c++(0) sophus矩阵转换

1安装sophus

2 使用代码

2-1 R,t矩阵 q四元数转换so3和se3

 CMakeLists.txt

cmake_minimum_required(VERSION 3.0)
project(useSophus)

# 为使用 sophus，需要使用find_package命令找到它
find_package(Sophus REQUIRED)

# Eigen
include_directories("/usr/include/eigen3")
add_executable(useSophus useSophus.cpp)
target_link_libraries(useSophus Sophus::Sophus)

add_subdirectory(example)

　　useSophus.cpp

#include <iostream>
#include <cmath>
#include <Eigen/Core>
#include <Eigen/Geometry>
#include "sophus/se3.hpp"

using namespace std;
using namespace Eigen;

/// 本程序演示sophus的基本用法

int main(int argc, char **argv) {

  // 沿Z轴转90度的旋转矩阵
  Matrix3d R = AngleAxisd(M_PI / 2, Vector3d(0, 0, 1)).toRotationMatrix();
  // 或者四元数
  Quaterniond q(R);
  Sophus::SO3d SO3_R(R);              // Sophus::SO3d可以直接从旋转矩阵构造
  Sophus::SO3d SO3_q(q);              // 也可以通过四元数构造
  // 二者是等价的
  cout << "SO(3) from matrix:\n" << SO3_R.matrix() << endl;
  cout << "SO(3) from quaternion:\n" << SO3_q.matrix() << endl;
  cout << "they are equal" << endl;

  // 使用对数映射获得它的李代数
  Vector3d so3 = SO3_R.log();
  cout << "so3 = " << so3.transpose() << endl;
  // hat 为向量到反对称矩阵
  cout << "so3 hat=\n" << Sophus::SO3d::hat(so3) << endl;
  // 相对的，vee为反对称到向量
  cout << "so3 hat vee= " << Sophus::SO3d::vee(Sophus::SO3d::hat(so3)).transpose() << endl;

  // 增量扰动模型的更新
  Vector3d update_so3(1e-4, 0, 0); //假设更新量为这么多
  Sophus::SO3d SO3_updated = Sophus::SO3d::exp(update_so3) * SO3_R;
  cout << "SO3 updated = \n" << SO3_updated.matrix() << endl;

  cout << "*******************************" << endl;
  // 对SE(3)操作大同小异
  Vector3d t(1, 0, 0);           // 沿X轴平移1
  Sophus::SE3d SE3_Rt(R, t);           // 从R,t构造SE(3)
  Sophus::SE3d SE3_qt(q, t);            // 从q,t构造SE(3)
  cout << "SE3 from R,t= \n" << SE3_Rt.matrix() << endl;
  cout << "SE3 from q,t= \n" << SE3_qt.matrix() << endl;
  // 李代数se(3) 是一个六维向量，方便起见先typedef一下
  typedef Eigen::Matrix<double, 6, 1> Vector6d;
  Vector6d se3 = SE3_Rt.log();
  cout << "se3 = " << se3.transpose() << endl;
  // 观察输出，会发现在Sophus中，se(3)的平移在前，旋转在后.
  // 同样的，有hat和vee两个算符
  cout << "se3 hat = \n" << Sophus::SE3d::hat(se3) << endl;
  cout << "se3 hat vee = " << Sophus::SE3d::vee(Sophus::SE3d::hat(se3)).transpose() << endl;

  // 最后，演示一下更新
  Vector6d update_se3; //更新量
  update_se3.setZero();
  update_se3(0, 0) = 1e-4;
  Sophus::SE3d SE3_updated = Sophus::SE3d::exp(update_se3) * SE3_Rt;
  cout << "SE3 updated = " << endl << SE3_updated.matrix() << endl;

  return 0;
}

例子2  真值和测量值计算平均方误差

 CMakeLists.txt

option(USE_UBUNTU_20 "Set to ON if you are using Ubuntu 20.04" OFF)
find_package(Pangolin REQUIRED)
if(USE_UBUNTU_20)
    message("You are using Ubuntu 20.04, fmt::fmt will be linked")
    find_package(fmt REQUIRED)
    set(FMT_LIBRARIES fmt::fmt)
endif()
include_directories(${Pangolin_INCLUDE_DIRS})
add_executable(trajectoryError trajectoryError.cpp)
target_link_libraries(trajectoryError ${Pangolin_LIBRARIES} ${FMT_LIBRARIES})

　　trajectoryError.cpp

#include <iostream>
#include <fstream>
#include <unistd.h>
#include <pangolin/pangolin.h>
#include <sophus/se3.hpp>

using namespace Sophus;
using namespace std;

string groundtruth_file = "./example/groundtruth.txt";
string estimated_file = "./example/estimated.txt";

typedef vector<Sophus::SE3d, Eigen::aligned_allocator<Sophus::SE3d>> TrajectoryType;

void DrawTrajectory(const TrajectoryType &gt, const TrajectoryType &esti);

TrajectoryType ReadTrajectory(const string &path);

int main(int argc, char **argv) {
  TrajectoryType groundtruth = ReadTrajectory(groundtruth_file);
  TrajectoryType estimated = ReadTrajectory(estimated_file);
  assert(!groundtruth.empty() && !estimated.empty());
  assert(groundtruth.size() == estimated.size());

  // compute rmse
  double rmse = 0;
  for (size_t i = 0; i < estimated.size(); i++) {
    Sophus::SE3d p1 = estimated[i], p2 = groundtruth[i];
    double error = (p2.inverse() * p1).log().norm();
    rmse += error * error;
  }
  rmse = rmse / double(estimated.size());
  rmse = sqrt(rmse);
  cout << "RMSE = " << rmse << endl;

  DrawTrajectory(groundtruth, estimated);
  return 0;
}

TrajectoryType ReadTrajectory(const string &path) {
  ifstream fin(path);
  TrajectoryType trajectory;
  if (!fin) {
    cerr << "trajectory " << path << " not found." << endl;
    return trajectory;
  }

  while (!fin.eof()) {
    double time, tx, ty, tz, qx, qy, qz, qw;
    fin >> time >> tx >> ty >> tz >> qx >> qy >> qz >> qw;
    Sophus::SE3d p1(Eigen::Quaterniond(qw, qx, qy, qz), Eigen::Vector3d(tx, ty, tz));
    trajectory.push_back(p1);
  }
  return trajectory;
}

void DrawTrajectory(const TrajectoryType &gt, const TrajectoryType &esti) {
  // create pangolin window and plot the trajectory
  pangolin::CreateWindowAndBind("Trajectory Viewer", 1024, 768);
  glEnable(GL_DEPTH_TEST);
  glEnable(GL_BLEND);
  glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

  pangolin::OpenGlRenderState s_cam(
      pangolin::ProjectionMatrix(1024, 768, 500, 500, 512, 389, 0.1, 1000),
      pangolin::ModelViewLookAt(0, -0.1, -1.8, 0, 0, 0, 0.0, -1.0, 0.0)
  );

  pangolin::View &d_cam = pangolin::CreateDisplay()
      .SetBounds(0.0, 1.0, pangolin::Attach::Pix(175), 1.0, -1024.0f / 768.0f)
      .SetHandler(new pangolin::Handler3D(s_cam));


  while (pangolin::ShouldQuit() == false) {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    d_cam.Activate(s_cam);
    glClearColor(1.0f, 1.0f, 1.0f, 1.0f);

    glLineWidth(2);
    for (size_t i = 0; i < gt.size() - 1; i++) {
      glColor3f(0.0f, 0.0f, 1.0f);  // blue for ground truth
      glBegin(GL_LINES);
      auto p1 = gt[i], p2 = gt[i + 1];
      glVertex3d(p1.translation()[0], p1.translation()[1], p1.translation()[2]);
      glVertex3d(p2.translation()[0], p2.translation()[1], p2.translation()[2]);
      glEnd();
    }

    for (size_t i = 0; i < esti.size() - 1; i++) {
      glColor3f(1.0f, 0.0f, 0.0f);  // red for estimated
      glBegin(GL_LINES);
      auto p1 = esti[i], p2 = esti[i + 1];
      glVertex3d(p1.translation()[0], p1.translation()[1], p1.translation()[2]);
      glVertex3d(p2.translation()[0], p2.translation()[1], p2.translation()[2]);
      glEnd();
    }
    pangolin::FinishFrame();
    usleep(5000);   // sleep 5 ms
  }

}