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相机imu外参标定

1. 第一步初始化imu外参(可以从参数文档中读取，也可以计算出)，VINS中处理如下：

# Extrinsic parameter between IMU and Camera.
estimate_extrinsic: 0   # 0  Have an accurate extrinsic parameters. We will trust the following imu^R_cam, imu^T_cam, don't change it.
                        # 1  Have an initial guess about extrinsic parameters. We will optimize around your initial guess.
                        # 2  Don't know anything about extrinsic parameters. You don't need to give R,T. We will try to calibrate it. Do some rotation movement at beginning.                        
#If you choose 0 or 1, you should write down the following matrix.
#Rotation from camera frame to imu frame, imu^R_cam
extrinsicRotation: !!opencv-matrix
   rows: 3
   cols: 3
   dt: d
   data: [0.0148655429818, -0.999880929698, 0.00414029679422,
           0.999557249008, 0.0149672133247, 0.025715529948, 
           -0.0257744366974, 0.00375618835797, 0.999660727178]
#Translation from camera frame to imu frame, imu^T_cam
extrinsicTranslation: !!opencv-matrix
   rows: 3
   cols: 1
   dt: d
   data: [-0.0216401454975,-0.064676986768, 0.00981073058949]

2. 在优化中，每来一帧则对外参更新一次

Matrix3d ric[NUM_OF_CAM];
Vector3d tic[NUM_OF_CAM];

//添加参数块
ceres::LocalParameterization *local_parameterization = new PoseLocalParameterization();
problem.AddParameterBlock(para_Ex_Pose[i], SIZE_POSE, local_parameterization);
if (!ESTIMATE_EXTRINSIC)
{
    ROS_DEBUG("fix extinsic param");
    problem.SetParameterBlockConstant(para_Ex_Pose[i]);
}
else
    ROS_DEBUG("estimate extinsic param");

//添加残差块
if (ESTIMATE_TD)
{
        ProjectionTdFactor *f_td = new ProjectionTdFactor(pts_i, pts_j, it_per_id.feature_per_frame[0].velocity, it_per_frame
                                                         it_per_id.feature_per_frame[0].cur_td, it_per_frame.cur_td,
                                                         it_per_id.feature_per_frame[0].uv.y(), it_per_frame.uv.y());
        problem.AddResidualBlock(f_td, loss_function, para_Pose[imu_i], para_Pose[imu_j], para_Ex_Pose[0], para_Feature[feature_index], para_Td[0]);

}
else
{
    ProjectionFactor *f = new ProjectionFactor(pts_i, pts_j);
    problem.AddResidualBlock(f, loss_function, para_Pose[imu_i], para_Pose[imu_j], para_Ex_Pose[0], para_Feature[feature_inde
}

该残差块为视觉模型计算重投影误差 Vision Model

空间上的一个3D特征点会被camera多次观测到，j^th 图像帧的camera的残差值被定义为，考虑l^th特征点第一次在i^th图像帧中被观察到恢复的深度信息，投影到第j 帧图像帧的重投影误差。

3. 相机imu外参的重要性

外参是相机和imu之间的桥梁，后端优化是以imu的坐标系为优化基准，所以在进行重投影误差时需要使用外参将空间点转换到相机坐标系。
初始化的三角化时也会用到外参来求出两个相机之间的旋转平移。

f_manager.triangulate(Ps, &(TIC_TMP[0]), &(RIC[0]));

Eigen::Vector3d pts_camera_i = pts_i / inv_dep_i;
Eigen::Vector3d pts_imu_i = qic * pts_camera_i + tic;
Eigen::Vector3d pts_w = Qi * pts_imu_i + Pi;
Eigen::Vector3d pts_imu_j = Qj.inverse() * (pts_w - Pj);
Eigen::Vector3d pts_camera_j = qic.inverse() * (pts_imu_j - tic);
Eigen::Map<Eigen::Vector2d> residual(residuals);

$\begin{matrix} (1) & \begin{array}{rcl} r_{C} ({\hat{z}}_{l}^{c_{j}}, X) = {[\begin{matrix} b_{1} & b_{2} \end{matrix}]}^{T} \cdot ({\bar{P}}_{l}^{c_{j}} - \frac{P_{l}^{c_{j}}}{‖ P_{l}^{c_{j}} ‖}) \\ {\bar{P}}_{l}^{c_{j}} = π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{j}} \\ {\hat{v}}_{l}^{c_{j}} \end{matrix}]) \\ P_{l}^{c_{j}} = q_{b}^{c} (q_{w}^{b_{j}} (q_{b_{i}}^{w} (q_{c}^{b} \frac{1}{λ_{l}} π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{i}} \\ {\hat{v}}_{l}^{c_{i}} \end{matrix}]) + p_{c}^{b}) + p_{b_{i}}^{w} - p_{b_{j}}^{w}) - p_{b}^{c}) \end{array} \end{matrix}$ $\begin{matrix} (1) & \begin{array}{rcl} r_{C} ({\hat{z}}_{l}^{c_{j}}, X) = {[\begin{matrix} b_{1} & b_{2} \end{matrix}]}^{T} \cdot ({\bar{P}}_{l}^{c_{j}} - \frac{P_{l}^{c_{j}}}{‖ P_{l}^{c_{j}} ‖}) \\ {\bar{P}}_{l}^{c_{j}} = π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{j}} \\ {\hat{v}}_{l}^{c_{j}} \end{matrix}]) \\ P_{l}^{c_{j}} = q_{b}^{c} (q_{w}^{b_{j}} (q_{b_{i}}^{w} (q_{c}^{b} \frac{1}{λ_{l}} π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{i}} \\ {\hat{v}}_{l}^{c_{i}} \end{matrix}]) + p_{c}^{b}) + p_{b_{i}}^{w} - p_{b_{j}}^{w}) - p_{b}^{c}) \end{array} \end{matrix}$ $\begin{matrix} (1) & \begin{array}{rcl} r_{C} ({\hat{z}}_{l}^{c_{j}}, X) = {[\begin{matrix} b_{1} & b_{2} \end{matrix}]}^{T} \cdot ({\bar{P}}_{l}^{c_{j}} - \frac{P_{l}^{c_{j}}}{‖ P_{l}^{c_{j}} ‖}) \\ {\bar{P}}_{l}^{c_{j}} = π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{j}} \\ {\hat{v}}_{l}^{c_{j}} \end{matrix}]) \\ P_{l}^{c_{j}} = q_{b}^{c} (q_{w}^{b_{j}} (q_{b_{i}}^{w} (q_{c}^{b} \frac{1}{λ_{l}} π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{i}} \\ {\hat{v}}_{l}^{c_{i}} \end{matrix}]) + p_{c}^{b}) + p_{b_{i}}^{w} - p_{b_{j}}^{w}) - p_{b}^{c}) \end{array} \end{matrix}$ $\begin{matrix} (1) & \begin{array}{rcl} r_{C} ({\hat{z}}_{l}^{c_{j}}, X) = {[\begin{matrix} b_{1} & b_{2} \end{matrix}]}^{T} \cdot ({\bar{P}}_{l}^{c_{j}} - \frac{P_{l}^{c_{j}}}{‖ P_{l}^{c_{j}} ‖}) \\ {\bar{P}}_{l}^{c_{j}} = π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{j}} \\ {\hat{v}}_{l}^{c_{j}} \end{matrix}]) \\ P_{l}^{c_{j}} = q_{b}^{c} (q_{w}^{b_{j}} (q_{b_{i}}^{w} (q_{c}^{b} \frac{1}{λ_{l}} π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{i}} \\ {\hat{v}}_{l}^{c_{i}} \end{matrix}]) + p_{c}^{b}) + p_{b_{i}}^{w} - p_{b_{j}}^{w}) - p_{b}^{c}) \end{array} \end{matrix}$ $\begin{matrix} (1) & \begin{array}{rcl} r_{C} ({\hat{z}}_{l}^{c_{j}}, X) = {[\begin{matrix} b_{1} & b_{2} \end{matrix}]}^{T} \cdot ({\bar{P}}_{l}^{c_{j}} - \frac{P_{l}^{c_{j}}}{‖ P_{l}^{c_{j}} ‖}) \\ {\bar{P}}_{l}^{c_{j}} = π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{j}} \\ {\hat{v}}_{l}^{c_{j}} \end{matrix}]) \\ P_{l}^{c_{j}} = q_{b}^{c} (q_{w}^{b_{j}} (q_{b_{i}}^{w} (q_{c}^{b} \frac{1}{λ_{l}} π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{i}} \\ {\hat{v}}_{l}^{c_{i}} \end{matrix}]) + p_{c}^{b}) + p_{b_{i}}^{w} - p_{b_{j}}^{w}) - p_{b}^{c}) \end{array} \end{matrix}$ $\begin{matrix} (1) & \begin{array}{rcl} r_{C} ({\hat{z}}_{l}^{c_{j}}, X) = {[\begin{matrix} b_{1} & b_{2} \end{matrix}]}^{T} \cdot ({\bar{P}}_{l}^{c_{j}} - \frac{P_{l}^{c_{j}}}{‖ P_{l}^{c_{j}} ‖}) \\ {\bar{P}}_{l}^{c_{j}} = π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{j}} \\ {\hat{v}}_{l}^{c_{j}} \end{matrix}]) \\ P_{l}^{c_{j}} = q_{b}^{c} (q_{w}^{b_{j}} (q_{b_{i}}^{w} (q_{c}^{b} \frac{1}{λ_{l}} π_{c}^{- 1} ([\begin{matrix} {\hat{u}}_{l}^{c_{i}} \\ {\hat{v}}_{l}^{c_{i}} \end{matrix}]) + p_{c}^{b}) + p_{b_{i}}^{w} - p_{b_{j}}^{w}) - p_{b}^{c}) \end{array} \end{matrix}$

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原文地址：https://www.cnblogs.com/mybrave/p/9414034.html