hand），如果相机固定在机器人外面的底座上，则称之为“眼在外”（eye to hand）。
eye to hand

​​​​​​眼在手

1. eye in hand，这种关系下，两次运动，机器人底座和标定板的关系始终不变。求解的量为相机和机器人末端坐标系的位姿关系。

2. eye to hand，这种关系下，两次运动，机器人末端和标定板的位姿关系始终不变。求解的量为相机和机器人底座坐标系之间的位姿关系。

* Shiu Y C, Ahmad S. Calibration of wrist-mounted robotic sensors by solving
homogeneous transform equations of the form AX=XB[J]. IEEE Transactions on
Robotics & Automation, 1989, 5(1):16-29.

<http://math.loyola.edu/~mili/Calibration/index.html>其中也有一些AX=
XB的matlab代码可以使用。

ROS 下也有相关的一些package可以利用

https://github.com/IFL-CAMP/easy_handeye
<https://github.com/IFL-CAMP/easy_handeye>

http://wiki.ros.org/handeye <http://wiki.ros.org/handeye>

http://visp-doc.inria.fr/doxygen/visp-daily/calibrateTsai_8cpp-example.html#_a0

<http://visp-doc.inria.fr/doxygen/visp-daily/calibrateTsai_8cpp-example.html#_a0>

https://blog.csdn.net/u011089570/article/details/47945733
<https://blog.csdn.net/u011089570/article/details/47945733> 图不错

https://blog.csdn.net/qq_16481211/article/details/79764730
<https://blog.csdn.net/qq_16481211/article/details/79764730> 部分halocon代码

https://blog.csdn.net/qq_16481211/article/details/79767100
<https://blog.csdn.net/qq_16481211/article/details/79767100> halocon代码

https://blog.csdn.net/happyjume/article/details/80847822
<https://blog.csdn.net/happyjume/article/details/80847822> 部分原理

https://blog.csdn.net/zhang970187013/article/details/81098175
<https://blog.csdn.net/zhang970187013/article/details/81098175> UR5 与easy hand
eye

https://blog.csdn.net/yunlinwang/article/details/51622143
<https://blog.csdn.net/yunlinwang/article/details/51622143>

2017.08.29Kinova_pose_all_10_1.txt
0.475732,0.0143899,0.597381,-0.186261,-0.437222,2.36416
0.351412,0.268087,0.458479,0.0520873,-0.0950319,2.38993
0.251188,0.143736,0.426332,-0.216293,0.057463,-0.931251
0.243135,0.151277,0.464429,0.00644091,-0.039015,0.248319
0.288528,0.144912,0.409375,-0.456906,0.134654,-2.23237
0.240534,0.0828331,0.455197,-0.269758,-0.404214,-0.228711
0.358995,0.19536,0.504774,0.226276,0.237398,1.94334
0.188926,0.0555841,0.4517,0.441706,-0.250536,-0.0724471
0.19245,0.143225,0.489355,0.462128,-0.135995,-0.105669
0.379911,0.047085,0.543727,0.361346,-0.141438,3.0347
2017.08.29Pattern_pose_all_10_1.txt
0.147349 , -0.064831 , 0.509528 , 0.197843 , -0.500065 , 1.792583 -0.106272 ,
0.070595 , 0.633095 , 0.078063 , -0.128841 , 1.874043 0.144437 , -0.11512 ,
0.602498 , 2.77556 , 2.96201 , 2.070114 -0.042621 , -0.091343 , 0.598773 ,
2.95559 , -3.102323 , 0.890111 0.192328 , 0.027207 , 0.552456 , 0.097234 ,
0.637267 , 0.328188 0.074878 , -0.10344 , 0.539767 , 2.598053 , 2.800433 ,
1.189678 -0.100101 , 0.030685 , 0.526716 , 0.098909 , 0.176179 , 2.323831
0.11135 , -0.055337 , 0.534584 , -2.986191 , 2.769534 , 1.274791 0.018719 ,
-0.063078 , 0.525738 , -2.923126 , 2.874801 , 1.287745 0.193075 , 0.044841 ,
0.52557 , -0.13286 , -0.198836 , 1.280157
Jaco_handeye_rewrite_10.m
%% Eye to Hand calibration with Ensenso N20 and Kinova robotics arm. % input :
Pattern pose to camera and arm cartesian pose in base coordiante. % output: The
left eye of Ensenso N20 to the arm base coordiante. % % Robot Pose(Homogeneous)
stored in cell A. -------------------10 pose % clear; close all; clc;
JacoCartesianPose = importdata('D:\\jaco\\2017.08.29Kinova_pose_all_10_1.txt');
[m,n] = size(JacoCartesianPose); % 10* 6 A = cell(1,m); % 1*10 for i = 1: 1: m
A{1,i} = transl(JacoCartesianPose(i,1), JacoCartesianPose(i,2),
JacoCartesianPose(i,3)) * trotx(JacoCartesianPose(i,4)) *
troty(JacoCartesianPose(i,5))* trotz(JacoCartesianPose(i,6)); end % Pattern
Pose(Homogeneous) stored in cell B. patternInCamPose =
importdata('D:\\jaco\\2017.08.29Pattern_pose_all_10_1.txt'); [melem,nelem] =
size(patternInCamPose); % 10*6 B=cell(1,melem); for x=1:1:melem B{1,x} =
transl(patternInCamPose(x,1), patternInCamPose(x,2), patternInCamPose(x,3)) *
trotx(patternInCamPose(x,4)) * troty(patternInCamPose(x,5))*
trotz(patternInCamPose(x,6)); end % %机器人位姿获取记得以五角星的形式获取，参照Tsai的论文 n2=m;
TA=cell(1,n2); TB=cell(1,n2); %--------------------- 10
----------------------------------- % for j=[1,6]% Only begin. % %
TA{1,j}=A{1,j+1}*inv(A{1,j}); % TA{1,j+1}=A{1,j+2}*inv(A{1,j+1}); %
TA{1,j+2}=A{1,j+3}*inv(A{1,j+2}); % TA{1,j+3}=A{1,j+4}*inv(A{1,j+3}); %
TA{1,j+4}=A{1,j}*inv(A{1,j+4}); % % TB{1,j}=B{1,j+1}*inv(B{1,j}); %
TB{1,j+1}=B{1,j+2}*inv(B{1,j+1}); % TB{1,j+2}=B{1,j+3}*inv(B{1,j+2}); %
TB{1,j+3}=B{1,j+4}*inv(B{1,j+3}); % TB{1,j+4}=B{1,j}*inv(B{1,j+4}); % % end % %
M1=[TA{1,1} TA{1,2} TA{1,3} TA{1,4} TA{1,5} TA{1,6} TA{1,7} TA{1,8} TA{1,9}...
% TA{1,10} ]; % M2=[TB{1,1} TB{1,2} TB{1,3} TB{1,4} TB{1,5} TB{1,6} TB{1,7}
TB{1,8} TB{1,9}... % TB{1,10} ]; % M1=[TA{1,1} TA{1,2} TA{1,3} TA{1,4} TA{1,5}
TA{1,6} TA{1,7} TA{1,8} TA{1,9} ]; % M2=[TB{1,1} TB{1,2} TB{1,3} TB{1,4}
TB{1,5} TB{1,6} TB{1,7} TB{1,8} TB{1,9} ]; %--------------------- 10
----------------------------------- C_Tsai=tsai(M1,M2); T_Tsai =
C_Tsai_rad(1,3)); fprintf('Tsai(deg) = \n%f, %f, %f, %f, %f,
%f\n\n',T_Tsai(1,1), T_Tsai(1,2), T_Tsai(1,3), C_Tsai_rpy_rx_ry_rz(1,1),
C_Tsai_rpy_rx_ry_rz(1,2), C_Tsai_rpy_rx_ry_rz(1,3)); C_Shiu=shiu(M1,M2);
T_Shiu= [C_Shiu(1,4) C_Shiu(2,4) C_Shiu(3,4)] ; C_Shiu_rad = tr2rpy(C_Shiu);
%f, %f, %f\n',T_Shiu(1,1), T_Shiu(1,2), T_Shiu(1,3), C_Shiu_rad(1,1),
%f\n\n',T_Shiu(1,1), T_Shiu(1,2), T_Shiu(1,3), C_Shiu_rpy_rx_ry_rz(1,1),
C_Shiu_rpy_rx_ry_rz(1,2), C_Shiu_rpy_rx_ry_rz(1,3)); C_Ijrr=ijrr1995(M1,M2);
T_ijrr= [C_Ijrr(1,4) C_Ijrr(2,4) C_Ijrr(3,4)] ; C_ijrr_rad = tr2rpy(C_Ijrr);
%f, %f, %f\n',C_Ijrr(1,1), C_Ijrr(1,2), C_Ijrr(1,3), C_ijrr_rad(1,1),
%f\n\n',C_Ijrr(1,1), C_Ijrr(1,2), C_Ijrr(1,3), C_ijrr_rpy_rx_ry_rz(1,1),
C_ijrr_rpy_rx_ry_rz(1,2), C_ijrr_rpy_rx_ry_rz(1,3));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % robotHcam =[ -0.076, -0.674,
0.760631455868699, 178.7221124879378, -0.0735038591212, -11.5304192925905 ]; %
robotHcam1 = transl(robotHcam(1,1), robotHcam(1,2), robotHcam(1,3)) *
trotx(robotHcam(1,4),'deg') * troty(robotHcam(1,5), 'deg')*
trotz(robotHcam(1,6), 'deg')* trotx(90,'deg'); % rotx 90 robotHcam =[ 0.013,
-0.94, 0.86, -90.0, 0.0, 0.0 ]; % robotHcam =[ 0.25, 0.22, 1.1, 180.0, 0.0,
90.0 ]; % bind to the stack robotHcam1 = transl(robotHcam(1,1), robotHcam(1,2),
robotHcam(1,3)) * trotx(robotHcam(1,4),'deg') * troty(robotHcam(1,5), 'deg')*
trotz(robotHcam(1,6), 'deg'); fprintf('robotHcam used in Program(rad) = \n%f,
%f, %f, %f, %f, %f\n',robotHcam(1,1), robotHcam(1,2), robotHcam(1,3),
fprintf('robotHcam used in Program(deg) = \n%f, %f, %f, %f, %f,
%f\n\n',robotHcam(1,1), robotHcam(1,2), robotHcam(1,3), robotHcam(1,4),
robotHcam(1,5), robotHcam(1,6)); t1 = eye(4);
trplot(t1,'frame','R','arrow','width', '1', 'color', 'r', 'text_opts',
{'FontSize', 10, 'FontWeight', 'light'},'view', [-0.3 0.5
0.6],'thick',0.9,'dispar',0.8 );% Display Robot coordinate hold on;
trplot(robotHcam1,'frame','C', 'color', 'black'); % Display Camera coordinate
used in Program trplot(C_Tsai,'frame','T', 'color', 'b'); % Display Tsai
trplot(C_Shiu,'frame','S', 'color', 'g'); % Display Shiu clc; clear; close all;
% D:\jaco\ConsoleApplication1/get_saveCartesian.cpp——Kinova_pose.txt robotAeef
= [-0.0860801, -0.641813, -0.0987199, 3.13316, 0.000389122, -0.297456];
robotBeef = transl(robotAeef(1,1), robotAeef(1,2), robotAeef(1,3)) *
trotx(robotAeef(1,4)) * troty(robotAeef(1,5))* trotz(robotAeef(1,6)); %
D:\jaco\C#\nxCsExamples.sln —— Pattern_pose_all.txt camAobj = [0.011651 ,
-0.069043 , 0.857845 , -3.12825 , 3.137609 , 3.048224]; camBobj
=transl(camAobj(1,1), camAobj(1,2), camAobj(1,3)) * trotx(camAobj(1,4)) *
troty(camAobj(1,5))* trotz(camAobj(1,6)); robotAcam = robotBeef * inv(camBobj);
robotAcam_Trans0 = (transl(robotAcam))'; fprintf('robotAcam_T = \n%f, %f,
%f\n',robotAcam_Trans0(1,1), robotAcam_Trans0(1,2), robotAcam_Trans0(1,3));
%f\n\n',R_degree0(1,1), R_degree0(1,2), R_degree0(1,3)); % [theta, v] =
tr2angvec(robotAcam) % robotAcam = [ % robotAcam(1, 1) robotAcam(1, 2)
robotAcam(1, 3) -0.097; % robotAcam(2, 1) robotAcam(2, 2) robotAcam(2, 3)
-0.695; % robotAcam(3, 1) robotAcam(3,2) robotAcam(3, 3) robotAcam(3, 4); % 0 0
0 1; % ] % Trans1 = (transl(robotAcam))' % R_rad1 = tr2rpy((robotAcam)) %
point===============\n'); % camAobj2= [ 0.011634 , -0.068815 , 0.858039 ,
-3.124779 , 3.139759 , 3.046957]; % Workspace home. camAobj2= [ -0.102468 ,
-0.059197 , 0.858 , -3.127464 , 3.136249 , 3.053341 ]; camBobj2 =
transl(camAobj2(1,1), camAobj2(1,2), camAobj2(1,3)) * trotx(camAobj2(1,4)) *
troty(camAobj2(1,5))* trotz(camAobj2(1,6)); robotAobj2 = robotAcam * camBobj2;
robotAobj2_T = (transl(robotAobj2))'; fprintf('robotAobj2_T = \n%f, %f,
%f\n',robotAobj2_T(1,1), robotAobj2_T(1,2), robotAobj2_T(1,3));
\n%f, %f, %f\n',robotAobj2_R_degree(1,1), robotAobj2_R_degree(1,2),
robotAobj2_R_degree(1,3));
====================平面九点标定法====================

//Solve equation:AX=b #include <cv.h> #include<opencv2/opencv.hpp> using
namespace std; using namespace cv; int main(int argc, char** argv) {
printf("\nSolve equation:AX=b\n\n"); //Mat A = (Mat_<float>(6, 3) << //480.8,
639.4, 1, //227.1, 317.5, 1, //292.4, 781.6, 1, //597.4, 1044.1, 1, //557.7,
491.6, 1, //717.8, 263.7, 1 // );// 4x3 //Mat B = (Mat_<float>(6, 3) <<
//197170, 185349, 1, //195830, 186789, 1, //196174, 184591, 1, //197787,
183176, 1, //197575, 186133, 1, //198466, 187335, 1 // ); Mat A =
(Mat_<float>(4, 3) << 2926.36, 2607.79, 1, 587.093, 2616.89, 1, 537.031,
250.311, 1, 1160.53, 1265.21, 1);// 4x3 Mat B = (Mat_<float>(4, 3) << 320.389,
208.197, 1, 247.77, 209.726, 1, 242.809, 283.182, 1, 263.152, 253.715, 1); Mat
X; cout << "A=" << endl << A << endl; cout << "B=" << endl << B << endl;
solve(A, B, X, CV_SVD); cout << "X=" << endl << X << endl; Mat a1 =
(Mat_<float>(1, 3) << 1864, 1273, 1); Mat b1 = a1*X; cout << "b1=" << endl <<
b1 << endl; cout << "真实值为：" << "283.265, 253.049, 1" << endl; getchar(); return
0; }

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