四元數操作中角度距離計算

0 相關參考

四元數
VINS-Mono代碼筆記（七）

《Quaternion kinematics for error-state kalman filter》、《Indirect Kalman Filter for 3D Attitude Estimation》、《SLAM十四講》

1 旋轉角度距離計算

2VINS中相關代碼

bool InitialEXRotation::CalibrationExRotation(vector<pair<Vector3d, Vector3d>> corres, Quaterniond delta_q_imu, Matrix3d &calib_ric_result)
{
    frame_count++;
    //solveRelativeR函數中可以根據corres中特徵點的對應關係計算出前後兩幀圖像之間的旋轉矩陣，加到Rc中，Rc表示相機位姿的旋轉矩陣
    Rc.push_back(solveRelativeR(corres));
    //delta_q_imu爲IMU預積分得到的旋轉四元數，轉換成矩陣形式存入Rimu當中。則Rimu中存放的是imu預積分得到的旋轉矩陣
    Rimu.push_back(delta_q_imu.toRotationMatrix());
    //每幀IMU相對於起始幀IMU的R,ric初始化值爲單位矩陣，則Rc_g中存入的第一個旋轉向量爲IMU的旋轉矩陣
    Rc_g.push_back(ric.inverse() * delta_q_imu * ric);

    Eigen::MatrixXd A(frame_count * 4, 4);
    A.setZero();
    int sum_ok = 0;
    //遍歷滑動窗口中的每一幀
    for (int i = 1; i <= frame_count; i++)
    {
        Quaterniond r1(Rc[i]);      //相機位姿的旋轉矩陣
        Quaterniond r2(Rc_g[i]);    //IMU的旋轉矩陣
        //旋轉角度距離計算，這裏計算的是圖像幀和IMU數據之間的旋轉角度的距離
        //TODO 四元數函數angularDistance()操作參考鏈接：[https://blog.csdn.net/hzwwpgmwy/article/details/84846016#1__116]
        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;
        ++sum_ok;
        Matrix4d L, R;

        double w = Quaterniond(Rc[i]).w();
        Vector3d q = Quaterniond(Rc[i]).vec();
        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);
    ric = estimated_R.toRotationMatrix().inverse();
    //cout << svd.singularValues().transpose() << endl;
    //cout << ric << endl;
    Vector3d ric_cov;
    ric_cov = svd.singularValues().tail<3>();
    if (frame_count >= WINDOW_SIZE && ric_cov(1) > 0.25)
    {
        calib_ric_result = ric;
        return true;
    }
    else
        return false;
}