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视觉SLAM十四讲学习笔记——ch10 后端2

發布時間：2023/12/10 编程问答 35 豆豆

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文章目錄

10.1理論部分
10.2實踐部分
- 10.2.1 李代數上的位姿圖優化
- 10.2.2 g2o原聲位姿圖優化
- 調試遇到問題bug
參考博客

10.1理論部分

推薦參考博文推導:

SLAM十四講-后端2-ch10-代碼注釋(位姿圖優化)

SLAM14講學習筆記（七）后端（BA與圖優化，Pose Graph優化的理論與公式詳解、因子圖優化）

10.2實踐部分

10.2.1 李代數上的位姿圖優化

代碼及詳細注釋如下:

#include <iostream> #include <fstream> #include <string> #include <Eigen/Core>#include <g2o/core/base_vertex.h> #include <g2o/core/base_binary_edge.h> #include <g2o/core/block_solver.h> #include <g2o/core/optimization_algorithm_levenberg.h> #include <g2o/solvers/eigen/linear_solver_eigen.h>#include <sophus/se3.hpp>using namespace std; using namespace Eigen; using Sophus::SE3d; using Sophus::SO3d;/************************************************* 本程序演示如何用g2o solver進行位姿圖優化* sphere.g2o是人工生成的一個Pose graph，我們來優化它。* 盡管可以直接通過load函數讀取整個圖，但我們還是自己來實現讀取代碼，以期獲得更深刻的理解* 本節使用李代數表達位姿圖，節點和邊的方式為自定義* 利用 g2o對sphere.g2o文件進行優化優化前用g20——viewer顯示為橢球 * 用g2o的話需要定義頂點和邊 * 位姿圖優化就是只優化位姿不優化路標點 * 頂點應該相機的位姿 * 邊是相鄰兩個位姿的變換 * error誤差是觀測的相鄰相機的位姿變換的逆 * 待優化的相鄰相機的位姿變換 * 我們希望這個誤差接近I矩陣給誤差取ln后誤差接近 0 * 該程序用李代數描述誤差* 這里把J矩陣的計算放在JRInv(const SE3d & e)函數里 * 這里的J矩陣還不是雅克比矩陣具體雅克比見書上公式 p272頁公式10.9 10.10 * 李代數應該是向量形式 * 李代數的hat 也就是李代數向量變為反對稱矩陣* **********************************************/typedef Matrix<double, 6, 6> Matrix6d;// 給定誤差求J_R^{-1}的近似 Matrix6d JRInv(const SE3d &e) {Matrix6d J;J.block(0, 0, 3, 3) = SO3d::hat(e.so3().log());J.block(0, 3, 3, 3) = SO3d::hat(e.translation());J.block(3, 0, 3, 3) = Matrix3d::Zero(3, 3);J.block(3, 3, 3, 3) = SO3d::hat(e.so3().log());// J = J * 0.5 + Matrix6d::Identity();J = Matrix6d::Identity(); // try Identity if you wantreturn J; }// 李代數頂點 typedef Matrix<double, 6, 1> Vector6d;class VertexSE3LieAlgebra : public g2o::BaseVertex<6, SE3d> { public:EIGEN_MAKE_ALIGNED_OPERATOR_NEW//讀取數據virtual bool read(istream &is) override {double data[7];for (int i = 0; i < 7; i++)is >> data[i];setEstimate(SE3d(Quaterniond(data[6], data[3], data[4], data[5]),Vector3d(data[0], data[1], data[2])));}//將優化的位姿存入內存 virtual bool write(ostream &os) const override {os << id() << " ";Quaterniond q = _estimate.unit_quaternion();os << _estimate.translation().transpose() << " ";//coeffs順序是 x y z w ,w是實部os << q.coeffs()[0] << " " << q.coeffs()[1] << " " << q.coeffs()[2] << " " << q.coeffs()[3] << endl;return true;}virtual void setToOriginImpl() override {_estimate = SE3d();//李代數}// 左乘更新virtual void oplusImpl(const double *update) override {Vector6d upd;//六維向量 upd接收 updateupd << update[0], update[1], update[2], update[3], update[4], update[5];_estimate = SE3d::exp(upd) * _estimate;//更新位姿} };// 兩個李代數節點之邊 // 定義邊兩個李代數頂點的邊邊就是兩個頂點之間的變換即位姿之間的變換 class EdgeSE3LieAlgebra : public g2o::BaseBinaryEdge<6, SE3d, VertexSE3LieAlgebra, VertexSE3LieAlgebra> { public:EIGEN_MAKE_ALIGNED_OPERATOR_NEW//讀取觀測值和構造信息矩陣virtual bool read(istream &is) override {//這里觀測值是位子之間的變換，當然包括旋轉和平移所以 data[]是7維平移加四元數double data[7];for (int i = 0; i < 7; i++)is >> data[i];//流入data[]Quaterniond q(data[6], data[3], data[4], data[5]);q.normalize();//歸一化setMeasurement(SE3d(q, Vector3d(data[0], data[1], data[2])));for (int i = 0; i < information().rows() && is.good(); i++)for (int j = i; j < information().cols() && is.good(); j++) {is >> information()(i, j);if (i != j) //不是對角線的地方information()(j, i) = information()(i, j);}return true;}//這個函數就是為了把優化好的相機位姿放進指定文件中去virtual bool write(ostream &os) const override {//v1,V2分別指向兩個頂點VertexSE3LieAlgebra *v1 = static_cast<VertexSE3LieAlgebra *> (_vertices[0]);VertexSE3LieAlgebra *v2 = static_cast<VertexSE3LieAlgebra *> (_vertices[1]);os << v1->id() << " " << v2->id() << " "; //把兩個定點的編號流入osSE3d m = _measurement;Eigen::Quaterniond q = m.unit_quaternion(); //獲取單位四元數//先傳入平移再傳入四元數os << m.translation().transpose() << " ";os << q.coeffs()[0] << " " << q.coeffs()[1] << " " << q.coeffs()[2] << " " << q.coeffs()[3] << " ";// information matrix 信息矩陣for (int i = 0; i < information().rows(); i++)for (int j = i; j < information().cols(); j++) {os << information()(i, j) << " ";}os << endl;return true;}// 誤差計算與書中推導一致virtual void computeError() override {//v1,V2分別指向兩頂點的位姿SE3d v1 = (static_cast<VertexSE3LieAlgebra *> (_vertices[0]))->estimate();SE3d v2 = (static_cast<VertexSE3LieAlgebra *> (_vertices[1]))->estimate();_error = (_measurement.inverse() * v1.inverse() * v2).log();}// 雅可比計算virtual void linearizeOplus() override {SE3d v1 = (static_cast<VertexSE3LieAlgebra *> (_vertices[0]))->estimate();SE3d v2 = (static_cast<VertexSE3LieAlgebra *> (_vertices[1]))->estimate();Matrix6d J = JRInv(SE3d::exp(_error)); //計算d// 嘗試把J近似為I//雅克比有兩個,一個是誤差對相機i位姿的雅克比,另一個是誤差對相機j位姿的雅克比_jacobianOplusXi = -J * v2.inverse().Adj();_jacobianOplusXj = J * v2.inverse().Adj();} };int main(int argc, char **argv) {if (argc != 2) {cout << "Usage: pose_graph_g2o_SE3_lie sphere.g2o" << endl;return 1;}//將sphere.g2o文件流入finifstream fin(argv[1]);if (!fin) {cout << "file " << argv[1] << " does not exist." << endl;return 1;}// 設定g2otypedef g2o::BlockSolver<g2o::BlockSolverTraits<6, 6>> BlockSolverType; //6,6是頂點和邊的維度typedef g2o::LinearSolverEigen<BlockSolverType::PoseMatrixType> LinearSolverType; //線性求解//設置梯度下降的方法auto solver = new g2o::OptimizationAlgorithmLevenberg(g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));g2o::SparseOptimizer optimizer; // 圖模型optimizer.setAlgorithm(solver); // 設置求解器optimizer.setVerbose(true); // 打開調試輸出int vertexCnt = 0, edgeCnt = 0; // 頂點和邊的數量//容器 vectices 和edges 存放各個頂點和邊vector<VertexSE3LieAlgebra *> vectices;vector<EdgeSE3LieAlgebra *> edges;while (!fin.eof()) {string name;fin >> name;//將文件中的頂點數據流入,頂點就是各個相機的位姿if (name == "VERTEX_SE3:QUAT") {// 頂點VertexSE3LieAlgebra *v = new VertexSE3LieAlgebra();int index = 0;fin >> index;v->setId(index);v->read(fin); //這里是setEstimateoptimizer.addVertex(v);vertexCnt++;vectices.push_back(v);if (index == 0)v->setFixed(true);} else if (name == "EDGE_SE3:QUAT") {// SE3-SE3 邊EdgeSE3LieAlgebra *e = new EdgeSE3LieAlgebra();int idx1, idx2; // 關聯的兩個頂點fin >> idx1 >> idx2; //頂點的IDe->setId(edgeCnt++); ///設置邊的ID//設置頂點e->setVertex(0, optimizer.vertices()[idx1]);e->setVertex(1, optimizer.vertices()[idx2]);e->read(fin); //讀取觀測值optimizer.addEdge(e);edges.push_back(e);}if (!fin.good()) break;}//輸出邊的頂點的合的個數cout << "read total " << vertexCnt << " vertices, " << edgeCnt << " edges." << endl;cout << "optimizing ..." << endl;optimizer.initializeOptimization(); //優化初始化optimizer.optimize(30); //迭代次數cout << "saving optimization results ..." << endl;// 因為用了自定義頂點且沒有向g2o注冊，這里保存自己來實現// 偽裝成 SE3 頂點和邊，讓 g2o_viewer 可以認出ofstream fout("result_lie.g2o");for (VertexSE3LieAlgebra *v:vectices) {fout << "VERTEX_SE3:QUAT ";v->write(fout); //把優化的頂點放進 result_lie.g2o}for (EdgeSE3LieAlgebra *e:edges) {fout << "EDGE_SE3:QUAT ";e->write(fout); //把優化的邊放進 result_lie.g2o}fout.close();return 0; }

結果如下所示:

read total 2500 vertices, 9799 edges. optimizing ... iteration= 0 chi2= 674837160.579970 time= 0.566391 cumTime= 0.566391 edges= 9799 schur= 0 lambda= 6658.554263 levenbergIter= 1 iteration= 1 chi2= 234706314.970484 time= 0.506822 cumTime= 1.07321 edges= 9799 schur= 0 lambda= 2219.518088 levenbergIter= 1 iteration= 2 chi2= 142146174.348537 time= 0.502332 cumTime= 1.57554 edges= 9799 schur= 0 lambda= 739.839363 levenbergIter= 1 iteration= 3 chi2= 83834595.145595 time= 0.617319 cumTime= 2.19286 edges= 9799 schur= 0 lambda= 246.613121 levenbergIter= 1 iteration= 4 chi2= 41878079.903257 time= 0.542277 cumTime= 2.73514 edges= 9799 schur= 0 lambda= 82.204374 levenbergIter= 1 iteration= 5 chi2= 16598628.119947 time= 0.519183 cumTime= 3.25432 edges= 9799 schur= 0 lambda= 27.401458 levenbergIter= 1 iteration= 6 chi2= 6137666.739405 time= 0.53891 cumTime= 3.79323 edges= 9799 schur= 0 lambda= 9.133819 levenbergIter= 1 iteration= 7 chi2= 2182986.250593 time= 0.535928 cumTime= 4.32916 edges= 9799 schur= 0 lambda= 3.044606 levenbergIter= 1 iteration= 8 chi2= 732676.668220 time= 0.477907 cumTime= 4.80707 edges= 9799 schur= 0 lambda= 1.014869 levenbergIter= 1 iteration= 9 chi2= 284457.115176 time= 0.48001 cumTime= 5.28708 edges= 9799 schur= 0 lambda= 0.338290 levenbergIter= 1 iteration= 10 chi2= 170796.109734 time= 0.497792 cumTime= 5.78487 edges= 9799 schur= 0 lambda= 0.181974 levenbergIter= 1 iteration= 11 chi2= 145466.315841 time= 0.527085 cumTime= 6.31196 edges= 9799 schur= 0 lambda= 0.060658 levenbergIter= 1 iteration= 12 chi2= 142373.179500 time= 0.546491 cumTime= 6.85845 edges= 9799 schur= 0 lambda= 0.020219 levenbergIter= 1 iteration= 13 chi2= 137485.756901 time= 0.544264 cumTime= 7.40271 edges= 9799 schur= 0 lambda= 0.006740 levenbergIter= 1 iteration= 14 chi2= 131202.175668 time= 0.484477 cumTime= 7.88719 edges= 9799 schur= 0 lambda= 0.002247 levenbergIter= 1 iteration= 15 chi2= 128006.202530 time= 0.481649 cumTime= 8.36884 edges= 9799 schur= 0 lambda= 0.000749 levenbergIter= 1 iteration= 16 chi2= 127587.860945 time= 0.707194 cumTime= 9.07603 edges= 9799 schur= 0 lambda= 0.000250 levenbergIter= 1 iteration= 17 chi2= 127578.599359 time= 0.537201 cumTime= 9.61323 edges= 9799 schur= 0 lambda= 0.000083 levenbergIter= 1 iteration= 18 chi2= 127578.573853 time= 0.476409 cumTime= 10.0896 edges= 9799 schur= 0 lambda= 0.000028 levenbergIter= 1 iteration= 19 chi2= 127578.573840 time= 0.504015 cumTime= 10.5937 edges= 9799 schur= 0 lambda= 0.000018 levenbergIter= 1 iteration= 20 chi2= 127578.573840 time= 0.488356 cumTime= 11.082 edges= 9799 schur= 0 lambda= 0.000012 levenbergIter= 1 iteration= 21 chi2= 127578.573840 time= 0.486927 cumTime= 11.5689 edges= 9799 schur= 0 lambda= 0.000008 levenbergIter= 1 iteration= 22 chi2= 127578.573840 time= 1.51253 cumTime= 13.0815 edges= 9799 schur= 0 lambda= 0.000044 levenbergIter= 3 iteration= 23 chi2= 127578.573840 time= 1.47973 cumTime= 14.5612 edges= 9799 schur= 0 lambda= 0.000234 levenbergIter= 3 iteration= 24 chi2= 127578.573840 time= 4.95243 cumTime= 19.5136 edges= 9799 schur= 0 lambda= 5483030743.383683 levenbergIter= 10 saving optimization results ...

10.2.2 g2o原聲位姿圖優化

代碼及詳細注釋如下:

#include <iostream> #include <fstream> #include <string>#include <g2o/types/slam3d/types_slam3d.h> #include <g2o/core/block_solver.h> #include <g2o/core/optimization_algorithm_levenberg.h> #include <g2o/solvers/eigen/linear_solver_eigen.h>using namespace std;/************************************************* 本程序演示如何用g2o solver進行位姿圖優化* sphere.g2o是人工生成的一個Pose graph，我們來優化它。* 盡管可以直接通過load函數讀取整個圖，但我們還是自己來實現讀取代碼，以期獲得更深刻的理解* 這里使用g2o/types/slam3d/中的SE3表示位姿，它實質上是四元數而非李代數.* **********************************************/int main(int argc, char **argv) {//不用定義頂點和邊if (argc != 2) {cout << "Usage: pose_graph_g2o_SE3 sphere.g2o" << endl;return 1;}ifstream fin(argv[1]);if (!fin) {cout << "file " << argv[1] << " does not exist." << endl;return 1;}// 設定g2o// 使用g2o/types/slam3d/中的SE3表示位姿，它實質上是四元數而非李代數typedef g2o::BlockSolver<g2o::BlockSolverTraits<6, 6>> BlockSolverType; //頂點6維，邊6維typedef g2o::LinearSolverEigen<BlockSolverType::PoseMatrixType> LinearSolverType;auto solver = new g2o::OptimizationAlgorithmLevenberg(g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));g2o::SparseOptimizer optimizer; // 圖模型optimizer.setAlgorithm(solver); // 設置求解器optimizer.setVerbose(true); // 打開調試輸出int vertexCnt = 0, edgeCnt = 0; // 頂點和邊的數量while (!fin.eof()) {string name;fin >> name;if (name == "VERTEX_SE3:QUAT") {// SE3 頂點g2o::VertexSE3 *v = new g2o::VertexSE3();int index = 0;fin>>index;//編號v->setId(index);//設置頂點編號v->read(fin);//讀取邊就是setEstimate()optimizer.addVertex(v);//加入頂點vertexCnt++;//頂點個數++//設置是否固定，第一幀固定if (index == 0)v->setFixed(true);} else if (name == "EDGE_SE3:QUAT") {// SE3-SE3 邊g2o::EdgeSE3 *e = new g2o::EdgeSE3();int idx1, idx2; // 關聯的兩個頂點fin >> idx1 >> idx2;e->setId(edgeCnt++);//設置idx所對應的頂點e->setVertex(0, optimizer.vertices()[idx1]);e->setVertex(1, optimizer.vertices()[idx2]);e->read(fin); //讀取觀測數據optimizer.addEdge(e); //加入邊}if (!fin.good()) break;}cout << "read total " << vertexCnt << " vertices, " << edgeCnt << " edges." << endl;cout << "optimizing ..." << endl;optimizer.initializeOptimization(); //優化初始化optimizer.optimize(30); //迭代次數cout << "saving optimization results ..." << endl;optimizer.save("result.g2o");//保存優化后的文件return 0; }

結果如下所示:

read total 2500 vertices, 9799 edges. optimizing ... iteration= 0 chi2= 1023011093.967642 time= 0.422639 cumTime= 0.422639 edges= 9799 schur= 0 lambda= 805.622433 levenbergIter= 1 iteration= 1 chi2= 385118688.233188 time= 0.382178 cumTime= 0.804817 edges= 9799 schur= 0 lambda= 537.081622 levenbergIter= 1 iteration= 2 chi2= 166223726.693658 time= 0.42988 cumTime= 1.2347 edges= 9799 schur= 0 lambda= 358.054415 levenbergIter= 1 iteration= 3 chi2= 86610874.269316 time= 0.462892 cumTime= 1.69759 edges= 9799 schur= 0 lambda= 238.702943 levenbergIter= 1 iteration= 4 chi2= 40582782.710190 time= 0.420185 cumTime= 2.11777 edges= 9799 schur= 0 lambda= 159.135295 levenbergIter= 1 iteration= 5 chi2= 15055383.753040 time= 0.39671 cumTime= 2.51448 edges= 9799 schur= 0 lambda= 101.425210 levenbergIter= 1 iteration= 6 chi2= 6715193.487654 time= 0.377734 cumTime= 2.89222 edges= 9799 schur= 0 lambda= 37.664667 levenbergIter= 1 iteration= 7 chi2= 2171949.168383 time= 0.405097 cumTime= 3.29732 edges= 9799 schur= 0 lambda= 12.554889 levenbergIter= 1 iteration= 8 chi2= 740566.827049 time= 0.370052 cumTime= 3.66737 edges= 9799 schur= 0 lambda= 4.184963 levenbergIter= 1 iteration= 9 chi2= 313641.802464 time= 0.360452 cumTime= 4.02782 edges= 9799 schur= 0 lambda= 2.583432 levenbergIter= 1 iteration= 10 chi2= 82659.743578 time= 0.367851 cumTime= 4.39567 edges= 9799 schur= 0 lambda= 0.861144 levenbergIter= 1 iteration= 11 chi2= 58220.369189 time= 0.384526 cumTime= 4.7802 edges= 9799 schur= 0 lambda= 0.287048 levenbergIter= 1 iteration= 12 chi2= 52214.188561 time= 0.36656 cumTime= 5.14676 edges= 9799 schur= 0 lambda= 0.095683 levenbergIter= 1 iteration= 13 chi2= 50948.580336 time= 0.382879 cumTime= 5.52963 edges= 9799 schur= 0 lambda= 0.031894 levenbergIter= 1 iteration= 14 chi2= 50587.776729 time= 0.3974 cumTime= 5.92703 edges= 9799 schur= 0 lambda= 0.016436 levenbergIter= 1 iteration= 15 chi2= 50233.038802 time= 0.388748 cumTime= 6.31578 edges= 9799 schur= 0 lambda= 0.010957 levenbergIter= 1 iteration= 16 chi2= 49995.082836 time= 0.41957 cumTime= 6.73535 edges= 9799 schur= 0 lambda= 0.007305 levenbergIter= 1 iteration= 17 chi2= 48876.738968 time= 0.757956 cumTime= 7.49331 edges= 9799 schur= 0 lambda= 0.009298 levenbergIter= 2 iteration= 18 chi2= 48806.625520 time= 0.373177 cumTime= 7.86648 edges= 9799 schur= 0 lambda= 0.006199 levenbergIter= 1 iteration= 19 chi2= 47790.891374 time= 0.788389 cumTime= 8.65487 edges= 9799 schur= 0 lambda= 0.008265 levenbergIter= 2 iteration= 20 chi2= 47713.626578 time= 0.427388 cumTime= 9.08226 edges= 9799 schur= 0 lambda= 0.005510 levenbergIter= 1 iteration= 21 chi2= 46869.323691 time= 0.799491 cumTime= 9.88175 edges= 9799 schur= 0 lambda= 0.007347 levenbergIter= 2 iteration= 22 chi2= 46802.585509 time= 0.393055 cumTime= 10.2748 edges= 9799 schur= 0 lambda= 0.004898 levenbergIter= 1 iteration= 23 chi2= 46128.758046 time= 0.736299 cumTime= 11.0111 edges= 9799 schur= 0 lambda= 0.006489 levenbergIter= 2 iteration= 24 chi2= 46069.133544 time= 0.389972 cumTime= 11.4011 edges= 9799 schur= 0 lambda= 0.004326 levenbergIter= 1 iteration= 25 chi2= 45553.862168 time= 0.960659 cumTime= 12.3617 edges= 9799 schur= 0 lambda= 0.005595 levenbergIter= 2 iteration= 26 chi2= 45511.762622 time= 0.480517 cumTime= 12.8423 edges= 9799 schur= 0 lambda= 0.003730 levenbergIter= 1 iteration= 27 chi2= 45122.763002 time= 0.701183 cumTime= 13.5434 edges= 9799 schur= 0 lambda= 0.004690 levenbergIter= 2 iteration= 28 chi2= 45095.174401 time= 0.426408 cumTime= 13.9698 edges= 9799 schur= 0 lambda= 0.003127 levenbergIter= 1 iteration= 29 chi2= 44811.248507 time= 0.788535 cumTime= 14.7584 edges= 9799 schur= 0 lambda= 0.003785 levenbergIter= 2 saving optimization results ...

利用g2o_viewer 顯示結果如下:(注意文件路徑)

g2o_viewer sphere.g2o g2o_viewer result_lie.g2o

sphere.g2o
result_lie.g2o

調試遇到問題bug

本章調試遇到bug和第8章基本一致,此外還遇到fmt報錯問題,都可以通過修改CmakeList調試通過
修改如下:set(CMAKE_CXX_FLAGS "-O3 -std=c++11")改為set(CMAKE_CXX_FLAGS "-std=c++14 -O2 ${SSE_FLAGS} -msse4"),在每一個target_link_libraries末尾加上 fmt.

cmake_minimum_required(VERSION 2.8) project(pose_graph)set(CMAKE_BUILD_TYPE "Release") #set(CMAKE_CXX_FLAGS "-std=c++11 -O2") set(CMAKE_CXX_FLAGS "-std=c++14 -O2 ${SSE_FLAGS} -msse4")list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake_modules)# Eigen include_directories("/usr/include/eigen3")# sophus find_package(Sophus REQUIRED) include_directories(${Sophus_INCLUDE_DIRS})# g2o find_package(G2O REQUIRED) include_directories(${G2O_INCLUDE_DIRS})add_executable(pose_graph_g2o_SE3 pose_graph_g2o_SE3.cpp) target_link_libraries(pose_graph_g2o_SE3g2o_core g2o_stuff g2o_types_slam3d ${CHOLMOD_LIBRARIES} fmt)add_executable(pose_graph_g2o_lie pose_graph_g2o_lie_algebra.cpp) target_link_libraries(pose_graph_g2o_lieg2o_core g2o_stuff${CHOLMOD_LIBRARIES}${Sophus_LIBRARIES} fmt)

參考博客

SLAM十四講-后端2-ch10-代碼注釋(位姿圖優化)

SLAM14講學習筆記（七）后端（BA與圖優化，Pose Graph優化的理論與公式詳解、因子圖優化）

總結

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