VINS初始化之外参在线标定

一、理论推导

估计旋转外参数Qbc具体公式推导：

二、代码实现

initial_ex_rotation.cpp

if (ESTIMATE_EXTRINSIC == 2)
    {
        cout << "calibrating extrinsic param, rotation movement is needed" << endl;
        if (frame_count != 0)
        {
            vector<pair<Vector3d, Vector3d>> corres = f_manager.getCorresponding(frame_count - 1, frame_count);
            Matrix3d calib_ric;
            if (initial_ex_rotation.CalibrationExRotation(corres, pre_integrations[frame_count]->delta_q, calib_ric))
            {
                // ROS_WARN("initial extrinsic rotation calib success");
                // ROS_WARN_STREAM("initial extrinsic rotation: " << endl
                                                            //    << calib_ric);
                                                            
                ric[0] = calib_ric;
                RIC[0] = calib_ric;
                ESTIMATE_EXTRINSIC = 1;
            }
        }
    }

/**
 * @Description:  在线标定相机到imu之间的相对旋转Rbc
 * @param:corres: 两帧之间多个匹配点的归一化坐标
 * @param:delta_q_imu: 两帧陀螺仪积分得到的相对旋转
 * @return:calib_ric_result: 标定结果
 */
int flag = 0;
bool InitialEXRotation::CalibrationExRotation(vector<pair<Vector3d, Vector3d>> corres, Quaterniond delta_q_imu, Matrix3d &calib_ric_result)
{
    frame_count++;
    // std::cout << "frame_count"<<frame_count << std::endl;
    Rc.push_back(solveRelativeR(corres));
    Rimu.push_back(delta_q_imu.toRotationMatrix());

    // std::cout << "ric" << ric << std::endl;

    Rc_g.push_back(ric.inverse() * delta_q_imu * ric);

    // std::cout << "Rc: " <<Rc.at(flag)<< std::endl;
    // std::cout << "Rc_g: " << Rc_g.at(flag)<< std::endl;

    flag++;
    Eigen::MatrixXd A(frame_count * 4, 4);
    A.setZero();
    int sum_ok = 0;
    for (int i = 1; i <= frame_count; i++)
    {
        Quaterniond r1(Rc[i]);
        Quaterniond r2(Rc_g[i]);

        double angular_distance = 180 / M_PI * r1.angularDistance(r2);
        //ROS_DEBUG("%d %f", i, angular_distance);

        double huber = angular_distance > 5.0 ? 5.0 / angular_distance : 1.0;//鲁棒核权重
        ++sum_ok;
        Matrix4d L, R;

        double w = Quaterniond(Rc[i]).w();
        Vector3d q = Quaterniond(Rc[i]).vec();//x,y,z
        L.block<3, 3>(0, 0) = w * Matrix3d::Identity() + Utility::skewSymmetric(q);
        L.block<3, 1>(0, 3) = q;
        L.block<1, 3>(3, 0) = -q.transpose();
        L(3, 3) = w;

        Quaterniond R_ij(Rimu[i]);
        w = R_ij.w();
        q = R_ij.vec();
        R.block<3, 3>(0, 0) = w * Matrix3d::Identity() - Utility::skewSymmetric(q);
        R.block<3, 1>(0, 3) = q;
        R.block<1, 3>(3, 0) = -q.transpose();
        R(3, 3) = w;

        A.block<4, 4>((i - 1) * 4, 0) = huber * (L - R);
    }

    JacobiSVD<MatrixXd> svd(A, ComputeFullU | ComputeFullV);
    Matrix<double, 4, 1> x = svd.matrixV().col(3);
    Quaterniond estimated_R(x);
    std::cout << "x: " << x << std::endl;
    std::cout << "estimated_R" << estimated_R.coeffs() << std::endl;
    ric = estimated_R.toRotationMatrix().inverse();
    //cout << svd.singularValues().transpose() << endl;
    //cout << ric << endl;
    Vector3d ric_cov;
    ric_cov = svd.singularValues().tail<3>();
    std::cout << "svd " << svd.singularValues() << std::endl;
    std::cout << "ric_cov " << ric_cov << std::endl;
    if (frame_count >= WINDOW_SIZE && ric_cov(1) > 0.25) {
        calib_ric_result = ric;
        std::cout << "calib_ric_result: " << calib_ric_result << std::endl;
        return true;
    }
    else 
    return false;
}

Matrix3d InitialEXRotation::solveRelativeR(const vector<pair<Vector3d, Vector3d>> &corres)
{
    std::cout <<"corres.size()"<< corres.size() << std::endl;
    if (corres.size() >= 9) {
        vector<cv::Point2f> ll, rr;
        for (int i = 0; i < int(corres.size()); i++)
        {
            ll.push_back(cv::Point2f(corres[i].first(0), corres[i].first(1)));
            rr.push_back(cv::Point2f(corres[i].second(0), corres[i].second(1)));
            // std::cout << " ll :   ******************" <<ll<< std::endl;
            // std::cout << " rr :" << rr<< std::endl;
        }
        cv::Mat E = cv::findFundamentalMat(ll, rr);
        // std::cout << "solve fundamental " << E << std::endl;
        cv::Mat_<double> R1, R2, t1, t2;
        decomposeE(E, R1, R2, t1, t2);

        if (determinant(R1) + 1.0 < 1e-09)
        {
            E = -E;
            decomposeE(E, R1, R2, t1, t2);
        }
        double ratio1 = max(testTriangulation(ll, rr, R1, t1), testTriangulation(ll, rr, R1, t2));
        double ratio2 = max(testTriangulation(ll, rr, R2, t1), testTriangulation(ll, rr, R2, t2));
        cv::Mat_<double> ans_R_cv = ratio1 > ratio2 ? R1 : R2;

        Matrix3d ans_R_eigen;
        for (int i = 0; i < 3; i++)
            for (int j = 0; j < 3; j++)
                ans_R_eigen(j, i) = ans_R_cv(i, j);
        return ans_R_eigen;
    }
    return Matrix3d::Identity();
}

double InitialEXRotation::testTriangulation(const vector<cv::Point2f> &l,
                                          const vector<cv::Point2f> &r,
                                          cv::Mat_<double> R, cv::Mat_<double> t)
{
    cv::Mat pointcloud;
    cv::Matx34f P = cv::Matx34f(1, 0, 0, 0,
                                0, 1, 0, 0,
                                0, 0, 1, 0);
    cv::Matx34f P1 = cv::Matx34f(R(0, 0), R(0, 1), R(0, 2), t(0),
                                 R(1, 0), R(1, 1), R(1, 2), t(1),
                                 R(2, 0), R(2, 1), R(2, 2), t(2));
    cv::triangulatePoints(P, P1, l, r, pointcloud);
    // std::cout << "pointcloud: " << pointcloud.size()<< std::endl;//150*4
    int front_count = 0;
    for (int i = 0; i < pointcloud.cols; i++)
    {
        double normal_factor = pointcloud.col(i).at<float>(3);

        cv::Mat_<double> p_3d_l = cv::Mat(P) * (pointcloud.col(i) / normal_factor);
        // std::cout << "p_3d_l:" << p_3d_l << std::endl;//3*1
        // std::cout << "p_3d_l(2)" << p_3d_l(2) << std::endl;
        cv::Mat_<double> p_3d_r = cv::Mat(P1) * (pointcloud.col(i) / normal_factor);
        if (p_3d_l(2) > 0 && p_3d_r(2) > 0)
            front_count++;
    }
    std::cout << "front_count" << front_count << std::endl;
    // ROS_DEBUG("MotionEstimator: %f", 1.0 * front_count / pointcloud.cols);
    return 1.0 * front_count / pointcloud.cols;
}

void InitialEXRotation::decomposeE(cv::Mat E,
                                 cv::Mat_<double> &R1, cv::Mat_<double> &R2,
                                 cv::Mat_<double> &t1, cv::Mat_<double> &t2)
{
    cv::SVD svd(E, cv::SVD::MODIFY_A);
    cv::Matx33d W(0, -1, 0,
                  1, 0, 0,
                  0, 0, 1);
    cv::Matx33d Wt(0, 1, 0,
                   -1, 0, 0,
                   0, 0, 1);
    R1 = svd.u * cv::Mat(W) * svd.vt;
    R2 = svd.u * cv::Mat(Wt) * svd.vt;
    t1 = svd.u.col(2);
    t2 = -svd.u.col(2);
    /*******************验证视觉SLAM十四讲公式是否正确**************/
    // cv::Mat_<double> t3;
    // cv::Mat_<double> ut;
    // cv::transpose(svd.u, ut);
    // cv::Matx33d t(1, 0, 0, 0, 1, 0, 0, 0, 0);
    // std::cout << " Wt: " <<t.col(0)<< std::endl;
    // std::cout << "svd.u " << svd.u << std::endl;
    // std::cout << "svd.vt" << svd.vt << std::endl;
    // t3 = svd.u * cv::Mat(W) *cv::Mat(t)*ut;
    // std::cout << " t1: " << t1 << std::endl;
    // std::cout << " t: " << t3<< std::endl;
}

VINS Mono CalibrationExRotation函数解析