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1.眼在手外原理
2.附上眼在手外求得手眼矩阵的python代码
3.眼在手外标定步骤
1#xff09;打印棋盘格
2#xff09;得到hand数据
3#xff09;得到camera数据
4.运行python得到手眼矩阵 1.眼在手外原理 眼在手外所求的手眼矩阵是基坐标到相机的转换矩阵
2.附上…目录
1.眼在手外原理
2.附上眼在手外求得手眼矩阵的python代码
3.眼在手外标定步骤
1打印棋盘格
2得到hand数据
3得到camera数据
4.运行python得到手眼矩阵 1.眼在手外原理 眼在手外所求的手眼矩阵是基坐标到相机的转换矩阵
2.附上眼在手外求得手眼矩阵的python代码
#!/usr/bin/env python
# coding: utf-8
import transforms3d as tfs
import numpy as np
import mathdef get_matrix_eular_radu(x, y, z, rx, ry, rz):rmat tfs.euler.euler2mat(math.radians(rx), math.radians(ry), math.radians(rz))rmat tfs.affines.compose(np.squeeze(np.asarray((x, y, z))), rmat, [1, 1, 1])return rmatdef skew(v):return np.array([[0, -v[2], v[1]],[v[2], 0, -v[0]],[-v[1], v[0], 0]])def rot2quat_minimal(m):quat tfs.quaternions.mat2quat(m[0:3, 0:3])return quat[1:]def quatMinimal2rot(q):p np.dot(q.T, q)w np.sqrt(np.subtract(1, p[0][0]))return tfs.quaternions.quat2mat([w, q[0], q[1], q[2]])# hand [1.1988093940033604, -0.42405585264804424, 0.18828251788562061, 151.3390418721659, -18.612399542280507,
# 153.05074895025035,
# 1.1684831621733476, -0.183273375514656, 0.12744868246620855, -161.57083804238462, 9.07159838346732,
# 89.1641128844487,
# 1.1508343174145468, -0.22694301453461405, 0.26625166858469146, 177.8815855486261, 0.8991159570568988,
# 77.67286224959672]
hand [# -0.05448,-0.15018,0.06552,89.61059916,-2.119943842,-1.031324031,# -0.10149,-0.23025,0.04023,96.7725716,6.187944187,5.328507495,# -0.10114,-0.2207,0.04853,97.00175472,5.729577951,1.375098708 毫米单位# -54.48, -150.18, 65.52, 89.61059916, -2.119943842, -1.031324031,
# -101.49,-230.25, 40.23, 96.7725716, 6.187944187, 5.328507495,
# -101.14,-220.7 , 48.53, 97.00175472, 5.729577951, 1.375098708# -122.12, -323.09, -206.86, 82.62051406, -7.161972439 ,1.948056503,
# -96.54, -324.53, -215.59, 83.70913387, -7.734930234 ,7.276563998,
# -116.41, -325.50, -202.05, 81.18811957, -7.505747116 ,6.187944187# zed
-54.29, -95.24, 199.74, 80.45, -5.88, 8.8,
-54.28, -95.25, 199.73, 80.66, -6.62, 18.13,
-54.3, -95.27, 199.75, 81.57, -0.76, 13.05]# camera [-0.16249272227287292, -0.047310635447502136, 0.4077761471271515, -56.98037030812389, -6.16739631361851,
# -115.84333735802369,
# 0.03955405578017235, -0.013497642241418362, 0.33975949883461, -100.87129330834215, -17.192685528625265,
# -173.07354634882094,
# -0.08517949283123016, 0.00957852229475975, 0.46546608209609985, -90.85270962096058, 0.9315977976503153,
# 175.2059707654342]camera [# -0.0794887,-0.0812433,0.0246,0.0008,0.0033,0.0182,# -0.078034,-0.0879632,0.4881494,-0.1085,0.0925,-0.1569,# -0.1086702,-0.0881681,0.4240367,-0.1052,0.1251,-0.1124,# -79.4887, -81.2433, 24.6, 0.0008, 0.0033, 0.0182,
# -78.034, -87.9632, 488.1494, -0.1085, 0.0925, -0.1569,
# -108.6702, -88.1681, 424.0367, -0.1052, 0.1251, -0.1124,# 23.22020448 ,-69.45610195 ,370.5620915 ,0.2530 ,-0.0707, -1.5724,
# 46.8704669 ,-60.19912413 ,263.9729574 ,0.1473 ,-0.1117 ,-1.6090,
# 53.92881454 ,-39.52795178 ,453.4331562 ,0.2702 ,-0.1256, -1.6270,
-174.01022, 1797.687613, 2425.313638, 1.2710, 0.1238, 0.0033,
-175.3384083, 260.4775862, 1349.136325, 1.5191, 0.0664, 0.0058,
123.6753385, -109.6917624, 695.5448714 , 0.4651, -0.1328, -0.2488]Hgs, Hcs [], []
for i in range(0, len(hand), 6):Hgs.append(get_matrix_eular_radu(hand[i], hand[i 1], hand[i 2], hand[i 3], hand[i 4], hand[i 5],))Hcs.append(get_matrix_eular_radu(camera[i], camera[i 1], camera[i 2], camera[i 3], camera[i 4], camera[i 5]))Hgijs []
Hcijs []
A []
B []
size 0
for i in range(len(Hgs)):for j in range(i 1, len(Hgs)):size 1Hgij np.dot(np.linalg.inv(Hgs[j]), Hgs[i])Hgijs.append(Hgij)Pgij np.dot(2, rot2quat_minimal(Hgij))Hcij np.dot(Hcs[j], np.linalg.inv(Hcs[i]))Hcijs.append(Hcij)Pcij np.dot(2, rot2quat_minimal(Hcij))A.append(skew(np.add(Pgij, Pcij)))B.append(np.subtract(Pcij, Pgij))
MA np.asarray(A).reshape(size * 3, 3)
MB np.asarray(B).reshape(size * 3, 1)
Pcg_ np.dot(np.linalg.pinv(MA), MB)
pcg_norm np.dot(np.conjugate(Pcg_).T, Pcg_)
Pcg np.sqrt(np.add(1, np.dot(Pcg_.T, Pcg_)))
Pcg np.dot(np.dot(2, Pcg_), np.linalg.inv(Pcg))
Rcg quatMinimal2rot(np.divide(Pcg, 2)).reshape(3, 3)A []
B []
id 0
for i in range(len(Hgs)):for j in range(i 1, len(Hgs)):Hgij Hgijs[id]Hcij Hcijs[id]A.append(np.subtract(Hgij[0:3, 0:3], np.eye(3, 3)))B.append(np.subtract(np.dot(Rcg, Hcij[0:3, 3:4]), Hgij[0:3, 3:4]))id 1MA np.asarray(A).reshape(size * 3, 3)
MB np.asarray(B).reshape(size * 3, 1)
Tcg np.dot(np.linalg.pinv(MA), MB).reshape(3, )
print(tfs.affines.compose(Tcg, np.squeeze(Rcg), [1, 1, 1]))其中 hand为基坐标系下抓夹的位姿一般从示教器上获取我用的是ur5机械臂注意单位mm和rad三行为三组数据hand(x,y,z,rx,ry,rz)同时应将弧度制rad转为角度制° camera为相机中标定板的位姿为相机的外参平移矩阵、旋转矩阵三行为三组数据camera(x,y,z,rx,ry,rz)同时应将弧度制转为角度制 3.眼在手外标定步骤
1打印棋盘格
为了使标定精度更加准确棋盘格精度越高越好角点数越多越好尽量减少相机中心到标定板的距离适当小的标定板等
参考资料
手眼标定我的结果显示手和眼相距上千米手眼标定结果准确率如何提高_提高手眼标定精度_鱼香ROS的博客-CSDN博客
这里我选择4*4的棋盘格
2得到hand数据
示教器右侧为hand数据记录五组并转化为角度制 3得到camera数据
将相机固定在距离机械臂基坐标的一定距离的地方固定相机记住距离
将棋盘格粘贴在机械臂末端执行器上用相机拍摄五组棋盘格图片使用matlab计算相机外参TR将得到的TR转换为欧拉角
matlab工具箱使用单目标定其中得到的T为translationvectorsR为rotationvectors 不知道这个棋盘格不正会不会有影响
matlab标定得到的是旋转向量/旋转矩阵得到的数据转化为欧拉角参考下面的链接手眼标定必备——旋转向量转换为旋转矩阵python——罗德里格斯公式Rodrigues_python rodrigues_邸笠佘司的博客-CSDN博客
手眼标定中旋转矩阵转欧拉角——matlab_邸笠佘司的博客-CSDN博客 4.运行python得到手眼矩阵
