機器人手眼標定(eye to hand和eye in hand)

發布時間：2018-09-27 18:10,

瀏覽次數：3200

, 標簽：

eye

to

hand

in

一、背景

機器人視覺應用中，手眼標定是一個非常基礎且關鍵的問題。簡單來說手眼標定的目的就是獲取機器人坐標系和相機坐標系的關系，最后將視覺識別的結果轉移到機器人坐標系下。

手眼標定行業內分為兩種形式，根據相機固定的地方不同，如果相機和機器人末端固定在一起，就稱之為“眼在手”(eye in

hand)，如果相機固定在機器人外面的底座上，則稱之為“眼在外”(eye to hand)。

eye to hand

眼在外eye in hand

??????眼在手

二、手眼關系的數學描述

1. eye in hand，這種關系下，兩次運動，機器人底座和標定板的關系始終不變。求解的量為相機和機器人末端坐標系的位姿關系。

2. eye to hand，這種關系下，兩次運動，機器人末端和標定板的位姿關系始終不變。求解的量為相機和機器人底座坐標系之間的位姿關系。

三、AX = XB問題的求解

* 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.

相關網上的英文教程?http://math.loyola.edu/~mili/Calibration/index.html

其中也有一些AX=

XB的matlab代碼可以使用。

ROS 下也有相關的一些package可以利用

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

http://wiki.ros.org/handeye

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

四、其他參考資料

https://blog.csdn.net/u011089570/article/details/47945733

?圖不錯

https://blog.csdn.net/qq_16481211/article/details/79764730

?部分halocon代碼

https://blog.csdn.net/qq_16481211/article/details/79767100

?halocon代碼

https://blog.csdn.net/happyjume/article/details/80847822

?部分原理

https://blog.csdn.net/zhang970187013/article/details/81098175

?UR5 與easy hand

eye

一般用“兩步法”求解基本方程，即先從基本方程上式求解出旋轉部分，再代入求解出平移部分。

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 % %機器人位姿獲取記得以五角星的形式獲取，參照Tsai的論文 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 =

(transl(C_Tsai))'; C_Tsai_rad = tr2rpy(C_Tsai); C_Tsai_rpy_rx_ry_rz

=rad2deg(C_Tsai_rad); fprintf('Tsai(rad) = \n%f, %f, %f, %f, %f,

%f\n',T_Tsai(1,1), T_Tsai(1,2), T_Tsai(1,3), C_Tsai_rad(1,1), C_Tsai_rad(1,2),

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);

C_Shiu_rpy_rx_ry_rz = rad2deg(C_Shiu_rad); fprintf('Shiu(rad) = \n%f, %f, %f,

%f, %f, %f\n',T_Shiu(1,1), T_Shiu(1,2), T_Shiu(1,3), C_Shiu_rad(1,1),

C_Shiu_rad(1,2), C_Shiu_rad(1,3)); fprintf('Shiu(deg) = \n%f, %f, %f, %f, %f,

%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);

C_ijrr_rpy_rx_ry_rz = rad2deg(C_ijrr_rad); fprintf('Ijrr(rad) = \n%f, %f, %f,

%f, %f, %f\n',C_Ijrr(1,1), C_Ijrr(1,2), C_Ijrr(1,3), C_ijrr_rad(1,1),

C_ijrr_rad(1,2), C_ijrr_rad(1,3)); fprintf('Ijrr(deg) = \n%f, %f, %f, %f, %f,

%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),

deg2rad(robotHcam(1,4)), deg2rad(robotHcam(1,5)), deg2rad(robotHcam(1,6)));

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));

robotAcam_R_rad = tr2rpy((robotAcam)); fprintf('robotAcam_R(rad) = \n%f, %f,

%f\n',robotAcam_R_rad(1,1), robotAcam_R_rad(1,2), robotAcam_R_rad(1,3));

R_degree0 = rad2deg(robotAcam_R_rad); fprintf('robotAcam_R(deg) = \n%f, %f,

%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)) %

R_degree1 = rad2deg(R_rad1) fprintf('===============Test

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));

robotAobj2_R_rad = tr2rpy((robotAobj2)); fprintf('robotAobj2_R(rad) = \n%f, %f,

%f\n',robotAobj2_R_rad(1,1), robotAobj2_R_rad(1,2), robotAobj2_R_rad(1,3));

robotAobj2_R_degree = rad2deg(robotAobj2_R_rad); fprintf('robotAobj2_R(deg) =

\n%f, %f, %f\n',robotAobj2_R_degree(1,1), robotAobj2_R_degree(1,2),

robotAobj2_R_degree(1,3));

====================平面九點標定法====================

相機坐標和機器人坐標寫成齊次的形式，九個未知量，九組對應點，奇異值分解。

//Solve equation:AX=b #include #include using

namespace std; using namespace cv; int main(int argc, char** argv) {

printf("\nSolve equation:AX=b\n\n"); //Mat A = (Mat_(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_(6, 3) <<

//197170, 185349, 1, //195830, 186789, 1, //196174, 184591, 1, //197787,

183176, 1, //197575, 186133, 1, //198466, 187335, 1 // ); Mat A =

(Mat_(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_(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_(1, 3) << 1864, 1273, 1); Mat b1 = a1*X; cout << "b1=" << endl <<

b1 << endl; cout << "真實值為：" << "283.265, 253.049, 1" << endl; getchar(); return

0; }

https://docs.opencv.org/3.1.0/d2/de8/group__core__array.html#ga12b43690dbd31fed96f213eefead2373

結果對比：左halcon C#，右opencv c++，底下為Matlab結果，三者一致，算法檢測通過。

總結

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