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calibration.py
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calibration.py
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import numpy as np
import cv2
import vrep
from scene import Scene
from matplotlib import pyplot as plt
from tool import *
import time
import os
# vrep
ip = '127.0.0.1'
port = 19997
cam_num = 3
train_size = 50
sample_size = 20
iteration=100
score_threshold=0.02
scalar_threshold = 0.0005
def get_sub_mat(qa, qa_prime, qb, qb_prime):
mat = np.zeros((6,8))
# equation 1
mat[:3, 0] = qa[1:] - qb[1:]
mat[:3, 1:4] = cross_mat(qa[1:] + qb[1:])
# equation 2
mat[3:, 0] = qa_prime[1:] - qb_prime[1:]
mat[3:, 1:4] = cross_mat(qa_prime[1:] + qb_prime[1:])
mat[3:, 4] = qa[1:] - qb[1:]
mat[3:, 5:] = cross_mat(qa[1:] + qb[1:])
return mat
# solve AX=XB by dual quaternion
def dual_quaternion_approach(motionAs, motionBs):
size = motionAs.shape[0]
T = []
for j in range(size):
motionA = motionAs[j]
motionB = motionBs[j]
ra, ta = mat_to_r_t(motionA)
rb, tb = mat_to_r_t(motionB)
qa, qa_prime = rot2dualquat(ra, ta)
qb, qb_prime = rot2dualquat(rb, tb)
T.append(get_sub_mat(qa, qa_prime, qb, qb_prime))
T = np.concatenate(T)
U, s, V = np.linalg.svd(T)
idx1, idx2 = np.argsort(s)[:2].tolist()
v7 = V[idx1]
v8 = V[idx2]
u1 = v7[:4]
v1 = v7[4:]
u2 = v8[:4]
v2 = v8[4:]
a = np.dot(u1,v1)
b = np.dot(u1,v2) + np.dot(u2,v1)
c = np.dot(u2,v2)
s1 = (-b + np.sqrt(b*b-4*a*c)) / (2*a)
s2 = (-b - np.sqrt(b*b-4*a*c)) / (2*a)
x1 = s1**2 * np.dot(u1,u1) + 2*s1*np.dot(u1,u2) + np.dot(u2,u2)
x2 = s2**2 * np.dot(u1,u1) + 2*s2*np.dot(u1,u2) + np.dot(u2,u2)
(x,s) = (x1,s1) if x1 >= x2 else (x2,s2)
lambda2 = np.sqrt(1/x)
lambda1 = s * lambda2
q = lambda1 * u1 + lambda2 * u2
q_ = lambda1 * v1 + lambda2 * v2
r_ba, t_ba = dualquat2r_t(q, q_)
return r_t_to_mat(r_ba, t_ba), s
def get_error(T_world_cam, motionAs, motionBs, score_threshold):
motionAs_ = np.matmul(T_world_cam, motionBs)
motionAs_ = np.matmul(motionAs_, np.linalg.inv(T_world_cam))
error = np.linalg.norm(motionAs - motionAs_) / np.linalg.norm(motionAs)
tAs_ = motionAs_[:, :3, 3]
tAs = motionAs[:, :3, 3]
error = np.linalg.norm(tAs_ - tAs) / np.linalg.norm(tAs)
return error
def ransac_for_calibration(motionAs, motionBs, sample_size=20, iteration=10, score_threshold=0.002, show=False):
best_error = np.inf
best_result = None
for i in range(iteration):
sample_idxs = np.random.randint(0,motionAs.shape[0],size=(1,sample_size))
sampled_motionAs = motionAs[sample_idxs.ravel().tolist()]
sampled_motionBs = motionBs[sample_idxs.ravel().tolist()]
result, singular_values = dual_quaternion_approach(sampled_motionAs, sampled_motionBs)
error = get_error(result, motionAs, motionBs, score_threshold)
if error < best_error:
best_error = error
best_result = result
if show:
print("iter ", i, "error: ", error)
return best_result, best_error
def get_motion(A, B, scalar_threshold=0.0005, train_size=20, show=False):
size = A.shape[0]
motionAs = []
motionBs = []
for i in range(size):
Ai = A[i]
Bi = B[i]
for j in range(i+1,size):
Aj = A[j]
Bj = B[j]
motionA = np.matmul(np.linalg.inv(Aj), Ai)
motionB = np.matmul(Bj, np.linalg.inv(Bi))
ra, ta = mat_to_r_t(motionA)
rb, tb = mat_to_r_t(motionB)
qa, qa_prime = rot2dualquat(ra, ta)
qb, qb_prime = rot2dualquat(rb, tb)
# check scalar be equivalent
diff_scalar = np.abs(qa[0]-qb[0])
diff_scalar_ = np.abs(qa_prime[0]-qb_prime[0])
# if show:
# print(j, diff_scalar, diff_scalar_)
if(diff_scalar < scalar_threshold and diff_scalar_ < scalar_threshold):
motionAs.append(motionA)
motionBs.append(motionB)
shuffle_idxs = [i for i in range(len(motionAs))]
np.random.shuffle(shuffle_idxs)
if show:
print('valid motion size: ', len(motionAs))
print('train size: ', train_size)
return np.stack(motionAs)[shuffle_idxs][:train_size], np.stack(motionBs)[shuffle_idxs][:train_size]
def hand_eye_calibration(A, B, sample_size=20, iteration=10, score_threshold=0.002, scalar_threshold=0.0005, train_size=20, show=False):
motionAs, motionBs = get_motion(
A,
B,
scalar_threshold=scalar_threshold,
train_size=train_size,
show=show
)
T_world_cam, error = ransac_for_calibration(
motionAs,
motionBs,
sample_size,
iteration,
score_threshold,
show=show
)
if show:
print('best error:', error)
return T_world_cam
def main():
input_path = "./calibration"
cam_paths = [os.path.join(input_path,'camera{:d}'.format(i)) for i in range(cam_num)]
scene = Scene(ip, port)
T_world_cams = scene.get_cam_matrixs()
theta = np.pi
l = np.array([0,0,1])
q = np.array([np.cos(theta/2)]+(np.sin(theta/2) * l).tolist())
r = quat2rot(q)
cam_fix = r_t_to_mat(r, np.zeros(3))
T_world_cams = [np.matmul(T_world_cams[i],cam_fix) for i in range(cam_num)]
for i in range(cam_num):
print('camera ',i)
cam_path = cam_paths[i]
T_world_end = np.loadtxt(os.path.join(cam_path, 'world_end.txt')).reshape((-1,4,4))
T_cam_obj = np.loadtxt(os.path.join(cam_path, 'cam_obj.txt')).reshape((-1,4,4))
# hand eye calibration
T_world_cam = hand_eye_calibration(
np.linalg.inv(T_world_end)[::-1],
T_cam_obj[::-1],
sample_size=sample_size,
iteration=iteration,
score_threshold=score_threshold,
scalar_threshold=scalar_threshold,
train_size=train_size,
show=True
)
# check X
print('final check')
thetaj, nj, tj = mat_to_theta_n_t(T_world_cam)
thetaj_, nj_, tj_ = mat_to_theta_n_t(T_world_cams[i])
print(thetaj, nj, tj)
print(thetaj_, nj_, tj_)
print(
"theta:{:6f} n:{:6f} t:{:6f}".format(
np.linalg.norm(thetaj-thetaj_),
np.linalg.norm(nj-nj_)/np.linalg.norm(nj),
np.linalg.norm(tj-tj_)/np.linalg.norm(tj)
)
)
print('-----------------------------------------------------')
np.savetxt(os.path.join(cam_path, 'world_cam.txt'),T_world_cam)
if __name__ == "__main__":
main()