mirror of https://github.com/opencv/opencv.git
Merge pull request #13880 from catree:add_hand_eye_calibration
Alexander Alekhin
6 years ago
commit
d2f70f61aa
5 changed files with 1358 additions and 1 deletions
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// This file is part of OpenCV project.
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// It is subject to the license terms in the LICENSE file found in the top-level directory
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// of this distribution and at http://opencv.org/license.html.
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#include "precomp.hpp" |
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#include "opencv2/calib3d.hpp" |
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namespace cv { |
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static Mat homogeneousInverse(const Mat& T) |
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{ |
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CV_Assert(T.rows == 4 && T.cols == 4); |
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Mat R = T(Rect(0, 0, 3, 3)); |
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Mat t = T(Rect(3, 0, 1, 3)); |
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Mat Rt = R.t(); |
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Mat tinv = -Rt * t; |
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Mat Tinv = Mat::eye(4, 4, T.type()); |
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Rt.copyTo(Tinv(Rect(0, 0, 3, 3))); |
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tinv.copyTo(Tinv(Rect(3, 0, 1, 3))); |
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return Tinv; |
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} |
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// q = rot2quatMinimal(R)
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//
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// R - 3x3 rotation matrix, or 4x4 homogeneous matrix
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// q - 3x1 unit quaternion <qx, qy, qz>
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// q = sin(theta/2) * v
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// theta - rotation angle
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// v - unit rotation axis, |v| = 1
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static Mat rot2quatMinimal(const Mat& R) |
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{ |
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CV_Assert(R.type() == CV_64FC1 && R.rows >= 3 && R.cols >= 3); |
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double m00 = R.at<double>(0,0), m01 = R.at<double>(0,1), m02 = R.at<double>(0,2); |
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double m10 = R.at<double>(1,0), m11 = R.at<double>(1,1), m12 = R.at<double>(1,2); |
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double m20 = R.at<double>(2,0), m21 = R.at<double>(2,1), m22 = R.at<double>(2,2); |
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double trace = m00 + m11 + m22; |
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double qx, qy, qz; |
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if (trace > 0) { |
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double S = sqrt(trace + 1.0) * 2; // S=4*qw
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qx = (m21 - m12) / S; |
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qy = (m02 - m20) / S; |
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qz = (m10 - m01) / S; |
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} else if ((m00 > m11)&(m00 > m22)) { |
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double S = sqrt(1.0 + m00 - m11 - m22) * 2; // S=4*qx
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qx = 0.25 * S; |
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qy = (m01 + m10) / S; |
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qz = (m02 + m20) / S; |
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} else if (m11 > m22) { |
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double S = sqrt(1.0 + m11 - m00 - m22) * 2; // S=4*qy
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qx = (m01 + m10) / S; |
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qy = 0.25 * S; |
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qz = (m12 + m21) / S; |
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} else { |
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double S = sqrt(1.0 + m22 - m00 - m11) * 2; // S=4*qz
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qx = (m02 + m20) / S; |
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qy = (m12 + m21) / S; |
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qz = 0.25 * S; |
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} |
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return (Mat_<double>(3,1) << qx, qy, qz); |
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} |
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static Mat skew(const Mat& v) |
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{ |
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CV_Assert(v.type() == CV_64FC1 && v.rows == 3 && v.cols == 1); |
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double vx = v.at<double>(0,0); |
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double vy = v.at<double>(1,0); |
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double vz = v.at<double>(2,0); |
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return (Mat_<double>(3,3) << 0, -vz, vy, |
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vz, 0, -vx, |
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-vy, vx, 0); |
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} |
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// R = quatMinimal2rot(q)
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//
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// q - 3x1 unit quaternion <qx, qy, qz>
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// R - 3x3 rotation matrix
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// q = sin(theta/2) * v
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// theta - rotation angle
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// v - unit rotation axis, |v| = 1
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static Mat quatMinimal2rot(const Mat& q) |
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{ |
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CV_Assert(q.type() == CV_64FC1 && q.rows == 3 && q.cols == 1); |
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Mat p = q.t()*q; |
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double w = sqrt(1 - p.at<double>(0,0)); |
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Mat diag_p = Mat::eye(3,3,CV_64FC1)*p.at<double>(0,0); |
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return 2*q*q.t() + 2*w*skew(q) + Mat::eye(3,3,CV_64FC1) - 2*diag_p; |
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} |
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// q = rot2quat(R)
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//
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// q - 4x1 unit quaternion <qw, qx, qy, qz>
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// R - 3x3 rotation matrix
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static Mat rot2quat(const Mat& R) |
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{ |
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CV_Assert(R.type() == CV_64FC1 && R.rows >= 3 && R.cols >= 3); |
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double m00 = R.at<double>(0,0), m01 = R.at<double>(0,1), m02 = R.at<double>(0,2); |
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double m10 = R.at<double>(1,0), m11 = R.at<double>(1,1), m12 = R.at<double>(1,2); |
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double m20 = R.at<double>(2,0), m21 = R.at<double>(2,1), m22 = R.at<double>(2,2); |
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double trace = m00 + m11 + m22; |
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double qw, qx, qy, qz; |
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if (trace > 0) { |
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double S = sqrt(trace + 1.0) * 2; // S=4*qw
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qw = 0.25 * S; |
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qx = (m21 - m12) / S; |
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qy = (m02 - m20) / S; |
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qz = (m10 - m01) / S; |
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} else if ((m00 > m11)&(m00 > m22)) { |
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double S = sqrt(1.0 + m00 - m11 - m22) * 2; // S=4*qx
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qw = (m21 - m12) / S; |
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qx = 0.25 * S; |
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qy = (m01 + m10) / S; |
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qz = (m02 + m20) / S; |
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} else if (m11 > m22) { |
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double S = sqrt(1.0 + m11 - m00 - m22) * 2; // S=4*qy
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qw = (m02 - m20) / S; |
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qx = (m01 + m10) / S; |
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qy = 0.25 * S; |
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qz = (m12 + m21) / S; |
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} else { |
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double S = sqrt(1.0 + m22 - m00 - m11) * 2; // S=4*qz
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qw = (m10 - m01) / S; |
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qx = (m02 + m20) / S; |
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qy = (m12 + m21) / S; |
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qz = 0.25 * S; |
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} |
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return (Mat_<double>(4,1) << qw, qx, qy, qz); |
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} |
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// R = quat2rot(q)
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//
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// q - 4x1 unit quaternion <qw, qx, qy, qz>
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// R - 3x3 rotation matrix
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static Mat quat2rot(const Mat& q) |
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{ |
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CV_Assert(q.type() == CV_64FC1 && q.rows == 4 && q.cols == 1); |
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double qw = q.at<double>(0,0); |
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double qx = q.at<double>(1,0); |
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double qy = q.at<double>(2,0); |
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double qz = q.at<double>(3,0); |
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Mat R(3, 3, CV_64FC1); |
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R.at<double>(0, 0) = 1 - 2*qy*qy - 2*qz*qz; |
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R.at<double>(0, 1) = 2*qx*qy - 2*qz*qw; |
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R.at<double>(0, 2) = 2*qx*qz + 2*qy*qw; |
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R.at<double>(1, 0) = 2*qx*qy + 2*qz*qw; |
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R.at<double>(1, 1) = 1 - 2*qx*qx - 2*qz*qz; |
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R.at<double>(1, 2) = 2*qy*qz - 2*qx*qw; |
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R.at<double>(2, 0) = 2*qx*qz - 2*qy*qw; |
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R.at<double>(2, 1) = 2*qy*qz + 2*qx*qw; |
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R.at<double>(2, 2) = 1 - 2*qx*qx - 2*qy*qy; |
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return R; |
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} |
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// Kronecker product or tensor product
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// https://stackoverflow.com/a/36552682
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static Mat kron(const Mat& A, const Mat& B) |
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{ |
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CV_Assert(A.channels() == 1 && B.channels() == 1); |
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Mat1d Ad, Bd; |
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A.convertTo(Ad, CV_64F); |
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B.convertTo(Bd, CV_64F); |
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Mat1d Kd(Ad.rows * Bd.rows, Ad.cols * Bd.cols, 0.0); |
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for (int ra = 0; ra < Ad.rows; ra++) |
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{ |
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for (int ca = 0; ca < Ad.cols; ca++) |
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{ |
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Kd(Range(ra*Bd.rows, (ra + 1)*Bd.rows), Range(ca*Bd.cols, (ca + 1)*Bd.cols)) = Bd.mul(Ad(ra, ca)); |
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} |
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} |
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Mat K; |
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Kd.convertTo(K, A.type()); |
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return K; |
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} |
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// quaternion multiplication
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static Mat qmult(const Mat& s, const Mat& t) |
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{ |
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CV_Assert(s.type() == CV_64FC1 && t.type() == CV_64FC1); |
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CV_Assert(s.rows == 4 && s.cols == 1); |
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CV_Assert(t.rows == 4 && t.cols == 1); |
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double s0 = s.at<double>(0,0); |
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double s1 = s.at<double>(1,0); |
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double s2 = s.at<double>(2,0); |
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double s3 = s.at<double>(3,0); |
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double t0 = t.at<double>(0,0); |
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double t1 = t.at<double>(1,0); |
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double t2 = t.at<double>(2,0); |
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double t3 = t.at<double>(3,0); |
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Mat q(4, 1, CV_64FC1); |
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q.at<double>(0,0) = s0*t0 - s1*t1 - s2*t2 - s3*t3; |
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q.at<double>(1,0) = s0*t1 + s1*t0 + s2*t3 - s3*t2; |
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q.at<double>(2,0) = s0*t2 - s1*t3 + s2*t0 + s3*t1; |
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q.at<double>(3,0) = s0*t3 + s1*t2 - s2*t1 + s3*t0; |
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return q; |
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} |
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// dq = homogeneous2dualQuaternion(H)
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//
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// H - 4x4 homogeneous transformation: [R | t; 0 0 0 | 1]
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// dq - 8x1 dual quaternion: <q (rotation part), qprime (translation part)>
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static Mat homogeneous2dualQuaternion(const Mat& H) |
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{ |
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CV_Assert(H.type() == CV_64FC1 && H.rows == 4 && H.cols == 4); |
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Mat dualq(8, 1, CV_64FC1); |
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Mat R = H(Rect(0, 0, 3, 3)); |
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Mat t = H(Rect(3, 0, 1, 3)); |
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Mat q = rot2quat(R); |
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Mat qt = Mat::zeros(4, 1, CV_64FC1); |
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t.copyTo(qt(Rect(0, 1, 1, 3))); |
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Mat qprime = 0.5 * qmult(qt, q); |
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q.copyTo(dualq(Rect(0, 0, 1, 4))); |
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qprime.copyTo(dualq(Rect(0, 4, 1, 4))); |
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return dualq; |
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} |
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// H = dualQuaternion2homogeneous(dq)
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//
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// H - 4x4 homogeneous transformation: [R | t; 0 0 0 | 1]
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// dq - 8x1 dual quaternion: <q (rotation part), qprime (translation part)>
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static Mat dualQuaternion2homogeneous(const Mat& dualq) |
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{ |
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CV_Assert(dualq.type() == CV_64FC1 && dualq.rows == 8 && dualq.cols == 1); |
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Mat q = dualq(Rect(0, 0, 1, 4)); |
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Mat qprime = dualq(Rect(0, 4, 1, 4)); |
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Mat R = quat2rot(q); |
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q.at<double>(1,0) = -q.at<double>(1,0); |
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q.at<double>(2,0) = -q.at<double>(2,0); |
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q.at<double>(3,0) = -q.at<double>(3,0); |
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Mat qt = 2*qmult(qprime, q); |
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Mat t = qt(Rect(0, 1, 1, 3)); |
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Mat H = Mat::eye(4, 4, CV_64FC1); |
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R.copyTo(H(Rect(0, 0, 3, 3))); |
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t.copyTo(H(Rect(3, 0, 1, 3))); |
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return H; |
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} |
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//Reference:
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//R. Y. Tsai and R. K. Lenz, "A new technique for fully autonomous and efficient 3D robotics hand/eye calibration."
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//In IEEE Transactions on Robotics and Automation, vol. 5, no. 3, pp. 345-358, June 1989.
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//C++ code converted from Zoran Lazarevic's Matlab code:
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//http://lazax.com/www.cs.columbia.edu/~laza/html/Stewart/matlab/handEye.m
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static void calibrateHandEyeTsai(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc, |
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Mat& R_cam2gripper, Mat& t_cam2gripper) |
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{ |
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//Number of unique camera position pairs
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int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0); |
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//Will store: skew(Pgij+Pcij)
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Mat A(3*K, 3, CV_64FC1); |
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//Will store: Pcij - Pgij
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Mat B(3*K, 1, CV_64FC1); |
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std::vector<Mat> vec_Hgij, vec_Hcij; |
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vec_Hgij.reserve(static_cast<size_t>(K)); |
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vec_Hcij.reserve(static_cast<size_t>(K)); |
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int idx = 0; |
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for (size_t i = 0; i < Hg.size(); i++) |
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{ |
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for (size_t j = i+1; j < Hg.size(); j++, idx++) |
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{ |
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//Defines coordinate transformation from Gi to Gj
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//Hgi is from Gi (gripper) to RW (robot base)
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//Hgj is from Gj (gripper) to RW (robot base)
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Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i]; //eq 6
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vec_Hgij.push_back(Hgij); |
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//Rotation axis for Rgij which is the 3D rotation from gripper coordinate frame Gi to Gj
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Mat Pgij = 2*rot2quatMinimal(Hgij); |
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//Defines coordinate transformation from Ci to Cj
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//Hci is from CW (calibration target) to Ci (camera)
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//Hcj is from CW (calibration target) to Cj (camera)
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Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]); //eq 7
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vec_Hcij.push_back(Hcij); |
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//Rotation axis for Rcij
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Mat Pcij = 2*rot2quatMinimal(Hcij); |
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//Left-hand side: skew(Pgij+Pcij)
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skew(Pgij+Pcij).copyTo(A(Rect(0, idx*3, 3, 3))); |
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//Right-hand side: Pcij - Pgij
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Mat diff = Pcij - Pgij; |
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diff.copyTo(B(Rect(0, idx*3, 1, 3))); |
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} |
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} |
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Mat Pcg_; |
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//Rotation from camera to gripper is obtained from the set of equations:
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// skew(Pgij+Pcij) * Pcg_ = Pcij - Pgij (eq 12)
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solve(A, B, Pcg_, DECOMP_SVD); |
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Mat Pcg_norm = Pcg_.t() * Pcg_; |
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//Obtained non-unit quaternion is scaled back to unit value that
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//designates camera-gripper rotation
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Mat Pcg = 2 * Pcg_ / sqrt(1 + Pcg_norm.at<double>(0,0)); //eq 14
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Mat Rcg = quatMinimal2rot(Pcg/2.0); |
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idx = 0; |
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for (size_t i = 0; i < Hg.size(); i++) |
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{ |
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for (size_t j = i+1; j < Hg.size(); j++, idx++) |
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{ |
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//Defines coordinate transformation from Gi to Gj
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//Hgi is from Gi (gripper) to RW (robot base)
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//Hgj is from Gj (gripper) to RW (robot base)
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Mat Hgij = vec_Hgij[static_cast<size_t>(idx)]; |
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//Defines coordinate transformation from Ci to Cj
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//Hci is from CW (calibration target) to Ci (camera)
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//Hcj is from CW (calibration target) to Cj (camera)
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Mat Hcij = vec_Hcij[static_cast<size_t>(idx)]; |
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//Left-hand side: (Rgij - I)
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Mat diff = Hgij(Rect(0,0,3,3)) - Mat::eye(3,3,CV_64FC1); |
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diff.copyTo(A(Rect(0, idx*3, 3, 3))); |
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//Right-hand side: Rcg*Tcij - Tgij
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diff = Rcg*Hcij(Rect(3, 0, 1, 3)) - Hgij(Rect(3, 0, 1, 3)); |
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diff.copyTo(B(Rect(0, idx*3, 1, 3))); |
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} |
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} |
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Mat Tcg; |
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//Translation from camera to gripper is obtained from the set of equations:
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// (Rgij - I) * Tcg = Rcg*Tcij - Tgij (eq 15)
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solve(A, B, Tcg, DECOMP_SVD); |
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R_cam2gripper = Rcg; |
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t_cam2gripper = Tcg; |
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} |
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//Reference:
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//F. Park, B. Martin, "Robot Sensor Calibration: Solving AX = XB on the Euclidean Group."
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//In IEEE Transactions on Robotics and Automation, 10(5): 717-721, 1994.
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//Matlab code: http://math.loyola.edu/~mili/Calibration/
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static void calibrateHandEyePark(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc, |
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Mat& R_cam2gripper, Mat& t_cam2gripper) |
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{ |
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Mat M = Mat::zeros(3, 3, CV_64FC1); |
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for (size_t i = 0; i < Hg.size(); i++) |
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{ |
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for (size_t j = i+1; j < Hg.size(); j++) |
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{ |
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Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i]; |
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Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]); |
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Mat Rgij = Hgij(Rect(0, 0, 3, 3)); |
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Mat Rcij = Hcij(Rect(0, 0, 3, 3)); |
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Mat a, b; |
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Rodrigues(Rgij, a); |
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Rodrigues(Rcij, b); |
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M += b * a.t(); |
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} |
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} |
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Mat eigenvalues, eigenvectors; |
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eigen(M.t()*M, eigenvalues, eigenvectors); |
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Mat v = Mat::zeros(3, 3, CV_64FC1); |
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for (int i = 0; i < 3; i++) { |
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v.at<double>(i,i) = 1.0 / sqrt(eigenvalues.at<double>(i,0)); |
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} |
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Mat R = eigenvectors.t() * v * eigenvectors * M.t(); |
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R_cam2gripper = R; |
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int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0); |
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Mat C(3*K, 3, CV_64FC1); |
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Mat d(3*K, 1, CV_64FC1); |
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Mat I3 = Mat::eye(3, 3, CV_64FC1); |
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int idx = 0; |
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for (size_t i = 0; i < Hg.size(); i++) |
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{ |
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for (size_t j = i+1; j < Hg.size(); j++, idx++) |
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{ |
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Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i]; |
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Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]); |
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Mat Rgij = Hgij(Rect(0, 0, 3, 3)); |
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Mat tgij = Hgij(Rect(3, 0, 1, 3)); |
||||
Mat tcij = Hcij(Rect(3, 0, 1, 3)); |
||||
|
||||
Mat I_tgij = I3 - Rgij; |
||||
I_tgij.copyTo(C(Rect(0, 3*idx, 3, 3))); |
||||
|
||||
Mat A_RB = tgij - R*tcij; |
||||
A_RB.copyTo(d(Rect(0, 3*idx, 1, 3))); |
||||
} |
||||
} |
||||
|
||||
Mat t; |
||||
solve(C, d, t, DECOMP_SVD); |
||||
t_cam2gripper = t; |
||||
} |
||||
|
||||
//Reference:
|
||||
//R. Horaud, F. Dornaika, "Hand-Eye Calibration"
|
||||
//In International Journal of Robotics Research, 14(3): 195-210, 1995.
|
||||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||||
static void calibrateHandEyeHoraud(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc, |
||||
Mat& R_cam2gripper, Mat& t_cam2gripper) |
||||
{ |
||||
Mat A = Mat::zeros(4, 4, CV_64FC1); |
||||
|
||||
for (size_t i = 0; i < Hg.size(); i++) |
||||
{ |
||||
for (size_t j = i+1; j < Hg.size(); j++) |
||||
{ |
||||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i]; |
||||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]); |
||||
|
||||
Mat Rgij = Hgij(Rect(0, 0, 3, 3)); |
||||
Mat Rcij = Hcij(Rect(0, 0, 3, 3)); |
||||
|
||||
Mat qgij = rot2quat(Rgij); |
||||
double r0 = qgij.at<double>(0,0); |
||||
double rx = qgij.at<double>(1,0); |
||||
double ry = qgij.at<double>(2,0); |
||||
double rz = qgij.at<double>(3,0); |
||||
|
||||
// Q(r) Appendix A
|
||||
Matx44d Qvi(r0, -rx, -ry, -rz, |
||||
rx, r0, -rz, ry, |
||||
ry, rz, r0, -rx, |
||||
rz, -ry, rx, r0); |
||||
|
||||
Mat qcij = rot2quat(Rcij); |
||||
r0 = qcij.at<double>(0,0); |
||||
rx = qcij.at<double>(1,0); |
||||
ry = qcij.at<double>(2,0); |
||||
rz = qcij.at<double>(3,0); |
||||
|
||||
// W(r) Appendix A
|
||||
Matx44d Wvi(r0, -rx, -ry, -rz, |
||||
rx, r0, rz, -ry, |
||||
ry, -rz, r0, rx, |
||||
rz, ry, -rx, r0); |
||||
|
||||
// Ai = (Q(vi') - W(vi))^T (Q(vi') - W(vi))
|
||||
A += (Qvi - Wvi).t() * (Qvi - Wvi); |
||||
} |
||||
} |
||||
|
||||
Mat eigenvalues, eigenvectors; |
||||
eigen(A, eigenvalues, eigenvectors); |
||||
|
||||
Mat R = quat2rot(eigenvectors.row(3).t()); |
||||
R_cam2gripper = R; |
||||
|
||||
int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0); |
||||
Mat C(3*K, 3, CV_64FC1); |
||||
Mat d(3*K, 1, CV_64FC1); |
||||
Mat I3 = Mat::eye(3, 3, CV_64FC1); |
||||
|
||||
int idx = 0; |
||||
for (size_t i = 0; i < Hg.size(); i++) |
||||
{ |
||||
for (size_t j = i+1; j < Hg.size(); j++, idx++) |
||||
{ |
||||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i]; |
||||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]); |
||||
|
||||
Mat Rgij = Hgij(Rect(0, 0, 3, 3)); |
||||
|
||||
Mat tgij = Hgij(Rect(3, 0, 1, 3)); |
||||
Mat tcij = Hcij(Rect(3, 0, 1, 3)); |
||||
|
||||
Mat I_tgij = I3 - Rgij; |
||||
I_tgij.copyTo(C(Rect(0, 3*idx, 3, 3))); |
||||
|
||||
Mat A_RB = tgij - R*tcij; |
||||
A_RB.copyTo(d(Rect(0, 3*idx, 1, 3))); |
||||
} |
||||
} |
||||
|
||||
Mat t; |
||||
solve(C, d, t, DECOMP_SVD); |
||||
t_cam2gripper = t; |
||||
} |
||||
|
||||
// sign function, return -1 if negative values, +1 otherwise
|
||||
static int sign_double(double val) |
||||
{ |
||||
return (0 < val) - (val < 0); |
||||
} |
||||
|
||||
//Reference:
|
||||
//N. Andreff, R. Horaud, B. Espiau, "On-line Hand-Eye Calibration."
|
||||
//In Second International Conference on 3-D Digital Imaging and Modeling (3DIM'99), pages 430-436, 1999.
|
||||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||||
static void calibrateHandEyeAndreff(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc, |
||||
Mat& R_cam2gripper, Mat& t_cam2gripper) |
||||
{ |
||||
int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0); |
||||
Mat A(12*K, 12, CV_64FC1); |
||||
Mat B(12*K, 1, CV_64FC1); |
||||
|
||||
Mat I9 = Mat::eye(9, 9, CV_64FC1); |
||||
Mat I3 = Mat::eye(3, 3, CV_64FC1); |
||||
Mat O9x3 = Mat::zeros(9, 3, CV_64FC1); |
||||
Mat O9x1 = Mat::zeros(9, 1, CV_64FC1); |
||||
|
||||
int idx = 0; |
||||
for (size_t i = 0; i < Hg.size(); i++) |
||||
{ |
||||
for (size_t j = i+1; j < Hg.size(); j++, idx++) |
||||
{ |
||||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i]; |
||||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]); |
||||
|
||||
Mat Rgij = Hgij(Rect(0, 0, 3, 3)); |
||||
Mat Rcij = Hcij(Rect(0, 0, 3, 3)); |
||||
|
||||
Mat tgij = Hgij(Rect(3, 0, 1, 3)); |
||||
Mat tcij = Hcij(Rect(3, 0, 1, 3)); |
||||
|
||||
//Eq 10
|
||||
Mat a00 = I9 - kron(Rgij, Rcij); |
||||
Mat a01 = O9x3; |
||||
Mat a10 = kron(I3, tcij.t()); |
||||
Mat a11 = I3 - Rgij; |
||||
|
||||
a00.copyTo(A(Rect(0, idx*12, 9, 9))); |
||||
a01.copyTo(A(Rect(9, idx*12, 3, 9))); |
||||
a10.copyTo(A(Rect(0, idx*12 + 9, 9, 3))); |
||||
a11.copyTo(A(Rect(9, idx*12 + 9, 3, 3))); |
||||
|
||||
O9x1.copyTo(B(Rect(0, idx*12, 1, 9))); |
||||
tgij.copyTo(B(Rect(0, idx*12 + 9, 1, 3))); |
||||
} |
||||
} |
||||
|
||||
Mat X; |
||||
solve(A, B, X, DECOMP_SVD); |
||||
|
||||
Mat R = X(Rect(0, 0, 1, 9)); |
||||
int newSize[] = {3, 3}; |
||||
R = R.reshape(1, 2, newSize); |
||||
//Eq 15
|
||||
double det = determinant(R); |
||||
R = pow(sign_double(det) / abs(det), 1.0/3.0) * R; |
||||
|
||||
Mat w, u, vt; |
||||
SVDecomp(R, w, u, vt); |
||||
R = u*vt; |
||||
|
||||
if (determinant(R) < 0) |
||||
{ |
||||
Mat diag = (Mat_<double>(3,3) << 1.0, 0.0, 0.0, |
||||
0.0, 1.0, 0.0, |
||||
0.0, 0.0, -1.0); |
||||
R = u*diag*vt; |
||||
} |
||||
|
||||
R_cam2gripper = R; |
||||
|
||||
Mat t = X(Rect(0, 9, 1, 3)); |
||||
t_cam2gripper = t; |
||||
} |
||||
|
||||
//Reference:
|
||||
//K. Daniilidis, "Hand-Eye Calibration Using Dual Quaternions."
|
||||
//In The International Journal of Robotics Research,18(3): 286-298, 1998.
|
||||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||||
static void calibrateHandEyeDaniilidis(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc, |
||||
Mat& R_cam2gripper, Mat& t_cam2gripper) |
||||
{ |
||||
int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0); |
||||
Mat T = Mat::zeros(6*K, 8, CV_64FC1); |
||||
|
||||
int idx = 0; |
||||
for (size_t i = 0; i < Hg.size(); i++) |
||||
{ |
||||
for (size_t j = i+1; j < Hg.size(); j++, idx++) |
||||
{ |
||||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i]; |
||||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]); |
||||
|
||||
Mat dualqa = homogeneous2dualQuaternion(Hgij); |
||||
Mat dualqb = homogeneous2dualQuaternion(Hcij); |
||||
|
||||
Mat a = dualqa(Rect(0, 1, 1, 3)); |
||||
Mat b = dualqb(Rect(0, 1, 1, 3)); |
||||
|
||||
Mat aprime = dualqa(Rect(0, 5, 1, 3)); |
||||
Mat bprime = dualqb(Rect(0, 5, 1, 3)); |
||||
|
||||
//Eq 31
|
||||
Mat s00 = a - b; |
||||
Mat s01 = skew(a + b); |
||||
Mat s10 = aprime - bprime; |
||||
Mat s11 = skew(aprime + bprime); |
||||
Mat s12 = a - b; |
||||
Mat s13 = skew(a + b); |
||||
|
||||
s00.copyTo(T(Rect(0, idx*6, 1, 3))); |
||||
s01.copyTo(T(Rect(1, idx*6, 3, 3))); |
||||
s10.copyTo(T(Rect(0, idx*6 + 3, 1, 3))); |
||||
s11.copyTo(T(Rect(1, idx*6 + 3, 3, 3))); |
||||
s12.copyTo(T(Rect(4, idx*6 + 3, 1, 3))); |
||||
s13.copyTo(T(Rect(5, idx*6 + 3, 3, 3))); |
||||
} |
||||
} |
||||
|
||||
Mat w, u, vt; |
||||
SVDecomp(T, w, u, vt); |
||||
Mat v = vt.t(); |
||||
|
||||
Mat u1 = v(Rect(6, 0, 1, 4)); |
||||
Mat v1 = v(Rect(6, 4, 1, 4)); |
||||
Mat u2 = v(Rect(7, 0, 1, 4)); |
||||
Mat v2 = v(Rect(7, 4, 1, 4)); |
||||
|
||||
//Solves Eq 34, Eq 35
|
||||
Mat ma = u1.t()*v1; |
||||
Mat mb = u1.t()*v2 + u2.t()*v1; |
||||
Mat mc = u2.t()*v2; |
||||
|
||||
double a = ma.at<double>(0,0); |
||||
double b = mb.at<double>(0,0); |
||||
double c = mc.at<double>(0,0); |
||||
|
||||
double s1 = (-b + sqrt(b*b - 4*a*c)) / (2*a); |
||||
double s2 = (-b - sqrt(b*b - 4*a*c)) / (2*a); |
||||
|
||||
Mat sol1 = s1*s1*u1.t()*u1 + 2*s1*u1.t()*u2 + u2.t()*u2; |
||||
Mat sol2 = s2*s2*u1.t()*u1 + 2*s2*u1.t()*u2 + u2.t()*u2; |
||||
double s, val; |
||||
if (sol1.at<double>(0,0) > sol2.at<double>(0,0)) |
||||
{ |
||||
s = s1; |
||||
val = sol1.at<double>(0,0); |
||||
} |
||||
else |
||||
{ |
||||
s = s2; |
||||
val = sol2.at<double>(0,0); |
||||
} |
||||
|
||||
double lambda2 = sqrt(1.0 / val); |
||||
double lambda1 = s * lambda2; |
||||
|
||||
Mat dualq = lambda1 * v(Rect(6, 0, 1, 8)) + lambda2*v(Rect(7, 0, 1, 8)); |
||||
Mat X = dualQuaternion2homogeneous(dualq); |
||||
|
||||
Mat R = X(Rect(0, 0, 3, 3)); |
||||
Mat t = X(Rect(3, 0, 1, 3)); |
||||
R_cam2gripper = R; |
||||
t_cam2gripper = t; |
||||
} |
||||
|
||||
void calibrateHandEye(InputArrayOfArrays R_gripper2base, InputArrayOfArrays t_gripper2base, |
||||
InputArrayOfArrays R_target2cam, InputArrayOfArrays t_target2cam, |
||||
OutputArray R_cam2gripper, OutputArray t_cam2gripper, |
||||
HandEyeCalibrationMethod method) |
||||
{ |
||||
CV_Assert(R_gripper2base.isMatVector() && t_gripper2base.isMatVector() && |
||||
R_target2cam.isMatVector() && t_target2cam.isMatVector()); |
||||
|
||||
std::vector<Mat> R_gripper2base_, t_gripper2base_; |
||||
R_gripper2base.getMatVector(R_gripper2base_); |
||||
t_gripper2base.getMatVector(t_gripper2base_); |
||||
|
||||
std::vector<Mat> R_target2cam_, t_target2cam_; |
||||
R_target2cam.getMatVector(R_target2cam_); |
||||
t_target2cam.getMatVector(t_target2cam_); |
||||
|
||||
CV_Assert(R_gripper2base_.size() == t_gripper2base_.size() && |
||||
R_target2cam_.size() == t_target2cam_.size() && |
||||
R_gripper2base_.size() == R_target2cam_.size()); |
||||
CV_Assert(R_gripper2base_.size() >= 3); |
||||
|
||||
//Notation used in Tsai paper
|
||||
//Defines coordinate transformation from G (gripper) to RW (robot base)
|
||||
std::vector<Mat> Hg; |
||||
Hg.reserve(R_gripper2base_.size()); |
||||
for (size_t i = 0; i < R_gripper2base_.size(); i++) |
||||
{ |
||||
Mat m = Mat::eye(4, 4, CV_64FC1); |
||||
Mat R = m(Rect(0, 0, 3, 3)); |
||||
R_gripper2base_[i].convertTo(R, CV_64F); |
||||
|
||||
Mat t = m(Rect(3, 0, 1, 3)); |
||||
t_gripper2base_[i].convertTo(t, CV_64F); |
||||
|
||||
Hg.push_back(m); |
||||
} |
||||
|
||||
//Defines coordinate transformation from CW (calibration target) to C (camera)
|
||||
std::vector<Mat> Hc; |
||||
Hc.reserve(R_target2cam_.size()); |
||||
for (size_t i = 0; i < R_target2cam_.size(); i++) |
||||
{ |
||||
Mat m = Mat::eye(4, 4, CV_64FC1); |
||||
Mat R = m(Rect(0, 0, 3, 3)); |
||||
R_target2cam_[i].convertTo(R, CV_64F); |
||||
|
||||
Mat t = m(Rect(3, 0, 1, 3)); |
||||
t_target2cam_[i].convertTo(t, CV_64F); |
||||
|
||||
Hc.push_back(m); |
||||
} |
||||
|
||||
Mat Rcg = Mat::eye(3, 3, CV_64FC1); |
||||
Mat Tcg = Mat::zeros(3, 1, CV_64FC1); |
||||
|
||||
switch (method) |
||||
{ |
||||
case CALIB_HAND_EYE_TSAI: |
||||
calibrateHandEyeTsai(Hg, Hc, Rcg, Tcg); |
||||
break; |
||||
|
||||
case CALIB_HAND_EYE_PARK: |
||||
calibrateHandEyePark(Hg, Hc, Rcg, Tcg); |
||||
break; |
||||
|
||||
case CALIB_HAND_EYE_HORAUD: |
||||
calibrateHandEyeHoraud(Hg, Hc, Rcg, Tcg); |
||||
break; |
||||
|
||||
case CALIB_HAND_EYE_ANDREFF: |
||||
calibrateHandEyeAndreff(Hg, Hc, Rcg, Tcg); |
||||
break; |
||||
|
||||
case CALIB_HAND_EYE_DANIILIDIS: |
||||
calibrateHandEyeDaniilidis(Hg, Hc, Rcg, Tcg); |
||||
break; |
||||
|
||||
default: |
||||
break; |
||||
} |
||||
|
||||
Rcg.copyTo(R_cam2gripper); |
||||
Tcg.copyTo(t_cam2gripper); |
||||
} |
||||
} |
||||
@ -0,0 +1,381 @@ |
||||
// This file is part of OpenCV project.
|
||||
// It is subject to the license terms in the LICENSE file found in the top-level directory
|
||||
// of this distribution and at http://opencv.org/license.html.
|
||||
|
||||
#include "test_precomp.hpp" |
||||
#include "opencv2/calib3d.hpp" |
||||
|
||||
namespace opencv_test { namespace { |
||||
|
||||
class CV_CalibrateHandEyeTest : public cvtest::BaseTest |
||||
{ |
||||
public: |
||||
CV_CalibrateHandEyeTest() { |
||||
eps_rvec[CALIB_HAND_EYE_TSAI] = 1.0e-8; |
||||
eps_rvec[CALIB_HAND_EYE_PARK] = 1.0e-8; |
||||
eps_rvec[CALIB_HAND_EYE_HORAUD] = 1.0e-8; |
||||
eps_rvec[CALIB_HAND_EYE_ANDREFF] = 1.0e-8; |
||||
eps_rvec[CALIB_HAND_EYE_DANIILIDIS] = 1.0e-8; |
||||
|
||||
eps_tvec[CALIB_HAND_EYE_TSAI] = 1.0e-8; |
||||
eps_tvec[CALIB_HAND_EYE_PARK] = 1.0e-8; |
||||
eps_tvec[CALIB_HAND_EYE_HORAUD] = 1.0e-8; |
||||
eps_tvec[CALIB_HAND_EYE_ANDREFF] = 1.0e-8; |
||||
eps_tvec[CALIB_HAND_EYE_DANIILIDIS] = 1.0e-8; |
||||
|
||||
eps_rvec_noise[CALIB_HAND_EYE_TSAI] = 2.0e-2; |
||||
eps_rvec_noise[CALIB_HAND_EYE_PARK] = 2.0e-2; |
||||
eps_rvec_noise[CALIB_HAND_EYE_HORAUD] = 2.0e-2; |
||||
eps_rvec_noise[CALIB_HAND_EYE_ANDREFF] = 1.0e-2; |
||||
eps_rvec_noise[CALIB_HAND_EYE_DANIILIDIS] = 1.0e-2; |
||||
|
||||
eps_tvec_noise[CALIB_HAND_EYE_TSAI] = 5.0e-2; |
||||
eps_tvec_noise[CALIB_HAND_EYE_PARK] = 5.0e-2; |
||||
eps_tvec_noise[CALIB_HAND_EYE_HORAUD] = 5.0e-2; |
||||
eps_tvec_noise[CALIB_HAND_EYE_ANDREFF] = 5.0e-2; |
||||
eps_tvec_noise[CALIB_HAND_EYE_DANIILIDIS] = 5.0e-2; |
||||
} |
||||
protected: |
||||
virtual void run(int); |
||||
void generatePose(RNG& rng, double min_theta, double max_theta, |
||||
double min_tx, double max_tx, |
||||
double min_ty, double max_ty, |
||||
double min_tz, double max_tz, |
||||
Mat& R, Mat& tvec, |
||||
bool randSign=false); |
||||
void simulateData(RNG& rng, int nPoses, |
||||
std::vector<Mat> &R_gripper2base, std::vector<Mat> &t_gripper2base, |
||||
std::vector<Mat> &R_target2cam, std::vector<Mat> &t_target2cam, |
||||
bool noise, Mat& R_cam2gripper, Mat& t_cam2gripper); |
||||
Mat homogeneousInverse(const Mat& T); |
||||
std::string getMethodName(HandEyeCalibrationMethod method); |
||||
double sign_double(double val); |
||||
|
||||
double eps_rvec[5]; |
||||
double eps_tvec[5]; |
||||
double eps_rvec_noise[5]; |
||||
double eps_tvec_noise[5]; |
||||
}; |
||||
|
||||
void CV_CalibrateHandEyeTest::run(int) |
||||
{ |
||||
ts->set_failed_test_info(cvtest::TS::OK); |
||||
|
||||
RNG& rng = ts->get_rng(); |
||||
|
||||
std::vector<std::vector<double> > vec_rvec_diff(5); |
||||
std::vector<std::vector<double> > vec_tvec_diff(5); |
||||
std::vector<std::vector<double> > vec_rvec_diff_noise(5); |
||||
std::vector<std::vector<double> > vec_tvec_diff_noise(5); |
||||
|
||||
std::vector<HandEyeCalibrationMethod> methods; |
||||
methods.push_back(CALIB_HAND_EYE_TSAI); |
||||
methods.push_back(CALIB_HAND_EYE_PARK); |
||||
methods.push_back(CALIB_HAND_EYE_HORAUD); |
||||
methods.push_back(CALIB_HAND_EYE_ANDREFF); |
||||
methods.push_back(CALIB_HAND_EYE_DANIILIDIS); |
||||
|
||||
const int nTests = 100; |
||||
for (int i = 0; i < nTests; i++) |
||||
{ |
||||
const int nPoses = 10; |
||||
{ |
||||
//No noise
|
||||
std::vector<Mat> R_gripper2base, t_gripper2base; |
||||
std::vector<Mat> R_target2cam, t_target2cam; |
||||
Mat R_cam2gripper_true, t_cam2gripper_true; |
||||
|
||||
const bool noise = false; |
||||
simulateData(rng, nPoses, R_gripper2base, t_gripper2base, R_target2cam, t_target2cam, noise, R_cam2gripper_true, t_cam2gripper_true); |
||||
|
||||
for (size_t idx = 0; idx < methods.size(); idx++) |
||||
{ |
||||
Mat rvec_cam2gripper_true; |
||||
cv::Rodrigues(R_cam2gripper_true, rvec_cam2gripper_true); |
||||
|
||||
Mat R_cam2gripper_est, t_cam2gripper_est; |
||||
calibrateHandEye(R_gripper2base, t_gripper2base, R_target2cam, t_target2cam, R_cam2gripper_est, t_cam2gripper_est, methods[idx]); |
||||
|
||||
Mat rvec_cam2gripper_est; |
||||
cv::Rodrigues(R_cam2gripper_est, rvec_cam2gripper_est); |
||||
|
||||
double rvecDiff = cvtest::norm(rvec_cam2gripper_true, rvec_cam2gripper_est, NORM_L2); |
||||
double tvecDiff = cvtest::norm(t_cam2gripper_true, t_cam2gripper_est, NORM_L2); |
||||
|
||||
vec_rvec_diff[idx].push_back(rvecDiff); |
||||
vec_tvec_diff[idx].push_back(tvecDiff); |
||||
|
||||
const double epsilon_rvec = eps_rvec[idx]; |
||||
const double epsilon_tvec = eps_tvec[idx]; |
||||
|
||||
//Maybe a better accuracy test would be to compare the mean and std errors with some thresholds?
|
||||
if (rvecDiff > epsilon_rvec || tvecDiff > epsilon_tvec) |
||||
{ |
||||
ts->printf(cvtest::TS::LOG, "Invalid accuracy (no noise) for method: %s, rvecDiff: %f, epsilon_rvec: %f, tvecDiff: %f, epsilon_tvec: %f\n", |
||||
getMethodName(methods[idx]).c_str(), rvecDiff, epsilon_rvec, tvecDiff, epsilon_tvec); |
||||
ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); |
||||
} |
||||
} |
||||
} |
||||
|
||||
{ |
||||
//Gaussian noise on transformations between calibration target frame and camera frame and between gripper and robot base frames
|
||||
std::vector<Mat> R_gripper2base, t_gripper2base; |
||||
std::vector<Mat> R_target2cam, t_target2cam; |
||||
Mat R_cam2gripper_true, t_cam2gripper_true; |
||||
|
||||
const bool noise = true; |
||||
simulateData(rng, nPoses, R_gripper2base, t_gripper2base, R_target2cam, t_target2cam, noise, R_cam2gripper_true, t_cam2gripper_true); |
||||
|
||||
for (size_t idx = 0; idx < methods.size(); idx++) |
||||
{ |
||||
Mat rvec_cam2gripper_true; |
||||
cv::Rodrigues(R_cam2gripper_true, rvec_cam2gripper_true); |
||||
|
||||
Mat R_cam2gripper_est, t_cam2gripper_est; |
||||
calibrateHandEye(R_gripper2base, t_gripper2base, R_target2cam, t_target2cam, R_cam2gripper_est, t_cam2gripper_est, methods[idx]); |
||||
|
||||
Mat rvec_cam2gripper_est; |
||||
cv::Rodrigues(R_cam2gripper_est, rvec_cam2gripper_est); |
||||
|
||||
double rvecDiff = cvtest::norm(rvec_cam2gripper_true, rvec_cam2gripper_est, NORM_L2); |
||||
double tvecDiff = cvtest::norm(t_cam2gripper_true, t_cam2gripper_est, NORM_L2); |
||||
|
||||
vec_rvec_diff_noise[idx].push_back(rvecDiff); |
||||
vec_tvec_diff_noise[idx].push_back(tvecDiff); |
||||
|
||||
const double epsilon_rvec = eps_rvec_noise[idx]; |
||||
const double epsilon_tvec = eps_tvec_noise[idx]; |
||||
|
||||
//Maybe a better accuracy test would be to compare the mean and std errors with some thresholds?
|
||||
if (rvecDiff > epsilon_rvec || tvecDiff > epsilon_tvec) |
||||
{ |
||||
ts->printf(cvtest::TS::LOG, "Invalid accuracy (noise) for method: %s, rvecDiff: %f, epsilon_rvec: %f, tvecDiff: %f, epsilon_tvec: %f\n", |
||||
getMethodName(methods[idx]).c_str(), rvecDiff, epsilon_rvec, tvecDiff, epsilon_tvec); |
||||
ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); |
||||
} |
||||
} |
||||
} |
||||
} |
||||
|
||||
for (size_t idx = 0; idx < methods.size(); idx++) |
||||
{ |
||||
{ |
||||
double max_rvec_diff = *std::max_element(vec_rvec_diff[idx].begin(), vec_rvec_diff[idx].end()); |
||||
double mean_rvec_diff = std::accumulate(vec_rvec_diff[idx].begin(), |
||||
vec_rvec_diff[idx].end(), 0.0) / vec_rvec_diff[idx].size(); |
||||
double sq_sum_rvec_diff = std::inner_product(vec_rvec_diff[idx].begin(), vec_rvec_diff[idx].end(), |
||||
vec_rvec_diff[idx].begin(), 0.0); |
||||
double std_rvec_diff = std::sqrt(sq_sum_rvec_diff / vec_rvec_diff[idx].size() - mean_rvec_diff * mean_rvec_diff); |
||||
|
||||
double max_tvec_diff = *std::max_element(vec_tvec_diff[idx].begin(), vec_tvec_diff[idx].end()); |
||||
double mean_tvec_diff = std::accumulate(vec_tvec_diff[idx].begin(), |
||||
vec_tvec_diff[idx].end(), 0.0) / vec_tvec_diff[idx].size(); |
||||
double sq_sum_tvec_diff = std::inner_product(vec_tvec_diff[idx].begin(), vec_tvec_diff[idx].end(), |
||||
vec_tvec_diff[idx].begin(), 0.0); |
||||
double std_tvec_diff = std::sqrt(sq_sum_tvec_diff / vec_tvec_diff[idx].size() - mean_tvec_diff * mean_tvec_diff); |
||||
|
||||
std::cout << "\nMethod " << getMethodName(methods[idx]) << ":\n" |
||||
<< "Max rvec error: " << max_rvec_diff << ", Mean rvec error: " << mean_rvec_diff |
||||
<< ", Std rvec error: " << std_rvec_diff << "\n" |
||||
<< "Max tvec error: " << max_tvec_diff << ", Mean tvec error: " << mean_tvec_diff |
||||
<< ", Std tvec error: " << std_tvec_diff << std::endl; |
||||
} |
||||
{ |
||||
double max_rvec_diff = *std::max_element(vec_rvec_diff_noise[idx].begin(), vec_rvec_diff_noise[idx].end()); |
||||
double mean_rvec_diff = std::accumulate(vec_rvec_diff_noise[idx].begin(), |
||||
vec_rvec_diff_noise[idx].end(), 0.0) / vec_rvec_diff_noise[idx].size(); |
||||
double sq_sum_rvec_diff = std::inner_product(vec_rvec_diff_noise[idx].begin(), vec_rvec_diff_noise[idx].end(), |
||||
vec_rvec_diff_noise[idx].begin(), 0.0); |
||||
double std_rvec_diff = std::sqrt(sq_sum_rvec_diff / vec_rvec_diff_noise[idx].size() - mean_rvec_diff * mean_rvec_diff); |
||||
|
||||
double max_tvec_diff = *std::max_element(vec_tvec_diff_noise[idx].begin(), vec_tvec_diff_noise[idx].end()); |
||||
double mean_tvec_diff = std::accumulate(vec_tvec_diff_noise[idx].begin(), |
||||
vec_tvec_diff_noise[idx].end(), 0.0) / vec_tvec_diff_noise[idx].size(); |
||||
double sq_sum_tvec_diff = std::inner_product(vec_tvec_diff_noise[idx].begin(), vec_tvec_diff_noise[idx].end(), |
||||
vec_tvec_diff_noise[idx].begin(), 0.0); |
||||
double std_tvec_diff = std::sqrt(sq_sum_tvec_diff / vec_tvec_diff_noise[idx].size() - mean_tvec_diff * mean_tvec_diff); |
||||
|
||||
std::cout << "Method (noise) " << getMethodName(methods[idx]) << ":\n" |
||||
<< "Max rvec error: " << max_rvec_diff << ", Mean rvec error: " << mean_rvec_diff |
||||
<< ", Std rvec error: " << std_rvec_diff << "\n" |
||||
<< "Max tvec error: " << max_tvec_diff << ", Mean tvec error: " << mean_tvec_diff |
||||
<< ", Std tvec error: " << std_tvec_diff << std::endl; |
||||
} |
||||
} |
||||
} |
||||
|
||||
void CV_CalibrateHandEyeTest::generatePose(RNG& rng, double min_theta, double max_theta, |
||||
double min_tx, double max_tx, |
||||
double min_ty, double max_ty, |
||||
double min_tz, double max_tz, |
||||
Mat& R, Mat& tvec, |
||||
bool random_sign) |
||||
{ |
||||
Mat axis(3, 1, CV_64FC1); |
||||
for (int i = 0; i < 3; i++) |
||||
{ |
||||
axis.at<double>(i,0) = rng.uniform(-1.0, 1.0); |
||||
} |
||||
double theta = rng.uniform(min_theta, max_theta); |
||||
if (random_sign) |
||||
{ |
||||
theta *= sign_double(rng.uniform(-1.0, 1.0)); |
||||
} |
||||
|
||||
Mat rvec(3, 1, CV_64FC1); |
||||
rvec.at<double>(0,0) = theta*axis.at<double>(0,0); |
||||
rvec.at<double>(1,0) = theta*axis.at<double>(1,0); |
||||
rvec.at<double>(2,0) = theta*axis.at<double>(2,0); |
||||
|
||||
tvec.create(3, 1, CV_64FC1); |
||||
tvec.at<double>(0,0) = rng.uniform(min_tx, max_tx); |
||||
tvec.at<double>(1,0) = rng.uniform(min_ty, max_ty); |
||||
tvec.at<double>(2,0) = rng.uniform(min_tz, max_tz); |
||||
|
||||
if (random_sign) |
||||
{ |
||||
tvec.at<double>(0,0) *= sign_double(rng.uniform(-1.0, 1.0)); |
||||
tvec.at<double>(1,0) *= sign_double(rng.uniform(-1.0, 1.0)); |
||||
tvec.at<double>(2,0) *= sign_double(rng.uniform(-1.0, 1.0)); |
||||
} |
||||
|
||||
cv::Rodrigues(rvec, R); |
||||
} |
||||
|
||||
void CV_CalibrateHandEyeTest::simulateData(RNG& rng, int nPoses, |
||||
std::vector<Mat> &R_gripper2base, std::vector<Mat> &t_gripper2base, |
||||
std::vector<Mat> &R_target2cam, std::vector<Mat> &t_target2cam, |
||||
bool noise, Mat& R_cam2gripper, Mat& t_cam2gripper) |
||||
{ |
||||
//to avoid generating values close to zero,
|
||||
//we use positive range values and randomize the sign
|
||||
const bool random_sign = true; |
||||
generatePose(rng, 10.0*CV_PI/180.0, 50.0*CV_PI/180.0, |
||||
0.05, 0.5, 0.05, 0.5, 0.05, 0.5, |
||||
R_cam2gripper, t_cam2gripper, random_sign); |
||||
|
||||
Mat R_target2base, t_target2base; |
||||
generatePose(rng, 5.0*CV_PI/180.0, 85.0*CV_PI/180.0, |
||||
0.5, 3.5, 0.5, 3.5, 0.5, 3.5, |
||||
R_target2base, t_target2base, random_sign); |
||||
|
||||
for (int i = 0; i < nPoses; i++) |
||||
{ |
||||
Mat R_gripper2base_, t_gripper2base_; |
||||
generatePose(rng, 5.0*CV_PI/180.0, 45.0*CV_PI/180.0, |
||||
0.5, 1.5, 0.5, 1.5, 0.5, 1.5, |
||||
R_gripper2base_, t_gripper2base_, random_sign); |
||||
|
||||
R_gripper2base.push_back(R_gripper2base_); |
||||
t_gripper2base.push_back(t_gripper2base_); |
||||
|
||||
Mat T_cam2gripper = Mat::eye(4, 4, CV_64FC1); |
||||
R_cam2gripper.copyTo(T_cam2gripper(Rect(0, 0, 3, 3))); |
||||
t_cam2gripper.copyTo(T_cam2gripper(Rect(3, 0, 1, 3))); |
||||
|
||||
Mat T_gripper2base = Mat::eye(4, 4, CV_64FC1); |
||||
R_gripper2base_.copyTo(T_gripper2base(Rect(0, 0, 3, 3))); |
||||
t_gripper2base_.copyTo(T_gripper2base(Rect(3, 0, 1, 3))); |
||||
|
||||
Mat T_base2cam = homogeneousInverse(T_cam2gripper) * homogeneousInverse(T_gripper2base); |
||||
Mat T_target2base = Mat::eye(4, 4, CV_64FC1); |
||||
R_target2base.copyTo(T_target2base(Rect(0, 0, 3, 3))); |
||||
t_target2base.copyTo(T_target2base(Rect(3, 0, 1, 3))); |
||||
Mat T_target2cam = T_base2cam * T_target2base; |
||||
|
||||
if (noise) |
||||
{ |
||||
//Add some noise for the transformation between the target and the camera
|
||||
Mat R_target2cam_noise = T_target2cam(Rect(0, 0, 3, 3)); |
||||
Mat rvec_target2cam_noise; |
||||
cv::Rodrigues(R_target2cam_noise, rvec_target2cam_noise); |
||||
rvec_target2cam_noise.at<double>(0,0) += rng.gaussian(0.002); |
||||
rvec_target2cam_noise.at<double>(1,0) += rng.gaussian(0.002); |
||||
rvec_target2cam_noise.at<double>(2,0) += rng.gaussian(0.002); |
||||
|
||||
cv::Rodrigues(rvec_target2cam_noise, R_target2cam_noise); |
||||
|
||||
Mat t_target2cam_noise = T_target2cam(Rect(3, 0, 1, 3)); |
||||
t_target2cam_noise.at<double>(0,0) += rng.gaussian(0.005); |
||||
t_target2cam_noise.at<double>(1,0) += rng.gaussian(0.005); |
||||
t_target2cam_noise.at<double>(2,0) += rng.gaussian(0.005); |
||||
|
||||
//Add some noise for the transformation between the gripper and the robot base
|
||||
Mat R_gripper2base_noise = T_gripper2base(Rect(0, 0, 3, 3)); |
||||
Mat rvec_gripper2base_noise; |
||||
cv::Rodrigues(R_gripper2base_noise, rvec_gripper2base_noise); |
||||
rvec_gripper2base_noise.at<double>(0,0) += rng.gaussian(0.001); |
||||
rvec_gripper2base_noise.at<double>(1,0) += rng.gaussian(0.001); |
||||
rvec_gripper2base_noise.at<double>(2,0) += rng.gaussian(0.001); |
||||
|
||||
cv::Rodrigues(rvec_gripper2base_noise, R_gripper2base_noise); |
||||
|
||||
Mat t_gripper2base_noise = T_gripper2base(Rect(3, 0, 1, 3)); |
||||
t_gripper2base_noise.at<double>(0,0) += rng.gaussian(0.001); |
||||
t_gripper2base_noise.at<double>(1,0) += rng.gaussian(0.001); |
||||
t_gripper2base_noise.at<double>(2,0) += rng.gaussian(0.001); |
||||
} |
||||
|
||||
R_target2cam.push_back(T_target2cam(Rect(0, 0, 3, 3))); |
||||
t_target2cam.push_back(T_target2cam(Rect(3, 0, 1, 3))); |
||||
} |
||||
} |
||||
|
||||
Mat CV_CalibrateHandEyeTest::homogeneousInverse(const Mat& T) |
||||
{ |
||||
CV_Assert( T.rows == 4 && T.cols == 4 ); |
||||
|
||||
Mat R = T(Rect(0, 0, 3, 3)); |
||||
Mat t = T(Rect(3, 0, 1, 3)); |
||||
Mat Rt = R.t(); |
||||
Mat tinv = -Rt * t; |
||||
Mat Tinv = Mat::eye(4, 4, T.type()); |
||||
Rt.copyTo(Tinv(Rect(0, 0, 3, 3))); |
||||
tinv.copyTo(Tinv(Rect(3, 0, 1, 3))); |
||||
|
||||
return Tinv; |
||||
} |
||||
|
||||
std::string CV_CalibrateHandEyeTest::getMethodName(HandEyeCalibrationMethod method) |
||||
{ |
||||
std::string method_name = ""; |
||||
switch (method) |
||||
{ |
||||
case CALIB_HAND_EYE_TSAI: |
||||
method_name = "Tsai"; |
||||
break; |
||||
|
||||
case CALIB_HAND_EYE_PARK: |
||||
method_name = "Park"; |
||||
break; |
||||
|
||||
case CALIB_HAND_EYE_HORAUD: |
||||
method_name = "Horaud"; |
||||
break; |
||||
|
||||
case CALIB_HAND_EYE_ANDREFF: |
||||
method_name = "Andreff"; |
||||
break; |
||||
|
||||
case CALIB_HAND_EYE_DANIILIDIS: |
||||
method_name = "Daniilidis"; |
||||
break; |
||||
|
||||
default: |
||||
break; |
||||
} |
||||
|
||||
return method_name; |
||||
} |
||||
|
||||
double CV_CalibrateHandEyeTest::sign_double(double val) |
||||
{ |
||||
return (0 < val) - (val < 0); |
||||
} |
||||
|
||||
///////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
TEST(Calib3d_CalibrateHandEye, regression) { CV_CalibrateHandEyeTest test; test.safe_run(); } |
||||
|
||||
}} // namespace
|
||||
Loading…
Reference in new issue