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/**
BSD 3-Clause License
This file is part of the Basalt project.
https://gitlab.com/VladyslavUsenko/basalt-headers.git
Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of the copyright holder nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@file
@brief Definition of static IMU biases used for calibration
*/
#pragma once
#include <Eigen/Dense>
namespace basalt {
/// @brief Static calibration for accelerometer.
///
/// Calibrates axis scaling and misalignment and has 9 parameters \f$ [b_x,
/// b_y, b_z, s_1, s_2, s_3, s_4, s_5, s_6]^T \f$.
/// \f[
/// a_c = \begin{bmatrix} s_1 + 1 & 0 & 0 \\ s_2 & s_4 + 1 & 0 \\ s_3 & s_5 &
/// s_6 + 1 \\ \end{bmatrix} a_r - \begin{bmatrix} b_x \\ b_y \\ b_z
/// \end{bmatrix}
/// \f] where \f$ a_c \f$ is a calibrated measurement and \f$ a_r \f$ is a
/// raw measurement. When all elements are zero applying calibration results in
/// Identity mapping.
template <typename Scalar>
class CalibAccelBias {
public:
using Vec3 = Eigen::Matrix<Scalar, 3, 1>;
using Mat33 = Eigen::Matrix<Scalar, 3, 3>;
/// @brief Default constructor with zero initialization.
inline CalibAccelBias() { accel_bias_full_.setZero(); }
/// @brief Set calibration to random values (used in unit-tests).
inline void setRandom() {
accel_bias_full_.setRandom();
accel_bias_full_.template head<3>() /= 10;
accel_bias_full_.template tail<6>() /= 100;
}
/// @brief Return const vector of parameters.
/// See detailed description in \ref CalibAccelBias.
inline const Eigen::Matrix<Scalar, 9, 1>& getParam() const {
return accel_bias_full_;
}
/// @brief Return vector of parameters. See detailed description in \ref
/// CalibAccelBias.
inline Eigen::Matrix<Scalar, 9, 1>& getParam() { return accel_bias_full_; }
/// @brief Increment the calibration vector
///
/// @param inc increment vector
inline void operator+=(const Eigen::Matrix<Scalar, 9, 1>& inc) {
accel_bias_full_ += inc;
}
/// @brief Return bias vector and scale matrix. See detailed description in
/// \ref CalibAccelBias.
inline void getBiasAndScale(Vec3& accel_bias, Mat33& accel_scale) const {
accel_bias = accel_bias_full_.template head<3>();
accel_scale.setZero();
accel_scale.col(0) = accel_bias_full_.template segment<3>(3);
accel_scale(1, 1) = accel_bias_full_(6);
accel_scale(2, 1) = accel_bias_full_(7);
accel_scale(2, 2) = accel_bias_full_(8);
}
/// @brief Calibrate the measurement. See detailed description in
/// \ref CalibAccelBias.
///
/// @param raw_measurement
/// @return calibrated measurement
inline Vec3 getCalibrated(const Vec3& raw_measurement) const {
Vec3 accel_bias;
Mat33 accel_scale;
getBiasAndScale(accel_bias, accel_scale);
return (raw_measurement + accel_scale * raw_measurement - accel_bias);
}
/// @brief Invert calibration (used in unit-tests).
///
/// @param calibrated_measurement
/// @return raw measurement
inline Vec3 invertCalibration(const Vec3& calibrated_measurement) const {
Vec3 accel_bias;
Mat33 accel_scale;
getBiasAndScale(accel_bias, accel_scale);
Mat33 accel_scale_inv =
(Eigen::Matrix3d::Identity() + accel_scale).inverse();
return accel_scale_inv * (calibrated_measurement + accel_bias);
}
private:
Eigen::Matrix<Scalar, 9, 1> accel_bias_full_;
};
/// @brief Static calibration for gyroscope.
///
/// Calibrates rotation, axis scaling and misalignment and has 12 parameters \f$
/// [b_x, b_y, b_z, s_1, s_2, s_3, s_4, s_5, s_6, s_7, s_8, s_9]^T \f$. \f[
/// \omega_c = \begin{bmatrix} s_1 + 1 & s_4 & s_7 \\ s_2 & s_5 + 1 & s_8 \\ s_3
/// & s_6 & s_9 +1 \\ \end{bmatrix} \omega_r - \begin{bmatrix} b_x \\ b_y
/// \\ b_z \end{bmatrix} \f] where \f$ \omega_c \f$ is a calibrated measurement
/// and \f$ \omega_r \f$ is a raw measurement. When all elements are zero
/// applying calibration results in Identity mapping.
template <typename Scalar>
class CalibGyroBias {
public:
using Vec3 = Eigen::Matrix<Scalar, 3, 1>;
using Mat33 = Eigen::Matrix<Scalar, 3, 3>;
/// @brief Default constructor with zero initialization.
inline CalibGyroBias() { gyro_bias_full_.setZero(); }
/// @brief Set calibration to random values (used in unit-tests).
inline void setRandom() {
gyro_bias_full_.setRandom();
gyro_bias_full_.template head<3>() /= 10;
gyro_bias_full_.template tail<9>() /= 100;
}
/// @brief Return const vector of parameters.
/// See detailed description in \ref CalibGyroBias.
inline const Eigen::Matrix<Scalar, 12, 1>& getParam() const {
return gyro_bias_full_;
}
/// @brief Return vector of parameters.
/// See detailed description in \ref CalibGyroBias.
inline Eigen::Matrix<Scalar, 12, 1>& getParam() { return gyro_bias_full_; }
/// @brief Increment the calibration vector
///
/// @param inc increment vector
inline void operator+=(const Eigen::Matrix<Scalar, 12, 1>& inc) {
gyro_bias_full_ += inc;
}
/// @brief Return bias vector and scale matrix. See detailed description in
/// \ref CalibGyroBias.
inline void getBiasAndScale(Vec3& gyro_bias, Mat33& gyro_scale) const {
gyro_bias = gyro_bias_full_.template head<3>();
gyro_scale.col(0) = gyro_bias_full_.template segment<3>(3);
gyro_scale.col(1) = gyro_bias_full_.template segment<3>(6);
gyro_scale.col(2) = gyro_bias_full_.template segment<3>(9);
}
/// @brief Calibrate the measurement. See detailed description in
/// \ref CalibGyroBias.
///
/// @param raw_measurement
/// @return calibrated measurement
inline Vec3 getCalibrated(const Vec3& raw_measurement) const {
Vec3 gyro_bias;
Mat33 gyro_scale;
getBiasAndScale(gyro_bias, gyro_scale);
return (raw_measurement + gyro_scale * raw_measurement - gyro_bias);
}
/// @brief Invert calibration (used in unit-tests).
///
/// @param calibrated_measurement
/// @return raw measurement
inline Vec3 invertCalibration(const Vec3& calibrated_measurement) const {
Vec3 gyro_bias;
Mat33 gyro_scale;
getBiasAndScale(gyro_bias, gyro_scale);
Mat33 gyro_scale_inv = (Eigen::Matrix3d::Identity() + gyro_scale).inverse();
return gyro_scale_inv * (calibrated_measurement + gyro_bias);
}
private:
Eigen::Matrix<Scalar, 12, 1> gyro_bias_full_;
};
} // namespace basalt

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/**
BSD 3-Clause License
This file is part of the Basalt project.
https://gitlab.com/VladyslavUsenko/basalt-headers.git
Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of the copyright holder nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@file
@brief Calibration datatypes for muticam-IMU and motion capture calibration
*/
#pragma once
#include <memory>
#include <basalt/spline/rd_spline.h>
#include <basalt/calibration/calib_bias.hpp>
#include <basalt/camera/generic_camera.hpp>
namespace basalt {
/// @brief Struct to store camera-IMU calibration
template <class Scalar>
struct Calibration {
using Ptr = std::shared_ptr<Calibration>;
using SE3 = Sophus::SE3<Scalar>;
using Vec3 = Eigen::Matrix<Scalar, 3, 1>;
/// @brief Default constructor.
Calibration() {
cam_time_offset_ns = 0;
imu_update_rate = 200;
// reasonable defaults
gyro_noise_std.setConstant(0.000282);
accel_noise_std.setConstant(0.016);
accel_bias_std.setConstant(0.001);
gyro_bias_std.setConstant(0.0001);
}
/// @brief Cast to other scalar type
template <class Scalar2>
Calibration<Scalar2> cast() const {
Calibration<Scalar2> new_cam;
for (const auto& v : T_i_c)
new_cam.T_i_c.emplace_back(v.template cast<Scalar2>());
for (const auto& v : intrinsics)
new_cam.intrinsics.emplace_back(v.template cast<Scalar2>());
for (const auto& v : vignette)
new_cam.vignette.emplace_back(v.template cast<Scalar2>());
new_cam.resolution = resolution;
new_cam.cam_time_offset_ns = cam_time_offset_ns;
new_cam.calib_accel_bias.getParam() =
calib_accel_bias.getParam().template cast<Scalar2>();
new_cam.calib_gyro_bias.getParam() =
calib_gyro_bias.getParam().template cast<Scalar2>();
new_cam.imu_update_rate = imu_update_rate;
new_cam.gyro_noise_std = gyro_noise_std.template cast<Scalar2>();
new_cam.accel_noise_std = accel_noise_std.template cast<Scalar2>();
new_cam.gyro_bias_std = gyro_bias_std.template cast<Scalar2>();
new_cam.accel_bias_std = accel_bias_std.template cast<Scalar2>();
return new_cam;
}
/// @brief Vector of transformations from camera to IMU
///
/// Point in camera coordinate frame \f$ p_c \f$ can be transformed to the
/// point in IMU coordinate frame as \f$ p_i = T_{ic} p_c, T_{ic} \in
/// SE(3)\f$
Eigen::aligned_vector<SE3> T_i_c;
/// @brief Vector of camera intrinsics. Can store different camera models. See
/// \ref GenericCamera.
Eigen::aligned_vector<GenericCamera<Scalar>> intrinsics;
/// @brief Camera resolutions.
Eigen::aligned_vector<Eigen::Vector2i> resolution;
/// @brief Vector of splines representing radially symmetric vignetting for
/// each of the camera.
///
/// Splines use time in nanoseconds for evaluation, but in this case we use
/// distance from the optical center in pixels multiplied by 1e9 as a "time"
/// parameter.
std::vector<basalt::RdSpline<1, 4, Scalar>> vignette;
/// @brief Time offset between cameras and IMU in nanoseconds.
///
/// With raw image timestamp \f$ t_r \f$ and this offset \f$ o \f$ we cam get
/// a timestamp aligned with IMU clock as \f$ t_c = t_r + o \f$.
int64_t cam_time_offset_ns;
/// @brief Static accelerometer bias from calibration.
CalibAccelBias<Scalar> calib_accel_bias;
/// @brief Static gyroscope bias from calibration.
CalibGyroBias<Scalar> calib_gyro_bias;
/// @brief IMU update rate.
Scalar imu_update_rate;
/// @brief Continuous time gyroscope noise standard deviation.
Vec3 gyro_noise_std;
/// @brief Continuous time accelerometer noise standard deviation.
Vec3 accel_noise_std;
/// @brief Continuous time bias random walk standard deviation for gyroscope.
Vec3 gyro_bias_std;
/// @brief Continuous time bias random walk standard deviation for
/// accelerometer.
Vec3 accel_bias_std;
/// @brief Dicrete time gyroscope noise standard deviation.
///
/// \f$ \sigma_d = \sigma_c \sqrt{r} \f$, where \f$ r \f$ is IMU update
/// rate.
inline Vec3 dicrete_time_gyro_noise_std() const {
return gyro_noise_std * std::sqrt(imu_update_rate);
}
/// @brief Dicrete time accelerometer noise standard deviation.
///
/// \f$ \sigma_d = \sigma_c \sqrt{r} \f$, where \f$ r \f$ is IMU update
/// rate.
inline Vec3 dicrete_time_accel_noise_std() const {
return accel_noise_std * std::sqrt(imu_update_rate);
}
EIGEN_MAKE_ALIGNED_OPERATOR_NEW
};
/// @brief Struct to store motion capture to IMU calibration
template <class Scalar>
struct MocapCalibration {
using Ptr = std::shared_ptr<MocapCalibration>;
using SE3 = Sophus::SE3<Scalar>;
/// @brief Default constructor.
MocapCalibration() {
mocap_time_offset_ns = 0;
mocap_to_imu_offset_ns = 0;
}
/// @brief Transformation from motion capture origin to the world (calibration
/// pattern).
SE3 T_moc_w;
/// @brief Transformation from the coordinate frame of the markers attached to
/// the object to the IMU.
SE3 T_i_mark;
/// @brief Initial time alignment between IMU and MoCap clocks based on
/// message arrival time.
int64_t mocap_time_offset_ns;
/// @brief Time offset between IMU and motion capture clock.
int64_t mocap_to_imu_offset_ns;
};
} // namespace basalt