中文注释版本。本文大多注释来自 --- https://github.com/daobilige-su/loam_velodyne

laserOdometry节点接收scanResgistraion传过来的点云，进行点云匹配来估计位姿，并发布里程计以及去畸变的点云给mapping节点。下面先大体分析下算法原理。

算法概要分析

laserCloudXXXHandler()

TransformToStart()

TransformToEnd()

核心代码

点线匹配

点面匹配

最小二乘问题构建

遗留问题

算法概要分析

算法流程：

将上一帧( $t_{k}$ — $t_{k+1}$ )的点云补偿到 $t_{k+1}$ 时刻，表示为 $\bar{P}$ ；
将当前帧点云中的特征点（边缘点和平面点）补偿也补偿到 $t_{k+1}$ 时刻；
$\bar{p}$ 和特征点完成点线匹配和点面匹配
构建最小二乘问题进行优化

具体如何操作，在下面结合相关代码进行细致说明。

laserCloudXXXHandler()

订阅句柄的操作都相似，获取数据。

void laserCloudSharpHandler(const sensor_msgs::PointCloud2ConstPtr& cornerPointsSharp2)
{timeCornerPointsSharp = cornerPointsSharp2->header.stamp.toSec();cornerPointsSharp->clear();pcl::fromROSMsg(*cornerPointsSharp2, *cornerPointsSharp);std::vector<int> indices;//去除无效点pcl::removeNaNFromPointCloud(*cornerPointsSharp,*cornerPointsSharp, indices);newCornerPointsSharp = true;
}

TransformToStart()

功能：当前点云中的点相对第一个点去除因匀速运动产生的畸变(加速度畸变在上一个节点中补偿过了)，效果相当于得到在点云扫描开始位置静止扫描得到的点云(就是算法流程中的第二步)。

论文中上述公式对应代码，一个点云周期0.1s，上下同乘10。T用transform[6]来表示，代表上一帧到这一帧的变换，包含旋转向量和三维平移量。

对各个点进行补偿，注意要先平移再旋转，而且这里是从当前帧变换到上一帧，旋转矩阵是求个逆的。具体代码如下。

void TransformToStart(PointType const * const pi, PointType * const po)
{//插值系数计算，云中每个点的相对时间/点云周期10float s = 10 * (pi->intensity - int(pi->intensity));//线性插值：根据每个点在点云中的相对位置关系，乘以相应的旋转平移系数float rx = s * transform[0];float ry = s * transform[1];float rz = s * transform[2];float tx = s * transform[3];float ty = s * transform[4];float tz = s * transform[5];//变换到start时刻//平移后绕z轴旋转（-rz）float x1 = cos(rz) * (pi->x - tx) + sin(rz) * (pi->y - ty);float y1 = -sin(rz) * (pi->x - tx) + cos(rz) * (pi->y - ty);float z1 = (pi->z - tz);//绕x轴旋转（-rx）float x2 = x1;float y2 = cos(rx) * y1 + sin(rx) * z1;float z2 = -sin(rx) * y1 + cos(rx) * z1;//绕y轴旋转（-ry）po->x = cos(ry) * x2 - sin(ry) * z2;po->y = y2;po->z = sin(ry) * x2 + cos(ry) * z2;po->intensity = pi->intensity;
}

TransformToEnd()

功能：对点云向后补偿（算法流程第一步）。

思路：先把当前各点向前补偿，如TransformToStart()，流程一样的，再用transform整体向后补偿（transform正好是从上一帧到当前帧的变换）。具体看注释。

void TransformToEnd(PointType const * const pi, PointType * const po)
{//插值系数计算float s = 10 * (pi->intensity - int(pi->intensity));float rx = s * transform[0];float ry = s * transform[1];float rz = s * transform[2];float tx = s * transform[3];float ty = s * transform[4];float tz = s * transform[5];//先向前补偿//平移后绕z轴旋转（-rz）float x1 = cos(rz) * (pi->x - tx) + sin(rz) * (pi->y - ty);float y1 = -sin(rz) * (pi->x - tx) + cos(rz) * (pi->y - ty);float z1 = (pi->z - tz);//绕x轴旋转（-rx）float x2 = x1;float y2 = cos(rx) * y1 + sin(rx) * z1;float z2 = -sin(rx) * y1 + cos(rx) * z1;//绕y轴旋转（-ry）float x3 = cos(ry) * x2 - sin(ry) * z2;float y3 = y2;float z3 = sin(ry) * x2 + cos(ry) * z2;//求出了相对于起始点校正的坐标//整体向后补偿rx = transform[0];ry = transform[1];rz = transform[2];tx = transform[3];ty = transform[4];tz = transform[5];//绕y轴旋转（ry）float x4 = cos(ry) * x3 + sin(ry) * z3;float y4 = y3;float z4 = -sin(ry) * x3 + cos(ry) * z3;//绕x轴旋转（rx）float x5 = x4;float y5 = cos(rx) * y4 - sin(rx) * z4;float z5 = sin(rx) * y4 + cos(rx) * z4;//绕z轴旋转（rz），再平移float x6 = cos(rz) * x5 - sin(rz) * y5 + tx;float y6 = sin(rz) * x5 + cos(rz) * y5 + ty;float z6 = z5 + tz;// 我认为到这里其实就已经完成了补偿(局部坐标系下)，下面还有两次变换好像换到了世界坐标系了？// 不是很懂了，欢迎各位下方留言为小弟解惑//----------------------------//平移后绕z轴旋转（imuRollStart）float x7 = cos(imuRollStart) * (x6 - imuShiftFromStartX) - sin(imuRollStart) * (y6 - imuShiftFromStartY);float y7 = sin(imuRollStart) * (x6 - imuShiftFromStartX) + cos(imuRollStart) * (y6 - imuShiftFromStartY);float z7 = z6 - imuShiftFromStartZ;//绕x轴旋转（imuPitchStart）float x8 = x7;float y8 = cos(imuPitchStart) * y7 - sin(imuPitchStart) * z7;float z8 = sin(imuPitchStart) * y7 + cos(imuPitchStart) * z7;//绕y轴旋转（imuYawStart）float x9 = cos(imuYawStart) * x8 + sin(imuYawStart) * z8;float y9 = y8;float z9 = -sin(imuYawStart) * x8 + cos(imuYawStart) * z8;//绕y轴旋转（-imuYawLast）float x10 = cos(imuYawLast) * x9 - sin(imuYawLast) * z9;float y10 = y9;float z10 = sin(imuYawLast) * x9 + cos(imuYawLast) * z9;//绕x轴旋转（-imuPitchLast）float x11 = x10;float y11 = cos(imuPitchLast) * y10 + sin(imuPitchLast) * z10;float z11 = -sin(imuPitchLast) * y10 + cos(imuPitchLast) * z10;//绕z轴旋转（-imuRollLast）po->x = cos(imuRollLast) * x11 + sin(imuRollLast) * y11;po->y = -sin(imuRollLast) * x11 + cos(imuRollLast) * y11;po->z = z11;//只保留线号po->intensity = int(pi->intensity);
}

核心代码

下面进入主题。

先看看点线匹配、点面匹配的理论部分，说明一下论文和代码的对应部分。

点线匹配

正如之前所说的那样，我们在点云 $\bar{p}$ 中找匹配子，特征点表示为i，用kdtree查找第一个距离i最近点，记为点j；在j附近scan中查找另一个距离i最近的点，记为l。保证点j、l不在同一scan中，这样可以避免出现3点处于同一scan。

根据上式计算点到线的距离，通化优化transform来使d值最小。这个式子分子部分为两个向量(ij 和 il )叉乘的模，在几何意义上来说就是以这两向量为邻边围成平行四边形的面积，分子为向量jl的模，也就是低，高 = 面积/低。(图画得有点丑...)

代码具体注释看下方。

void edgeCor(){//处理当前点云中的曲率最大的特征点,从上个点云中曲率比较大的特征点中找两个最近距离点，一个点使用kd-tree查找，另一个根据找到的点在其相邻线找另外一个最近距离的点for (int i = 0; i < cornerPointsSharpNum; i++) {TransformToStart(&cornerPointsSharp->points[i], &pointSel);//每迭代五次，重新查找最近点if (iterCount % 5 == 0) {std::vector<int> indices;pcl::removeNaNFromPointCloud(*laserCloudCornerLast,*laserCloudCornerLast, indices);//kd-tree查找一个最近距离点，边沿点未经过体素栅格滤波，一般边沿点本来就比较少，不做滤波kdtreeCornerLast->nearestKSearch(pointSel, 1, pointSearchInd, pointSearchSqDis);int closestPointInd = -1, minPointInd2 = -1;//寻找相邻线距离目标点距离最小的点//再次提醒：velodyne是2度一线，scanID相邻并不代表线号相邻，相邻线度数相差2度，也即线号scanID相差2if (pointSearchSqDis[0] < 25) {//找到的最近点距离的确很近的话closestPointInd = pointSearchInd[0];//提取最近点线号int closestPointScan = int(laserCloudCornerLast->points[closestPointInd].intensity);float pointSqDis, minPointSqDis2 = 25;//初始门槛值5米，可大致过滤掉scanID相邻，但实际线不相邻的值//寻找距离目标点最近距离的平方和最小的点for (int j = closestPointInd + 1; j < cornerPointsSharpNum; j++) {//向scanID增大的方向查找if (int(laserCloudCornerLast->points[j].intensity) > closestPointScan + 2.5) {//非相邻线break;}pointSqDis = (laserCloudCornerLast->points[j].x - pointSel.x) * (laserCloudCornerLast->points[j].x - pointSel.x) + (laserCloudCornerLast->points[j].y - pointSel.y) * (laserCloudCornerLast->points[j].y - pointSel.y) + (laserCloudCornerLast->points[j].z - pointSel.z) * (laserCloudCornerLast->points[j].z - pointSel.z);if (int(laserCloudCornerLast->points[j].intensity) > closestPointScan) {//确保两个点不在同一条scan上（相邻线查找应该可以用scanID == closestPointScan +/- 1 来做）if (pointSqDis < minPointSqDis2) {//距离更近，要小于初始值5米//更新最小距离与点序minPointSqDis2 = pointSqDis;minPointInd2 = j;}}}//同理for (int j = closestPointInd - 1; j >= 0; j--) {//向scanID减小的方向查找if (int(laserCloudCornerLast->points[j].intensity) < closestPointScan - 2.5) {break;}pointSqDis = (laserCloudCornerLast->points[j].x - pointSel.x) * (laserCloudCornerLast->points[j].x - pointSel.x) + (laserCloudCornerLast->points[j].y - pointSel.y) * (laserCloudCornerLast->points[j].y - pointSel.y) + (laserCloudCornerLast->points[j].z - pointSel.z) * (laserCloudCornerLast->points[j].z - pointSel.z);if (int(laserCloudCornerLast->points[j].intensity) < closestPointScan) {if (pointSqDis < minPointSqDis2) {minPointSqDis2 = pointSqDis;minPointInd2 = j;}}}}//记住组成线的点序pointSearchCornerInd1[i] = closestPointInd;//kd-tree最近距离点，-1表示未找到满足的点pointSearchCornerInd2[i] = minPointInd2;//另一个最近的，-1表示未找到满足的点}if (pointSearchCornerInd2[i] >= 0) {//大于等于0，不等于-1，说明两个点都找到了tripod1 = laserCloudCornerLast->points[pointSearchCornerInd1[i]];tripod2 = laserCloudCornerLast->points[pointSearchCornerInd2[i]];//选择的特征点记为O，kd-tree最近距离点记为A，另一个最近距离点记为Bfloat x0 = pointSel.x;float y0 = pointSel.y;float z0 = pointSel.z;float x1 = tripod1.x;float y1 = tripod1.y;float z1 = tripod1.z;float x2 = tripod2.x;float y2 = tripod2.y;float z2 = tripod2.z;//向量OA = (x0 - x1, y0 - y1, z0 - z1), 向量OB = (x0 - x2, y0 - y2, z0 - z2)，向量AB = （x1 - x2, y1 - y2, z1 - z2）//向量OA OB的向量积(即叉乘)为：//|  i      j      k  |//|x0-x1  y0-y1  z0-z1|//|x0-x2  y0-y2  z0-z2|//模为：float a012 = sqrt(((x0 - x1)*(y0 - y2) - (x0 - x2)*(y0 - y1))* ((x0 - x1)*(y0 - y2) - (x0 - x2)*(y0 - y1)) + ((x0 - x1)*(z0 - z2) - (x0 - x2)*(z0 - z1))* ((x0 - x1)*(z0 - z2) - (x0 - x2)*(z0 - z1)) + ((y0 - y1)*(z0 - z2) - (y0 - y2)*(z0 - z1))* ((y0 - y1)*(z0 - z2) - (y0 - y2)*(z0 - z1)));//两个最近距离点之间的距离，即向量AB的模float l12 = sqrt((x1 - x2)*(x1 - x2) + (y1 - y2)*(y1 - y2) + (z1 - z2)*(z1 - z2));//AB方向的单位向量与OAB平面的单位法向量的向量积在各轴上的分量（d的方向）//x轴分量ifloat la = ((y1 - y2)*((x0 - x1)*(y0 - y2) - (x0 - x2)*(y0 - y1)) + (z1 - z2)*((x0 - x1)*(z0 - z2) - (x0 - x2)*(z0 - z1))) / a012 / l12;//y轴分量jfloat lb = -((x1 - x2)*((x0 - x1)*(y0 - y2) - (x0 - x2)*(y0 - y1)) - (z1 - z2)*((y0 - y1)*(z0 - z2) - (y0 - y2)*(z0 - z1))) / a012 / l12;//z轴分量kfloat lc = -((x1 - x2)*((x0 - x1)*(z0 - z2) - (x0 - x2)*(z0 - z1)) + (y1 - y2)*((y0 - y1)*(z0 - z2) - (y0 - y2)*(z0 - z1))) / a012 / l12;//点到线的距离，d = |向量OA 叉乘 向量OB|/|AB|float ld2 = a012 / l12;//unusedpointProj = pointSel;pointProj.x -= la * ld2;pointProj.y -= lb * ld2;pointProj.z -= lc * ld2;//权重计算，距离越大权重越小，距离越小权重越大，得到的权重范围<=1float s = 1;if (iterCount >= 5) {//5次迭代之后开始增加权重因素s = 1 - 1.8 * fabs(ld2);}//考虑权重coeff.x = s * la;coeff.y = s * lb;coeff.z = s * lc;coeff.intensity = s * ld2;if (s > 0.1 && ld2 != 0) {//只保留权重大的，也即距离比较小的点，同时也舍弃距离为零的laserCloudOri->push_back(cornerPointsSharp->points[i]);coeffSel->push_back(coeff);}}}
}

点面匹配

找距离i点最近点j；
在j附近scan中找距离 i 最近点m；
在j相同scan中找距离 i 最近点l；
点j、m、l构成平面，计算点 i 到平面距离；
优化transform使得点到平面距离最小，得到变换矩阵。

（这里注意点m、l 两个点中要有一个同j scan，另一个点不同，为了避免三点共线而导致没有平面的情况）

点到平面距离公式如上，分子是 $\vec{il} \cdot \left ( jl \times jm\right )$ 的模，几何意义为点i j l m四点在空间中所围立方体的体积，分母还是那个四边形面积。那么距离 = 体积/面积。

代码如下：

void surfCor(){
//对本次接收到的曲率最小的点,从上次接收到的点云曲率比较小的点中找三点组成平面，一个使用kd-tree查找，另外一个在同一线上查找满足要求的，第三个在不同线上查找满足要求的
for (int i = 0; i < surfPointsFlatNum; i++) {TransformToStart(&surfPointsFlat->points[i], &pointSel);if (iterCount % 5 == 0) {//kd-tree最近点查找，在经过体素栅格滤波之后的平面点中查找，一般平面点太多，滤波后最近点查找数据量小kdtreeSurfLast->nearestKSearch(pointSel, 1, pointSearchInd, pointSearchSqDis);int closestPointInd = -1, minPointInd2 = -1, minPointInd3 = -1;if (pointSearchSqDis[0] < 25) {closestPointInd = pointSearchInd[0];int closestPointScan = int(laserCloudSurfLast->points[closestPointInd].intensity);float pointSqDis, minPointSqDis2 = 25, minPointSqDis3 = 25;for (int j = closestPointInd + 1; j < surfPointsFlatNum; j++) {if (int(laserCloudSurfLast->points[j].intensity) > closestPointScan + 2.5) {break;}pointSqDis = (laserCloudSurfLast->points[j].x - pointSel.x) * (laserCloudSurfLast->points[j].x - pointSel.x) + (laserCloudSurfLast->points[j].y - pointSel.y) * (laserCloudSurfLast->points[j].y - pointSel.y) + (laserCloudSurfLast->points[j].z - pointSel.z) * (laserCloudSurfLast->points[j].z - pointSel.z);if (int(laserCloudSurfLast->points[j].intensity) <= closestPointScan) {//如果点的线号小于等于最近点的线号(应该最多取等，也即同一线上的点)if (pointSqDis < minPointSqDis2) {minPointSqDis2 = pointSqDis;minPointInd2 = j;}} else {//如果点处在大于该线上if (pointSqDis < minPointSqDis3) {minPointSqDis3 = pointSqDis;minPointInd3 = j;}}}//同理for (int j = closestPointInd - 1; j >= 0; j--) {if (int(laserCloudSurfLast->points[j].intensity) < closestPointScan - 2.5) {break;}pointSqDis = (laserCloudSurfLast->points[j].x - pointSel.x) * (laserCloudSurfLast->points[j].x - pointSel.x) + (laserCloudSurfLast->points[j].y - pointSel.y) * (laserCloudSurfLast->points[j].y - pointSel.y) + (laserCloudSurfLast->points[j].z - pointSel.z) * (laserCloudSurfLast->points[j].z - pointSel.z);if (int(laserCloudSurfLast->points[j].intensity) >= closestPointScan) {if (pointSqDis < minPointSqDis2) {minPointSqDis2 = pointSqDis;minPointInd2 = j;}} else {if (pointSqDis < minPointSqDis3) {minPointSqDis3 = pointSqDis;minPointInd3 = j;}}}}pointSearchSurfInd1[i] = closestPointInd;//kd-tree最近距离点,-1表示未找到满足要求的点pointSearchSurfInd2[i] = minPointInd2;//同一线号上的距离最近的点，-1表示未找到满足要求的点pointSearchSurfInd3[i] = minPointInd3;//不同线号上的距离最近的点，-1表示未找到满足要求的点}if (pointSearchSurfInd2[i] >= 0 && pointSearchSurfInd3[i] >= 0) {//找到了三个点tripod1 = laserCloudSurfLast->points[pointSearchSurfInd1[i]];//A点tripod2 = laserCloudSurfLast->points[pointSearchSurfInd2[i]];//B点tripod3 = laserCloudSurfLast->points[pointSearchSurfInd3[i]];//C点//向量AB = (tripod2.x - tripod1.x, tripod2.y - tripod1.y, tripod2.z - tripod1.z)//向量AC = (tripod3.x - tripod1.x, tripod3.y - tripod1.y, tripod3.z - tripod1.z)//向量AB AC的向量积（即叉乘），得到的是法向量//x轴方向分向量ifloat pa = (tripod2.y - tripod1.y) * (tripod3.z - tripod1.z) - (tripod3.y - tripod1.y) * (tripod2.z - tripod1.z);//y轴方向分向量jfloat pb = (tripod2.z - tripod1.z) * (tripod3.x - tripod1.x) - (tripod3.z - tripod1.z) * (tripod2.x - tripod1.x);//z轴方向分向量kfloat pc = (tripod2.x - tripod1.x) * (tripod3.y - tripod1.y) - (tripod3.x - tripod1.x) * (tripod2.y - tripod1.y);float pd = -(pa * tripod1.x + pb * tripod1.y + pc * tripod1.z);//法向量的模float ps = sqrt(pa * pa + pb * pb + pc * pc);//pa pb pc为法向量各方向上的单位向量pa /= ps;pb /= ps;pc /= ps;pd /= ps;//点到面的距离：向量OA与与法向量的点积除以法向量的模float pd2 = pa * pointSel.x + pb * pointSel.y + pc * pointSel.z + pd;//unusedpointProj = pointSel;pointProj.x -= pa * pd2;pointProj.y -= pb * pd2;pointProj.z -= pc * pd2;//同理计算权重float s = 1;if (iterCount >= 5) {s = 1 - 1.8 * fabs(pd2) / sqrt(sqrt(pointSel.x * pointSel.x+ pointSel.y * pointSel.y + pointSel.z * pointSel.z));}//考虑权重coeff.x = s * pa;coeff.y = s * pb;coeff.z = s * pc;coeff.intensity = s * pd2;if (s > 0.1 && pd2 != 0) {//保存原始点与相应的系数laserCloudOri->push_back(surfPointsFlat->points[i]);coeffSel->push_back(coeff);}}
}

最小二乘问题构建

建立最小二乘问题进行优化。

代码中MatA表示雅可比矩阵，MatB表示非线性方程。建立方程如下：

$J(x)J^{T}(x)\Delta x = -J(x)f(x)$

也就是matAtA * matX = matAtB，迭代法求matX。这里还是牛顿法。

{cv::Mat matA(pointSelNum, 6, CV_32F, cv::Scalar::all(0));cv::Mat matAt(6, pointSelNum, CV_32F, cv::Scalar::all(0));cv::Mat matAtA(6, 6, CV_32F, cv::Scalar::all(0));cv::Mat matB(pointSelNum, 1, CV_32F, cv::Scalar::all(0));cv::Mat matAtB(6, 1, CV_32F, cv::Scalar::all(0));cv::Mat matX(6, 1, CV_32F, cv::Scalar::all(0));//计算matA,matB矩阵for (int i = 0; i < pointSelNum; i++) {pointOri = laserCloudOri->points[i];coeff = coeffSel->points[i];float s = 1;float srx = sin(s * transform[0]);float crx = cos(s * transform[0]);float sry = sin(s * transform[1]);float cry = cos(s * transform[1]);float srz = sin(s * transform[2]);float crz = cos(s * transform[2]);float tx = s * transform[3];float ty = s * transform[4];float tz = s * transform[5];//求解雅可比矩阵//小弟不才，这里已经窒息了，雅各比各参数应该f(x)对寻优参数的一阶导数(可以参考视觉slam14讲)float arx = (-s*crx*sry*srz*pointOri.x + s*crx*crz*sry*pointOri.y + s*srx*sry*pointOri.z + s*tx*crx*sry*srz - s*ty*crx*crz*sry - s*tz*srx*sry) * coeff.x+ (s*srx*srz*pointOri.x - s*crz*srx*pointOri.y + s*crx*pointOri.z+ s*ty*crz*srx - s*tz*crx - s*tx*srx*srz) * coeff.y+ (s*crx*cry*srz*pointOri.x - s*crx*cry*crz*pointOri.y - s*cry*srx*pointOri.z+ s*tz*cry*srx + s*ty*crx*cry*crz - s*tx*crx*cry*srz) * coeff.z;float ary = ((-s*crz*sry - s*cry*srx*srz)*pointOri.x + (s*cry*crz*srx - s*sry*srz)*pointOri.y - s*crx*cry*pointOri.z + tx*(s*crz*sry + s*cry*srx*srz) + ty*(s*sry*srz - s*cry*crz*srx) + s*tz*crx*cry) * coeff.x+ ((s*cry*crz - s*srx*sry*srz)*pointOri.x + (s*cry*srz + s*crz*srx*sry)*pointOri.y - s*crx*sry*pointOri.z+ s*tz*crx*sry - ty*(s*cry*srz + s*crz*srx*sry) - tx*(s*cry*crz - s*srx*sry*srz)) * coeff.z;float arz = ((-s*cry*srz - s*crz*srx*sry)*pointOri.x + (s*cry*crz - s*srx*sry*srz)*pointOri.y+ tx*(s*cry*srz + s*crz*srx*sry) - ty*(s*cry*crz - s*srx*sry*srz)) * coeff.x+ (-s*crx*crz*pointOri.x - s*crx*srz*pointOri.y+ s*ty*crx*srz + s*tx*crx*crz) * coeff.y+ ((s*cry*crz*srx - s*sry*srz)*pointOri.x + (s*crz*sry + s*cry*srx*srz)*pointOri.y+ tx*(s*sry*srz - s*cry*crz*srx) - ty*(s*crz*sry + s*cry*srx*srz)) * coeff.z;float atx = -s*(cry*crz - srx*sry*srz) * coeff.x + s*crx*srz * coeff.y - s*(crz*sry + cry*srx*srz) * coeff.z;float aty = -s*(cry*srz + crz*srx*sry) * coeff.x - s*crx*crz * coeff.y - s*(sry*srz - cry*crz*srx) * coeff.z;float atz = s*crx*sry * coeff.x - s*srx * coeff.y - s*crx*cry * coeff.z;float d2 = coeff.intensity;matA.at<float>(i, 0) = arx;matA.at<float>(i, 1) = ary;matA.at<float>(i, 2) = arz;matA.at<float>(i, 3) = atx;matA.at<float>(i, 4) = aty;matA.at<float>(i, 5) = atz;matB.at<float>(i, 0) = -0.05 * d2;}cv::transpose(matA, matAt);matAtA = matAt * matA;matAtB = matAt * matB;//求解matAtA * matX = matAtBcv::solve(matAtA, matAtB, matX, cv::DECOMP_QR);if (iterCount == 0) {//特征值1*6矩阵cv::Mat matE(1, 6, CV_32F, cv::Scalar::all(0));//特征向量6*6矩阵cv::Mat matV(6, 6, CV_32F, cv::Scalar::all(0));cv::Mat matV2(6, 6, CV_32F, cv::Scalar::all(0));//求解特征值/特征向量cv::eigen(matAtA, matE, matV);matV.copyTo(matV2);isDegenerate = false;//特征值取值门槛float eignThre[6] = {10, 10, 10, 10, 10, 10};for (int i = 5; i >= 0; i--) {//从小到大查找if (matE.at<float>(0, i) < eignThre[i]) {//特征值太小，则认为处在兼并环境中，发生了退化for (int j = 0; j < 6; j++) {//对应的特征向量置为0matV2.at<float>(i, j) = 0;}isDegenerate = true;} else {break;}}//计算P矩阵matP = matV.inv() * matV2;}if (isDegenerate) {//如果发生退化，只使用预测矩阵P计算cv::Mat matX2(6, 1, CV_32F, cv::Scalar::all(0));matX.copyTo(matX2);matX = matP * matX2;}//累加每次迭代的旋转平移量transform[0] += matX.at<float>(0, 0);transform[1] += matX.at<float>(1, 0);transform[2] += matX.at<float>(2, 0);transform[3] += matX.at<float>(3, 0);transform[4] += matX.at<float>(4, 0);transform[5] += matX.at<float>(5, 0);for(int i=0; i<6; i++){if(isnan(transform[i]))//判断是否非数字transform[i]=0;}//计算旋转平移量，如果很小就停止迭代float deltaR = sqrt(pow(rad2deg(matX.at<float>(0, 0)), 2) +pow(rad2deg(matX.at<float>(1, 0)), 2) +pow(rad2deg(matX.at<float>(2, 0)), 2));float deltaT = sqrt(pow(matX.at<float>(3, 0) * 100, 2) +pow(matX.at<float>(4, 0) * 100, 2) +pow(matX.at<float>(5, 0) * 100, 2));if (deltaR < 0.1 && deltaT < 0.1) {//迭代终止条件break;}
}

下面放上完整的代码注解

int main(int argc, char** argv)
{ros::init(argc, argv, "laserOdometry");ros::NodeHandle nh;ros::Subscriber subCornerPointsSharp = nh.subscribe<sensor_msgs::PointCloud2>("/laser_cloud_sharp", 2, laserCloudSharpHandler);ros::Subscriber subCornerPointsLessSharp = nh.subscribe<sensor_msgs::PointCloud2>("/laser_cloud_less_sharp", 2, laserCloudLessSharpHandler);ros::Subscriber subSurfPointsFlat = nh.subscribe<sensor_msgs::PointCloud2>("/laser_cloud_flat", 2, laserCloudFlatHandler);ros::Subscriber subSurfPointsLessFlat = nh.subscribe<sensor_msgs::PointCloud2>("/laser_cloud_less_flat", 2, laserCloudLessFlatHandler);ros::Subscriber subLaserCloudFullRes = nh.subscribe<sensor_msgs::PointCloud2> ("/velodyne_cloud_2", 2, laserCloudFullResHandler);ros::Subscriber subImuTrans = nh.subscribe<sensor_msgs::PointCloud2> ("/imu_trans", 5, imuTransHandler);ros::Publisher pubLaserCloudCornerLast = nh.advertise<sensor_msgs::PointCloud2>("/laser_cloud_corner_last", 2);ros::Publisher pubLaserCloudSurfLast = nh.advertise<sensor_msgs::PointCloud2>("/laser_cloud_surf_last", 2);ros::Publisher pubLaserCloudFullRes = nh.advertise<sensor_msgs::PointCloud2> ("/velodyne_cloud_3", 2);ros::Publisher pubLaserOdometry = nh.advertise<nav_msgs::Odometry> ("/laser_odom_to_init", 5);nav_msgs::Odometry laserOdometry;laserOdometry.header.frame_id = "/camera_init";laserOdometry.child_frame_id = "/laser_odom";tf::TransformBroadcaster tfBroadcaster;tf::StampedTransform laserOdometryTrans;laserOdometryTrans.frame_id_ = "/camera_init";laserOdometryTrans.child_frame_id_ = "/laser_odom";std::vector<int> pointSearchInd;//搜索到的点序std::vector<float> pointSearchSqDis;//搜索到的点平方距离PointType pointOri, pointSel/*选中的特征点*/, tripod1, tripod2, tripod3/*特征点的对应点*/, pointProj/*unused*/, coeff;//退化标志bool isDegenerate = false;//P矩阵，预测矩阵cv::Mat matP(6, 6, CV_32F, cv::Scalar::all(0));int frameCount = skipFrameNum;ros::Rate rate(100);bool status = ros::ok();while (status) {ros::spinOnce();if (newCornerPointsSharp && newCornerPointsLessSharp && newSurfPointsFlat && newSurfPointsLessFlat && newLaserCloudFullRes && newImuTrans &&fabs(timeCornerPointsSharp - timeSurfPointsLessFlat) < 0.005 &&fabs(timeCornerPointsLessSharp - timeSurfPointsLessFlat) < 0.005 &&fabs(timeSurfPointsFlat - timeSurfPointsLessFlat) < 0.005 &&fabs(timeLaserCloudFullRes - timeSurfPointsLessFlat) < 0.005 &&fabs(timeImuTrans - timeSurfPointsLessFlat) < 0.005) {  //同步作用，确保同时收到同一个点云的特征点以及IMU信息才进入newCornerPointsSharp = false;newCornerPointsLessSharp = false;newSurfPointsFlat = false;newSurfPointsLessFlat = false;newLaserCloudFullRes = false;newImuTrans = false;//将第一个点云数据集发送给laserMapping,从下一个点云数据开始处理，我们需要两帧数据来进行匹配。if (!systemInited) {//将cornerPointsLessSharp与laserCloudCornerLast交换,目的保存cornerPointsLessSharp的值下轮使用pcl::PointCloud<PointType>::Ptr laserCloudTemp = cornerPointsLessSharp;cornerPointsLessSharp = laserCloudCornerLast;laserCloudCornerLast = laserCloudTemp;//将surfPointLessFlat与laserCloudSurfLast交换，目的保存surfPointsLessFlat的值下轮使用laserCloudTemp = surfPointsLessFlat;surfPointsLessFlat = laserCloudSurfLast;laserCloudSurfLast = laserCloudTemp;//使用上一帧的特征点构建kd-treekdtreeCornerLast->setInputCloud(laserCloudCornerLast);//所有的边沿点集合kdtreeSurfLast->setInputCloud(laserCloudSurfLast);//所有的平面点集合//将cornerPointsLessSharp和surfPointLessFlat点也即边沿点和平面点分别发送给laserMappingsensor_msgs::PointCloud2 laserCloudCornerLast2;pcl::toROSMsg(*laserCloudCornerLast, laserCloudCornerLast2);laserCloudCornerLast2.header.stamp = ros::Time().fromSec(timeSurfPointsLessFlat);laserCloudCornerLast2.header.frame_id = "/camera";pubLaserCloudCornerLast.publish(laserCloudCornerLast2);sensor_msgs::PointCloud2 laserCloudSurfLast2;pcl::toROSMsg(*laserCloudSurfLast, laserCloudSurfLast2);laserCloudSurfLast2.header.stamp = ros::Time().fromSec(timeSurfPointsLessFlat);laserCloudSurfLast2.header.frame_id = "/camera";pubLaserCloudSurfLast.publish(laserCloudSurfLast2);//记住原点的翻滚角和俯仰角transformSum[0] += imuPitchStart;transformSum[2] += imuRollStart;systemInited = true;continue;}//T平移量的初值赋值为加减速的位移量，为其梯度下降的方向（沿用上次转换的T（一个sweep匀速模型），同时在其基础上减去匀速运动位移，即只考虑加减速的位移量）transform[3] -= imuVeloFromStartX * scanPeriod;transform[4] -= imuVeloFromStartY * scanPeriod;transform[5] -= imuVeloFromStartZ * scanPeriod;if (laserCloudCornerLastNum > 10 && laserCloudSurfLastNum > 100) {std::vector<int> indices;pcl::removeNaNFromPointCloud(*cornerPointsSharp,*cornerPointsSharp, indices);int cornerPointsSharpNum = cornerPointsSharp->points.size();int surfPointsFlatNum = surfPointsFlat->points.size();//Levenberg-Marquardt算法(L-M method)，非线性最小二乘算法，最优化算法的一种//最多迭代25次for (int iterCount = 0; iterCount < 25; iterCount++) {laserCloudOri->clear();coeffSel->clear();//处理当前点云中的曲率最大的特征点,从上个点云中曲率比较大的特征点中找两个最近距离点，一个点使用kd-tree查找，另一个根据找到的点在其相邻线找另外一个最近距离的点edgeCor();surfCor();cv::Mat matA(pointSelNum, 6, CV_32F, cv::Scalar::all(0));cv::Mat matAt(6, pointSelNum, CV_32F, cv::Scalar::all(0));cv::Mat matAtA(6, 6, CV_32F, cv::Scalar::all(0));cv::Mat matB(pointSelNum, 1, CV_32F, cv::Scalar::all(0));cv::Mat matAtB(6, 1, CV_32F, cv::Scalar::all(0));cv::Mat matX(6, 1, CV_32F, cv::Scalar::all(0));//计算matA,matB矩阵for (int i = 0; i < pointSelNum; i++) {pointOri = laserCloudOri->points[i];coeff = coeffSel->points[i];float s = 1;float srx = sin(s * transform[0]);float crx = cos(s * transform[0]);float sry = sin(s * transform[1]);float cry = cos(s * transform[1]);float srz = sin(s * transform[2]);float crz = cos(s * transform[2]);float tx = s * transform[3];float ty = s * transform[4];float tz = s * transform[5];//求解雅可比矩阵float arx = (-s*crx*sry*srz*pointOri.x + s*crx*crz*sry*pointOri.y + s*srx*sry*pointOri.z + s*tx*crx*sry*srz - s*ty*crx*crz*sry - s*tz*srx*sry) * coeff.x+ (s*srx*srz*pointOri.x - s*crz*srx*pointOri.y + s*crx*pointOri.z+ s*ty*crz*srx - s*tz*crx - s*tx*srx*srz) * coeff.y+ (s*crx*cry*srz*pointOri.x - s*crx*cry*crz*pointOri.y - s*cry*srx*pointOri.z+ s*tz*cry*srx + s*ty*crx*cry*crz - s*tx*crx*cry*srz) * coeff.z;float ary = ((-s*crz*sry - s*cry*srx*srz)*pointOri.x + (s*cry*crz*srx - s*sry*srz)*pointOri.y - s*crx*cry*pointOri.z + tx*(s*crz*sry + s*cry*srx*srz) + ty*(s*sry*srz - s*cry*crz*srx) + s*tz*crx*cry) * coeff.x+ ((s*cry*crz - s*srx*sry*srz)*pointOri.x + (s*cry*srz + s*crz*srx*sry)*pointOri.y - s*crx*sry*pointOri.z+ s*tz*crx*sry - ty*(s*cry*srz + s*crz*srx*sry) - tx*(s*cry*crz - s*srx*sry*srz)) * coeff.z;float arz = ((-s*cry*srz - s*crz*srx*sry)*pointOri.x + (s*cry*crz - s*srx*sry*srz)*pointOri.y+ tx*(s*cry*srz + s*crz*srx*sry) - ty*(s*cry*crz - s*srx*sry*srz)) * coeff.x+ (-s*crx*crz*pointOri.x - s*crx*srz*pointOri.y+ s*ty*crx*srz + s*tx*crx*crz) * coeff.y+ ((s*cry*crz*srx - s*sry*srz)*pointOri.x + (s*crz*sry + s*cry*srx*srz)*pointOri.y+ tx*(s*sry*srz - s*cry*crz*srx) - ty*(s*crz*sry + s*cry*srx*srz)) * coeff.z;float atx = -s*(cry*crz - srx*sry*srz) * coeff.x + s*crx*srz * coeff.y - s*(crz*sry + cry*srx*srz) * coeff.z;float aty = -s*(cry*srz + crz*srx*sry) * coeff.x - s*crx*crz * coeff.y - s*(sry*srz - cry*crz*srx) * coeff.z;float atz = s*crx*sry * coeff.x - s*srx * coeff.y - s*crx*cry * coeff.z;float d2 = coeff.intensity;matA.at<float>(i, 0) = arx;matA.at<float>(i, 1) = ary;matA.at<float>(i, 2) = arz;matA.at<float>(i, 3) = atx;matA.at<float>(i, 4) = aty;matA.at<float>(i, 5) = atz;matB.at<float>(i, 0) = -0.05 * d2;}cv::transpose(matA, matAt);matAtA = matAt * matA;matAtB = matAt * matB;//求解matAtA * matX = matAtBcv::solve(matAtA, matAtB, matX, cv::DECOMP_QR);if (iterCount == 0) {//特征值1*6矩阵cv::Mat matE(1, 6, CV_32F, cv::Scalar::all(0));//特征向量6*6矩阵cv::Mat matV(6, 6, CV_32F, cv::Scalar::all(0));cv::Mat matV2(6, 6, CV_32F, cv::Scalar::all(0));//求解特征值/特征向量cv::eigen(matAtA, matE, matV);matV.copyTo(matV2);isDegenerate = false;//特征值取值门槛float eignThre[6] = {10, 10, 10, 10, 10, 10};for (int i = 5; i >= 0; i--) {//从小到大查找if (matE.at<float>(0, i) < eignThre[i]) {//特征值太小，则认为处在兼并环境中，发生了退化for (int j = 0; j < 6; j++) {//对应的特征向量置为0matV2.at<float>(i, j) = 0;}isDegenerate = true;} else {break;}}//计算P矩阵matP = matV.inv() * matV2;}if (isDegenerate) {//如果发生退化，只使用预测矩阵P计算cv::Mat matX2(6, 1, CV_32F, cv::Scalar::all(0));matX.copyTo(matX2);matX = matP * matX2;}//累加每次迭代的旋转平移量transform[0] += matX.at<float>(0, 0);transform[1] += matX.at<float>(1, 0);transform[2] += matX.at<float>(2, 0);transform[3] += matX.at<float>(3, 0);transform[4] += matX.at<float>(4, 0);transform[5] += matX.at<float>(5, 0);for(int i=0; i<6; i++){if(isnan(transform[i]))//判断是否非数字transform[i]=0;}//计算旋转平移量，如果很小就停止迭代float deltaR = sqrt(pow(rad2deg(matX.at<float>(0, 0)), 2) +pow(rad2deg(matX.at<float>(1, 0)), 2) +pow(rad2deg(matX.at<float>(2, 0)), 2));float deltaT = sqrt(pow(matX.at<float>(3, 0) * 100, 2) +pow(matX.at<float>(4, 0) * 100, 2) +pow(matX.at<float>(5, 0) * 100, 2));if (deltaR < 0.1 && deltaT < 0.1) {//迭代终止条件break;}}}float rx, ry, rz, tx, ty, tz;//求相对于原点的旋转量,垂直方向上1.05倍修正?AccumulateRotation(transformSum[0], transformSum[1], transformSum[2], -transform[0], -transform[1] * 1.05, -transform[2], rx, ry, rz);float x1 = cos(rz) * (transform[3] - imuShiftFromStartX) - sin(rz) * (transform[4] - imuShiftFromStartY);float y1 = sin(rz) * (transform[3] - imuShiftFromStartX) + cos(rz) * (transform[4] - imuShiftFromStartY);float z1 = transform[5] * 1.05 - imuShiftFromStartZ;float x2 = x1;float y2 = cos(rx) * y1 - sin(rx) * z1;float z2 = sin(rx) * y1 + cos(rx) * z1;//求相对于原点的平移量tx = transformSum[3] - (cos(ry) * x2 + sin(ry) * z2);ty = transformSum[4] - y2;tz = transformSum[5] - (-sin(ry) * x2 + cos(ry) * z2);//根据IMU修正旋转量PluginIMURotation(rx, ry, rz, imuPitchStart, imuYawStart, imuRollStart, imuPitchLast, imuYawLast, imuRollLast, rx, ry, rz);//得到世界坐标系下的转移矩阵transformSum[0] = rx;transformSum[1] = ry;transformSum[2] = rz;transformSum[3] = tx;transformSum[4] = ty;transformSum[5] = tz;//欧拉角转换成四元数geometry_msgs::Quaternion geoQuat = tf::createQuaternionMsgFromRollPitchYaw(rz, -rx, -ry);//publish四元数和平移量laserOdometry.header.stamp = ros::Time().fromSec(timeSurfPointsLessFlat);laserOdometry.pose.pose.orientation.x = -geoQuat.y;laserOdometry.pose.pose.orientation.y = -geoQuat.z;laserOdometry.pose.pose.orientation.z = geoQuat.x;laserOdometry.pose.pose.orientation.w = geoQuat.w;laserOdometry.pose.pose.position.x = tx;laserOdometry.pose.pose.position.y = ty;laserOdometry.pose.pose.position.z = tz;pubLaserOdometry.publish(laserOdometry);//广播新的平移旋转之后的坐标系(rviz)laserOdometryTrans.stamp_ = ros::Time().fromSec(timeSurfPointsLessFlat);laserOdometryTrans.setRotation(tf::Quaternion(-geoQuat.y, -geoQuat.z, geoQuat.x, geoQuat.w));laserOdometryTrans.setOrigin(tf::Vector3(tx, ty, tz));tfBroadcaster.sendTransform(laserOdometryTrans);//对点云的曲率比较大和比较小的点投影到扫描结束位置int cornerPointsLessSharpNum = cornerPointsLessSharp->points.size();for (int i = 0; i < cornerPointsLessSharpNum; i++) {TransformToEnd(&cornerPointsLessSharp->points[i], &cornerPointsLessSharp->points[i]);}int surfPointsLessFlatNum = surfPointsLessFlat->points.size();for (int i = 0; i < surfPointsLessFlatNum; i++) {TransformToEnd(&surfPointsLessFlat->points[i], &surfPointsLessFlat->points[i]);}frameCount++;//点云全部点，每间隔一个点云数据相对点云最后一个点进行畸变校正if (frameCount >= skipFrameNum + 1) {int laserCloudFullResNum = laserCloudFullRes->points.size();for (int i = 0; i < laserCloudFullResNum; i++) {TransformToEnd(&laserCloudFullRes->points[i], &laserCloudFullRes->points[i]);}}//畸变校正之后的点作为last点保存等下个点云进来进行匹配pcl::PointCloud<PointType>::Ptr laserCloudTemp = cornerPointsLessSharp;cornerPointsLessSharp = laserCloudCornerLast;laserCloudCornerLast = laserCloudTemp;laserCloudTemp = surfPointsLessFlat;surfPointsLessFlat = laserCloudSurfLast;laserCloudSurfLast = laserCloudTemp;laserCloudCornerLastNum = laserCloudCornerLast->points.size();laserCloudSurfLastNum = laserCloudSurfLast->points.size();//点足够多就构建kd-tree，否则弃用此帧，沿用上一帧数据的kd-treeif (laserCloudCornerLastNum > 10 && laserCloudSurfLastNum > 100) {kdtreeCornerLast->setInputCloud(laserCloudCornerLast);kdtreeSurfLast->setInputCloud(laserCloudSurfLast);}//按照跳帧数publich边沿点，平面点以及全部点给laserMapping(每隔一帧发一次)if (frameCount >= skipFrameNum + 1) {frameCount = 0;sensor_msgs::PointCloud2 laserCloudCornerLast2;pcl::toROSMsg(*laserCloudCornerLast, laserCloudCornerLast2);laserCloudCornerLast2.header.stamp = ros::Time().fromSec(timeSurfPointsLessFlat);laserCloudCornerLast2.header.frame_id = "/camera";pubLaserCloudCornerLast.publish(laserCloudCornerLast2);sensor_msgs::PointCloud2 laserCloudSurfLast2;pcl::toROSMsg(*laserCloudSurfLast, laserCloudSurfLast2);laserCloudSurfLast2.header.stamp = ros::Time().fromSec(timeSurfPointsLessFlat);laserCloudSurfLast2.header.frame_id = "/camera";pubLaserCloudSurfLast.publish(laserCloudSurfLast2);sensor_msgs::PointCloud2 laserCloudFullRes3;pcl::toROSMsg(*laserCloudFullRes, laserCloudFullRes3);laserCloudFullRes3.header.stamp = ros::Time().fromSec(timeSurfPointsLessFlat);laserCloudFullRes3.header.frame_id = "/camera";pubLaserCloudFullRes.publish(laserCloudFullRes3);}}status = ros::ok();rate.sleep();}return 0;
}

遗留问题

AccumulateRotation()、PluginIMURotation() 这两个函数，并没有完全看懂，就不乱说了。

如有问题，欢迎评论留言交流或私信。

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LOAM源码结合论文解析（二）laserOdometry

算法概要分析

laserCloudXXXHandler()

TransformToStart()

TransformToEnd()

核心代码

点线匹配

点面匹配

最小二乘问题构建

遗留问题

LOAM源码结合论文解析（二）laserOdometry相关推荐

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