matrix(alpha5, a5, d6, q6).subs(dh)
T6_G = TF_matrix(alpha6, a6, d7, q7).subs(dh)
T0_G = T0_1 * T1_2 * T2_3 * T3_4 * T4_5 * T5_6 * T6_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])
### Your IK code here
# Compensate for rotation discrepancy between DH parameters and Gazebo
# first get the orientation from roll, pitch, and yaw angles
R, P, Y = symbols('R P Y')
R_X = Matrix([[1, 0, 0],
[0, cos(R), -sin(R)],
[0, sin(R), cos(R)]]) #roll
R_Y = Matrix([[ cos(P), 0, sin(P)],
[ 0, 1, 0],
[-sin(P), 0, cos(P)]]) #pitch
R_Z = Matrix([[cos(Y), -sin(Y), 0],
[sin(Y), cos(Y), 0],
[ 0, 0, 1]]) #yaw
R_G = R_Z * R_Y * R_X
# second, make correction for DH vs URDF
R_corr = R_Z.subs(Y,radians(180)) * R_Y.subs(P,radians(-90))
R_G = R_G * R_corr
# evalueate at the given rpy
R_G = R_G.subs({'R': roll, 'P':pitch, 'Y':yaw})
G = Matrix([[px],
[py],
[pz]])
WC = G - (0.303)*R_G[:,2]
WCx = WC[0]
WCy = WC[1]
WCz = WC[2]
# Calculate joint angles using Geometric IK method
# theta 1
theta1 = atan2(WCy, WCx)
# theta 2 and 3
sideA = 1.501
sideB = sqrt((sqrt(WCx**2 + WCy**2) -0.35)**2 + (WCz-0.75)**2)
sideC = 1.25
angleA = acos((sideB**2 + sideC**2 - sideA**2)/(2*sideB*sideC))
angleB = acos((sideA**2 + sideC**2 - sideB**2)/(2*sideA*sideC))
angleWC2base = atan2((WCz-0.75),sqrt(WCx**2 + WCy**2) - 0.35)
angleWC2link3 = atan2(0.054,1.5)
theta2 = pi/2 - angleA - angleWC2base
theta3 = pi/2 - angleB - angleWC2link3
# theta 4, 5, and 6
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") * R_G
R3_6 = R0_3.transpose() * R_G
theta4 = atan2( R3_6[2,2], -R3_6[0,2])
theta5 = atan2(sqrt((R3_6[0,2])**2 + (R3_6[2,2])**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]
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 = [WCx, WCy, WCz] # <--- 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 is: %4.8f" % theta1)
print("Theta 2 is: %4.8f" % theta2)
print("Theta 3 is: %4.8f" % theta3)
print("Theta 4 is: %4.8f" % theta4)
print("Theta 5 is: %4.8f" % theta5)
print("Theta 6 is: %4.8f" % theta6)
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 = 3
test_code(test_cases[test_case_number])