平移标定的数学公式
安装方式1
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安装方式2
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平移九点标定
usingSystem;usingSystem.Collections.Generic;usingMathNet.Numerics.LinearAlgebra;namespace平移标定的数学公式{publicclassCoordinateCalibration{// 存储标定点对privateList<(PointF image,PointF robot)>calibrationPoints=newList<(PointF,PointF)>();// 仿射变换参数 [a, b, c; d, e, f]privateMatrix<double>transformMatrix;publicstructPointF{publicfloatX;publicfloatY;publicPointF(floatx,floaty){X=x;Y=y;}}// 添加标定点publicvoidAddCalibrationPoint(PointFimagePoint,PointFrobotPoint){calibrationPoints.Add((imagePoint,robotPoint));}// 执行标定计算publicboolCalculateCalibration(){if(calibrationPoints.Count<3){Console.WriteLine("至少需要3个标定点");returnfalse;}// 构建矩阵方程 A * params = B// 参数矩阵 params = [a, b, c, d, e, f]^Tintn=calibrationPoints.Count;Matrix<double>A=Matrix<double>.Build.Dense(2*n,6);Matrix<double>B=Matrix<double>.Build.Dense(2*n,1);for(inti=0;i<n;i++){var(image,robot)=calibrationPoints[i];// 填充A矩阵 - X坐标相关行A[2*i,0]=image.X;// xA[2*i,1]=image.Y;// yA[2*i,2]=1;// 1A[2*i,3]=0;A[2*i,4]=0;A[2*i,5]=0;// 填充A矩阵 - Y坐标相关行A[2*i+1,0]=0;A[2*i+1,1]=0;A[2*i+1,2]=0;A[2*i+1,3]=image.X;// xA[2*i+1,4]=image.Y;// yA[2*i+1,5]=1;// 1// 填充B矩阵B[2*i,0]=robot.X;B[2*i+1,0]=robot.Y;}// 使用最小二乘法求解try{// A * params = B => params = (A^T * A)^-1 * A^T * BvarAtA=A.Transpose()*A;varAtA_inv=AtA.Inverse();varAtB=A.Transpose()*B;varparamsVector=AtA_inv*AtB;// 转换为2x3变换矩阵transformMatrix=Matrix<double>.Build.Dense(2,3);transformMatrix[0,0]=paramsVector[0,0];// atransformMatrix[0,1]=paramsVector[1,0];// btransformMatrix[0,2]=paramsVector[2,0];// ctransformMatrix[1,0]=paramsVector[3,0];// dtransformMatrix[1,1]=paramsVector[4,0];// etransformMatrix[1,2]=paramsVector[5,0];// freturntrue;}catch(Exceptionex){Console.WriteLine($"标定计算失败:{ex.Message}");returnfalse;}}// 图像坐标转机械手坐标publicPointFImageToRobot(PointFimagePoint){if(transformMatrix==null){thrownewInvalidOperationException("尚未执行标定计算");}// 构建输入向量 [x, y, 1]Vector<double>input=Vector<double>.Build.Dense(new[]{imagePoint.X,imagePoint.Y,1.0});// 计算输出 [X, Y]Vector<double>output=transformMatrix*input;returnnewPointF((float)output[0],(float)output[1]);}// 机械手坐标转图像坐标（逆变换）publicPointFRobotToImage(PointFrobotPoint){if(transformMatrix==null){thrownewInvalidOperationException("尚未执行标定计算");}// 仿射变换的逆变换需要计算矩阵的逆Matrix<double>invTransform=Matrix<double>.Build.Dense(3,3);invTransform[0,0]=transformMatrix[0,0];invTransform[0,1]=transformMatrix[0,1];invTransform[0,2]=transformMatrix[0,2];invTransform[1,0]=transformMatrix[1,0];invTransform[1,1]=transformMatrix[1,1];invTransform[1,2]=transformMatrix[1,2];invTransform[2,0]=0;invTransform[2,1]=0;invTransform[2,2]=1;try{varinv=invTransform.Inverse();Vector<double>input=Vector<double>.Build.Dense(new[]{robotPoint.X,robotPoint.Y,1.0});Vector<double>output=inv*input;returnnewPointF((float)output[0],(float)output[1]);}catch{Console.WriteLine("逆变换计算失败，可能矩阵不可逆");returnnewPointF(0,0);}}}}
二 使用
usingSystem;usingSystem.Collections.Generic;usingSystem.ComponentModel;usingSystem.Data;usingSystem.Drawing;usingSystem.Linq;usingSystem.Text;usingSystem.Threading.Tasks;usingSystem.Windows.Forms;namespace平移标定的数学公式{publicpartialclassForm1:Form{publicForm1(){InitializeComponent();}privatevoidbutton1_Click(objectsender,EventArgse){varcalibrator=newCoordinateCalibration();// 添加9个标定点（示例数据，实际应用中需要真实测量）// 格式：(图像坐标X, 图像坐标Y), (机械手坐标X, 机械手坐标Y)calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(1588.7726f,596.46368f),newCoordinateCalibration.PointF(140,10));calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(2092.5125f,601.88007f),newCoordinateCalibration.PointF(140,-10));calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(2599.6616f,608.51514f),newCoordinateCalibration.PointF(140,-30));calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(1586.8936f,1092.2368f),newCoordinateCalibration.PointF(160,10));calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(2088.5759f,1099.787f),newCoordinateCalibration.PointF(160,-10));calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(2588.5093f,1111.1132f),newCoordinateCalibration.PointF(160,-30));calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(1573.5547f,1592.8459f),newCoordinateCalibration.PointF(180,10));calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(2082.4187f,1601.0065f),newCoordinateCalibration.PointF(180,-10));calibrator.AddCalibrationPoint(newCoordinateCalibration.PointF(2583.4763f,1615.3347f),newCoordinateCalibration.PointF(180,-30));// 执行标定计算if(calibrator.CalculateCalibration()){// 测试转换vartestImagePoint=newCoordinateCalibration.PointF(1200,1500);varrobotPoint=calibrator.ImageToRobot(testImagePoint);MessageBox.Show($"图像坐标({testImagePoint.X},{testImagePoint.Y}) -> 机械手坐标({robotPoint.X},{robotPoint.Y})");// 测试逆转换varbackToImage=calibrator.RobotToImage(robotPoint);MessageBox.Show($"机械手坐标({robotPoint.X},{robotPoint.Y}) -> 图像坐标({backToImage.X},{backToImage.Y})");}}}}
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