VINS（七）estimator_node 数据对齐 imu预积分 vision

首先通过vins_estimator mode监听几个Topic（频率2000Hz），将imu数据，feature数据，raw_image数据（用于回环检测）通过各自的回调函数封装起来

ros::Subscriber sub_imu = n.subscribe(IMU_TOPIC, 2000, imu_callback, ros::TransportHints().tcpNoDelay());
ros::Subscriber sub_image = n.subscribe("/feature_tracker/feature", 2000, feature_callback);
ros::Subscriber sub_raw_image = n.subscribe(IMAGE_TOPIC, 2000, raw_image_callback);

imu_buf.push(imu_msg);
feature_buf.push(feature_msg);
image_buf.push(make_pair(img_ptr->image, img_msg->header.stamp.toSec()));

然后开启处理measurement的线程

std::thread measurement_process{process};

process()函数中，首先将获取的传感器数据imu_buf feature_buf对齐，注意这里只保证了相邻的feature数据之间有完整的imu数据，并不能保证imu和feature数据的精确对齐

// multiple IMU measurements and only one vision(features) measurements
std::vector<std::pair<std::vector<sensor_msgs::ImuConstPtr>, sensor_msgs::PointCloudConstPtr>>
getMeasurements()
{
    std::vector<std::pair<std::vector<sensor_msgs::ImuConstPtr>, sensor_msgs::PointCloudConstPtr>> measurements;

    while (true)
    {
        if (imu_buf.empty() || feature_buf.empty())
            return measurements;

        // synchronize, if strictly synchronize, should change to ">="
        // end up with : imu_buf.front()->header.stamp < feature_buf.front()->header.stamp
        
        // 1. should have overlap
        if (!(imu_buf.back()->header.stamp > feature_buf.front()->header.stamp))
        {
            ROS_WARN("wait for imu, only should happen at the beginning");
            sum_of_wait++;
            return measurements;
        }

        // 2. should have complete imu measurements between two feature_buf msg
        if (!(imu_buf.front()->header.stamp < feature_buf.front()->header.stamp))
        {
            ROS_WARN("throw img, only should happen at the beginning");
            feature_buf.pop();
            continue;
        }
        
        sensor_msgs::PointCloudConstPtr img_msg = feature_buf.front();
        feature_buf.pop();

        std::vector<sensor_msgs::ImuConstPtr> IMUs;
        while (imu_buf.front()->header.stamp <= img_msg->header.stamp)
        {
            IMUs.emplace_back(imu_buf.front());
            imu_buf.pop();
        }

        measurements.emplace_back(IMUs, img_msg);
    }
    return measurements;
}

接下来进入对measurements数据的处理：

处理imu数据的接口函数是processIMU()

处理vision数据的借口函数是processImage()

（一）IMU

1. 核心API：

midPointIntegration(_dt, acc_0, gyr_0, _acc_1, _gyr_1, delta_p, delta_q, delta_v,
                            linearized_ba, linearized_bg,
                            result_delta_p, result_delta_q, result_delta_v,
                            result_linearized_ba, result_linearized_bg, 1);

其中，0代表上次测量值，1代表当前测量值，delta_p，delta_q，delta_v代表相对预积分初始参考系的位移，旋转四元数，以及速度（例如，从k帧预积分到k+1帧，则参考系是k帧的imu坐标系）

对应实现的是公式：

相应的离散实现使用Euler，Mid-point，或者龙格库塔（RK4）数值积分方法。

Euler方法如下：

2. 求状态向量对bias的Jacobian，当bias变化较小时，使用Jacobian去更新状态；否则需要以当前imu为参考系，重新预积分，对应repropagation()。同时，需要计算error state model中误差传播方程的系数矩阵F和V：

    // pre-integration 
    // time interval of two imu; last and current imu measurements; p,q,v relate to local frame; ba and bg; propagated p,q,v,ba,bg; 
    // whether to update Jacobian and calculate F,V
    void midPointIntegration(double _dt, 
                            const Eigen::Vector3d &_acc_0, const Eigen::Vector3d &_gyr_0,
                            const Eigen::Vector3d &_acc_1, const Eigen::Vector3d &_gyr_1,
                            const Eigen::Vector3d &delta_p, const Eigen::Quaterniond &delta_q, const Eigen::Vector3d &delta_v,
                            const Eigen::Vector3d &linearized_ba, const Eigen::Vector3d &linearized_bg,
                            Eigen::Vector3d &result_delta_p, Eigen::Quaterniond &result_delta_q, Eigen::Vector3d &result_delta_v,
                            Eigen::Vector3d &result_linearized_ba, Eigen::Vector3d &result_linearized_bg, bool update_jacobian)
    {
        //ROS_INFO("midpoint integration");
        // mid-point integration with bias = 0
        Vector3d un_acc_0 = delta_q * (_acc_0 - linearized_ba); 
        Vector3d un_gyr = 0.5 * (_gyr_0 + _gyr_1) - linearized_bg;
        result_delta_q = delta_q * Quaterniond(1, un_gyr(0) * _dt / 2, un_gyr(1) * _dt / 2, un_gyr(2) * _dt / 2);
        Vector3d un_acc_1 = result_delta_q * (_acc_1 - linearized_ba);
        Vector3d un_acc = 0.5 * (un_acc_0 + un_acc_1);
        result_delta_p = delta_p + delta_v * _dt + 0.5 * un_acc * _dt * _dt;
        result_delta_v = delta_v + un_acc * _dt;
        // ba and bg donot change
        result_linearized_ba = linearized_ba;
        result_linearized_bg = linearized_bg;

        // jacobian to bias, used when the bias changes slightly and no need of repropagation
        if(update_jacobian)
        {
            // same as un_gyr, gyrometer reference to the local frame bk
            Vector3d w_x = 0.5 * (_gyr_0 + _gyr_1) - linearized_bg;
            
            // last acceleration measurement
            Vector3d a_0_x = _acc_0 - linearized_ba;
            // current acceleration measurement
            Vector3d a_1_x = _acc_1 - linearized_ba;
            
            // used for cross-product
            // pay attention to derivation of matrix product
            Matrix3d R_w_x, R_a_0_x, R_a_1_x;

            R_w_x<<0, -w_x(2), w_x(1),
                w_x(2), 0, -w_x(0),
                -w_x(1), w_x(0), 0;
            R_a_0_x<<0, -a_0_x(2), a_0_x(1),
                a_0_x(2), 0, -a_0_x(0),
                -a_0_x(1), a_0_x(0), 0;
            R_a_1_x<<0, -a_1_x(2), a_1_x(1),
                a_1_x(2), 0, -a_1_x(0),
                -a_1_x(1), a_1_x(0), 0;

            // error state model
            // should use discrete format and mid-point approximation
            MatrixXd F = MatrixXd::Zero(15, 15);
            F.block<3, 3>(0, 0) = Matrix3d::Identity();
            F.block<3, 3>(0, 3) = -0.25 * delta_q.toRotationMatrix() * R_a_0_x * _dt * _dt + 
                                  -0.25 * result_delta_q.toRotationMatrix() * R_a_1_x * (Matrix3d::Identity() - R_w_x * _dt) * _dt * _dt;
            F.block<3, 3>(0, 6) = MatrixXd::Identity(3,3) * _dt;
            F.block<3, 3>(0, 9) = -0.25 * (delta_q.toRotationMatrix() + result_delta_q.toRotationMatrix()) * _dt * _dt;
            F.block<3, 3>(0, 12) = -0.25 * result_delta_q.toRotationMatrix() * R_a_1_x * _dt * _dt * -_dt;
            F.block<3, 3>(3, 3) = Matrix3d::Identity() - R_w_x * _dt;
            F.block<3, 3>(3, 12) = -1.0 * MatrixXd::Identity(3,3) * _dt;
            F.block<3, 3>(6, 3) = -0.5 * delta_q.toRotationMatrix() * R_a_0_x * _dt + 
                                  -0.5 * result_delta_q.toRotationMatrix() * R_a_1_x * (Matrix3d::Identity() - R_w_x * _dt) * _dt;
            F.block<3, 3>(6, 6) = Matrix3d::Identity();
            F.block<3, 3>(6, 9) = -0.5 * (delta_q.toRotationMatrix() + result_delta_q.toRotationMatrix()) * _dt;
            F.block<3, 3>(6, 12) = -0.5 * result_delta_q.toRotationMatrix() * R_a_1_x * _dt * -_dt;
            F.block<3, 3>(9, 9) = Matrix3d::Identity();
            F.block<3, 3>(12, 12) = Matrix3d::Identity();

            MatrixXd V = MatrixXd::Zero(15,18);
            V.block<3, 3>(0, 0) =  0.25 * delta_q.toRotationMatrix() * _dt * _dt;
            V.block<3, 3>(0, 3) =  0.25 * -result_delta_q.toRotationMatrix() * R_a_1_x  * _dt * _dt * 0.5 * _dt;
            V.block<3, 3>(0, 6) =  0.25 * result_delta_q.toRotationMatrix() * _dt * _dt;
            V.block<3, 3>(0, 9) =  V.block<3, 3>(0, 3);
            V.block<3, 3>(3, 3) =  0.5 * MatrixXd::Identity(3,3) * _dt;
            V.block<3, 3>(3, 9) =  0.5 * MatrixXd::Identity(3,3) * _dt;
            V.block<3, 3>(6, 0) =  0.5 * delta_q.toRotationMatrix() * _dt;
            V.block<3, 3>(6, 3) =  0.5 * -result_delta_q.toRotationMatrix() * R_a_1_x  * _dt * 0.5 * _dt;
            V.block<3, 3>(6, 6) =  0.5 * result_delta_q.toRotationMatrix() * _dt;
            V.block<3, 3>(6, 9) =  V.block<3, 3>(6, 3);
            V.block<3, 3>(9, 12) = MatrixXd::Identity(3,3) * _dt;
            V.block<3, 3>(12, 15) = MatrixXd::Identity(3,3) * _dt;

            //step_jacobian = F;
            //step_V = V;
            jacobian = F * jacobian;
            covariance = F * covariance * F.transpose() + V * noise * V.transpose();
        }
    }

（二）Vision

 首先判断该帧是否关键帧：

    if (f_manager.addFeatureCheckParallax(frame_count, image))
        marginalization_flag = MARGIN_OLD;
    else
        marginalization_flag = MARGIN_SECOND_NEW;

关键帧的判断依据是rotation-compensated过后的parallax足够大，并且tracking上的feature足够多；关键帧会保留在当前Sliding Window中，marginalize掉Sliding Window中最旧的状态，如果是非关键帧则优先marginalize掉。

1. 标定外参旋转矩阵

initial_ex_rotation.CalibrationExRotation(corres, pre_integrations[frame_count]->delta_q, calib_ric)

其中

pre_integrations[frame_count]->delta_q

是使用imu pre-integration获取的旋转矩阵，会和视觉跟踪求解fundamentalMatrix分解后获得的旋转矩阵构建约束方程，从而标定出外参旋转矩阵。

2. 线性初始化

    if (solver_flag == INITIAL)
    {
        if (frame_count == WINDOW_SIZE)
        {
            bool result = false;
            if( ESTIMATE_EXTRINSIC != 2 && (header.stamp.toSec() - initial_timestamp) > 0.1)
            {
               result = initialStructure();
               initial_timestamp = header.stamp.toSec();
            }
            if(result)
            {
                solver_flag = NON_LINEAR;
                solveOdometry();
                slideWindow();
                f_manager.removeFailures();
                ROS_INFO("Initialization finish!");
                last_R = Rs[WINDOW_SIZE];
                last_P = Ps[WINDOW_SIZE];
                last_R0 = Rs[0];
                last_P0 = Ps[0];
                
            }
            else
                slideWindow();
        }
        else
            frame_count++;
    }

3. 非线性优化

    else
    {
        TicToc t_solve;
        solveOdometry();
        ROS_DEBUG("solver costs: %fms", t_solve.toc());

        if (failureDetection())
        {
            ROS_WARN("failure detection!");
            failure_occur = 1;
            clearState();
            setParameter();
            ROS_WARN("system reboot!");
            return;
        }

        TicToc t_margin;
        slideWindow();
        f_manager.removeFailures();
        ROS_DEBUG("marginalization costs: %fms", t_margin.toc());
        // prepare output of VINS
        key_poses.clear();
        for (int i = 0; i <= WINDOW_SIZE; i++)
            key_poses.push_back(Ps[i]);

        last_R = Rs[WINDOW_SIZE];
        last_P = Ps[WINDOW_SIZE];
        last_R0 = Rs[0];
        last_P0 = Ps[0];
    }

 主要的初始化，非线性优化的api均在这里，因此放在后面去说明。