我正在开发一个机器人应用程序，其中我将一个摄像头固定在机器人抓手上。为了计算相机和夹具 Hcg 之间的矩阵变换，我使用 OpenCV 版本 4.1.0 中提供的 calibrateHandEye 新函数
我用安装在夹具上的相机拍摄了 10 张棋盘照片，同时记录了机器人的位置。
我正在编写的代码：
// My_handeye.cpp : This file contains the 'main' function. Program execution begins and ends there.
//
#include <iostream>
#include <sstream>
#include <string>
#include <ctime>
#include <cstdio>
#include "pch.h"
#include <opencv2/opencv.hpp>
#include <opencv2/core.hpp>
#include <opencv2/core/utility.hpp>
#include <opencv2/imgproc.hpp>
#include <opencv2/calib3d.hpp>
#include <opencv2/imgcodecs.hpp>
#include <opencv2/videoio.hpp>
#include <opencv2/highgui.hpp>
using namespace cv;
using namespace std;
Mat eulerAnglesToRotationMatrix(Vec3f &theta);
Vec3f rotationMatrixToEulerAngles(Mat &R);
float rad2deg(float radian);
float deg2rad(float degree);
int main()
{
// Camera calibration information
std::vector<double> distortionCoefficients(5); // camera distortion
distortionCoefficients[0] = 2.4472856611074989e-01;
distortionCoefficients[1] = -8.1042032574246325e-01;
distortionCoefficients[2] = 0;
distortionCoefficients[3] = 0;
distortionCoefficients[4] = 7.8769462320821060e-01;
double f_x = 1.3624172121852105e+03; // Focal length in x axis
double f_y = 1.3624172121852105e+03; // Focal length in y axis (usually the same?)
double c_x = 960; // Camera primary point x
double c_y = 540; // Camera primary point y
cv::Mat cameraMatrix(3, 3, CV_32FC1);
cameraMatrix.at<float>(0, 0) = f_x;
cameraMatrix.at<float>(0, 1) = 0.0;
cameraMatrix.at<float>(0, 2) = c_x;
cameraMatrix.at<float>(1, 0) = 0.0;
cameraMatrix.at<float>(1, 1) = f_y;
cameraMatrix.at<float>(1, 2) = c_y;
cameraMatrix.at<float>(2, 0) = 0.0;
cameraMatrix.at<float>(2, 1) = 0.0;
cameraMatrix.at<float>(2, 2) = 1.0;
Mat rvec(3, 1, CV_32F), tvec(3, 1, CV_32F);
//
std::vector<Mat> R_gripper2base;
std::vector<Mat> t_gripper2base;
std::vector<Mat> R_target2cam;
std::vector<Mat> t_target2cam;
Mat R_cam2gripper = (Mat_<float>(3, 3));
Mat t_cam2gripper = (Mat_<float>(3, 1));
vector<String> fn;
glob("images/*.bmp", fn, false);
vector<Mat> images;
size_t num_images = fn.size(); //number of bmp files in images folder
Size patternsize(6, 8); //number of centers
vector<Point2f> centers; //this will be filled by the detected centers
float cell_size = 30;
vector<Point3f> obj_points;
R_gripper2base.reserve(num_images);
t_gripper2base.reserve(num_images);
R_target2cam.reserve(num_images);
t_target2cam.reserve(num_images);
for (int i = 0; i < patternsize.height; ++i)
for (int j = 0; j < patternsize.width; ++j)
obj_points.push_back(Point3f(float(j*cell_size),
float(i*cell_size), 0.f));
for (size_t i = 0; i < num_images; i++)
images.push_back(imread(fn[i]));
Mat frame;
for (size_t i = 0; i < num_images; i++)
{
frame = imread(fn[i]); //source image
bool patternfound = findChessboardCorners(frame, patternsize, centers);
if (patternfound)
{
drawChessboardCorners(frame, patternsize, Mat(centers), patternfound);
//imshow("window", frame);
//int key = cv::waitKey(0) & 0xff;
solvePnP(Mat(obj_points), Mat(centers), cameraMatrix, distortionCoefficients, rvec, tvec);
Mat R;
Rodrigues(rvec, R); // R is 3x3
R_target2cam.push_back(R);
t_target2cam.push_back(tvec);
Mat T = Mat::eye(4, 4, R.type()); // T is 4x4
T(Range(0, 3), Range(0, 3)) = R * 1; // copies R into T
T(Range(0, 3), Range(3, 4)) = tvec * 1; // copies tvec into T
cout << "T = " << endl << " " << T << endl << endl;
}
cout << patternfound << endl;
}
Vec3f theta_01{ deg2rad(-153.61), deg2rad(8.3), deg2rad(-91.91) };
Vec3f theta_02{ deg2rad(-166.71), deg2rad(3.04), deg2rad(-93.31) };
Vec3f theta_03{ deg2rad(-170.04), deg2rad(24.92), deg2rad(-88.29) };
Vec3f theta_04{ deg2rad(-165.71), deg2rad(24.68), deg2rad(-84.85) };
Vec3f theta_05{ deg2rad(-160.18), deg2rad(-15.94),deg2rad(-56.24) };
Vec3f theta_06{ deg2rad(175.68), deg2rad(10.95), deg2rad(180) };
Vec3f theta_07{ deg2rad(175.73), deg2rad(45.78), deg2rad(-179.92) };
Vec3f theta_08{ deg2rad(-165.34), deg2rad(47.37), deg2rad(-166.25) };
Vec3f theta_09{ deg2rad(-165.62), deg2rad(17.95), deg2rad(-166.17) };
Vec3f theta_10{ deg2rad(-151.99), deg2rad(-14.59),deg2rad(-94.19) };
Mat robot_rot_01 = eulerAnglesToRotationMatrix(theta_01);
Mat robot_rot_02 = eulerAnglesToRotationMatrix(theta_02);
Mat robot_rot_03 = eulerAnglesToRotationMatrix(theta_03);
Mat robot_rot_04 = eulerAnglesToRotationMatrix(theta_04);
Mat robot_rot_05 = eulerAnglesToRotationMatrix(theta_05);
Mat robot_rot_06 = eulerAnglesToRotationMatrix(theta_06);
Mat robot_rot_07 = eulerAnglesToRotationMatrix(theta_07);
Mat robot_rot_08 = eulerAnglesToRotationMatrix(theta_08);
Mat robot_rot_09 = eulerAnglesToRotationMatrix(theta_09);
Mat robot_rot_10 = eulerAnglesToRotationMatrix(theta_10);
const Mat robot_tr_01 = (Mat_<float>(3, 1) << 781.2, 338.59, 903.48);
const Mat robot_tr_02 = (Mat_<float>(3, 1) << 867.65, 382.52, 884.42);
const Mat robot_tr_03 = (Mat_<float>(3, 1) << 856.91, 172.99, 964.61);
const Mat robot_tr_04 = (Mat_<float>(3, 1) << 748.81, 146.75, 1043.29);
const Mat robot_tr_05 = (Mat_<float>(3, 1) << 627.66, 554.08, 920.85);
const Mat robot_tr_06 = (Mat_<float>(3, 1) << 715.06, 195.96, 889.38);
const Mat robot_tr_07 = (Mat_<float>(3, 1) << 790.9, 196.29, 1117.38);
const Mat robot_tr_08 = (Mat_<float>(3, 1) << 743.5, 283.93, 1131.92);
const Mat robot_tr_09 = (Mat_<float>(3, 1) << 748.9, 288.19, 910.58);
const Mat robot_tr_10 = (Mat_<float>(3, 1) << 813.18, 400.44, 917.16);
R_gripper2base.push_back(robot_rot_01);
R_gripper2base.push_back(robot_rot_02);
R_gripper2base.push_back(robot_rot_03);
R_gripper2base.push_back(robot_rot_04);
R_gripper2base.push_back(robot_rot_05);
R_gripper2base.push_back(robot_rot_06);
R_gripper2base.push_back(robot_rot_07);
R_gripper2base.push_back(robot_rot_08);
R_gripper2base.push_back(robot_rot_09);
R_gripper2base.push_back(robot_rot_10);
t_gripper2base.push_back(robot_tr_01);
t_gripper2base.push_back(robot_tr_02);
t_gripper2base.push_back(robot_tr_03);
t_gripper2base.push_back(robot_tr_04);
t_gripper2base.push_back(robot_tr_05);
t_gripper2base.push_back(robot_tr_06);
t_gripper2base.push_back(robot_tr_07);
t_gripper2base.push_back(robot_tr_08);
t_gripper2base.push_back(robot_tr_09);
t_gripper2base.push_back(robot_tr_10);
calibrateHandEye(R_gripper2base, t_gripper2base, R_target2cam, t_target2cam, R_cam2gripper, t_cam2gripper, CALIB_HAND_EYE_TSAI);
Vec3f R_cam2gripper_r = rotationMatrixToEulerAngles(R_cam2gripper);
cout << "R_cam2gripper = " << endl << " " << R_cam2gripper << endl << endl;
cout << "R_cam2gripper_r = " << endl << " " << R_cam2gripper_r << endl << endl;
cout << "t_cam2gripper = " << endl << " " << t_cam2gripper << endl << endl;
}
Mat eulerAnglesToRotationMatrix(Vec3f &theta)
{
// Calculate rotation about x axis
Mat R_x = (Mat_<double>(3, 3) <<
1, 0, 0,
0, cos(theta[0]), -sin(theta[0]),
0, sin(theta[0]), cos(theta[0])
);
// Calculate rotation about y axis
Mat R_y = (Mat_<double>(3, 3) <<
cos(theta[1]), 0, sin(theta[1]),
0, 1, 0,
-sin(theta[1]), 0, cos(theta[1])
);
// Calculate rotation about z axis
Mat R_z = (Mat_<double>(3, 3) <<
cos(theta[2]), -sin(theta[2]), 0,
sin(theta[2]), cos(theta[2]), 0,
0, 0, 1);
// Combined rotation matrix
Mat R = R_z * R_y * R_x;
return R;
}
float rad2deg(float radian) {
double pi = 3.14159;
return(radian * (180 / pi));
}
float deg2rad(float degree) {
double pi = 3.14159;
return(degree * (pi / 180));
}
// Checks if a matrix is a valid rotation matrix.
bool isRotationMatrix(Mat &R)
{
Mat Rt;
transpose(R, Rt);
Mat shouldBeIdentity = Rt * R;
Mat I = Mat::eye(3, 3, shouldBeIdentity.type());
return norm(I, shouldBeIdentity) < 1e-6;
}
// Calculates rotation matrix to euler angles
// The result is the same as MATLAB except the order
// of the euler angles ( x and z are swapped ).
Vec3f rotationMatrixToEulerAngles(Mat &R)
{
assert(isRotationMatrix(R));
float sy = sqrt(R.at<double>(0, 0) * R.at<double>(0, 0) + R.at<double>(1, 0) * R.at<double>(1, 0));
bool singular = sy < 1e-6; // If
float x, y, z;
if (!singular)
{
x = atan2(R.at<double>(2, 1), R.at<double>(2, 2));
y = atan2(-R.at<double>(2, 0), sy);
z = atan2(R.at<double>(1, 0), R.at<double>(0, 0));
}
else
{
x = atan2(-R.at<double>(1, 2), R.at<double>(1, 1));
y = atan2(-R.at<double>(2, 0), sy);
z = 0;
}
return Vec3f(x, y, z);
}
该函数给我的结果是下一个：
R_cam2gripper =
[0.3099803593003124, -0.8923086952824562, -0.3281727733547833;
0.7129271761196039, 0.4465219155360299, -0.5406967916458927;
0.6290047840821058, -0.0663579028402444, 0.7745641421680119]
R_cam2gripper_r =
[-0.0854626, -0.680272, 1.16065]
t_cam2gripper =
[-35.02063730299775;
-74.80633768251272;
-307.6725851251873]
我得到了其他软件提供的“良好”结果。有了它们，机器人就到达了我在相机中指向的确切点（我有一个 3D 相机，我可以从相机世界中获取 x、y、z），所以它们当然是正确的，但我遇到了麻烦使用 OpenCV 函数重复相同的结果。
很抱歉对我的问题进行了冗长的介绍。是否理解为什么解决方案不是应有的样子？我的猜测是，我在理解角度或转换角度时遇到问题，但我找不到任何方法来解决这个问题。任何提示都将受到欢迎！
我实际上设法解决了这个问题。总体想法是正确的，但是：
无论如何，谢谢你的帮助。我坚持要在算法中获得更高的精度，但这是另一个问题。