397 lines
17 KiB
C++
397 lines
17 KiB
C++
/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file InertialNavFactor_GlobalVelocity.h
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* @author Vadim Indelman, Stephen Williams
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* @brief Inertial navigation factor (velocity in the global frame)
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* @date Sept 13, 2012
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**/
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#pragma once
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#include <gtsam/nonlinear/NonlinearFactor.h>
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#include <gtsam/linear/NoiseModel.h>
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#include <gtsam/geometry/Rot3.h>
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#include <gtsam/base/LieVector.h>
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#include <gtsam/base/Matrix.h>
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// Using numerical derivative to calculate d(Pose3::Expmap)/dw
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#include <gtsam/base/numericalDerivative.h>
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#include <boost/optional.hpp>
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#include <ostream>
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namespace gtsam {
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/*
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* NOTES:
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* =====
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* - The global frame (NED or ENU) is defined by the user by specifying the gravity vector in this frame.
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* - The IMU frame is implicitly defined by the user via the rotation matrix between global and imu frames.
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* - Camera and IMU frames are identical
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* - The user should specify a continuous equivalent noise covariance, which can be calculated using
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* the static function CalcEquivalentNoiseCov based on the IMU gyro and acc measurement noise covariance
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* matrices and the process\modeling covariance matrix. The IneritalNavFactor converts this into a
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* discrete form using the supplied delta_t between sub-sequential measurements.
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* - Earth-rate correction:
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* + Currently the user should supply R_ECEF_to_G, which is the rotation from ECEF to the global
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* frame (Local-Level system: ENU or NED, see above).
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* + R_ECEF_to_G can be calculated by approximated values of latitude and longitude of the system.
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* + Currently it is assumed that a relatively small distance is traveled w.r.t. to initial pose, since R_ECEF_to_G is constant.
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* Otherwise, R_ECEF_to_G should be updated each time using the current lat-lon.
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*
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* - Frame Notation:
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* Quantities are written as {Frame of Representation/Destination Frame}_{Quantity Type}_{Quatity Description/Origination Frame}
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* So, the rotational velocity of the sensor written in the body frame is: body_omega_sensor
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* And the transformation from the body frame to the world frame would be: world_P_body
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* This allows visual chaining. For example, converting the sensed angular velocity of the IMU
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* (angular velocity of the sensor in the sensor frame) into the world frame can be performed as:
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* world_R_body * body_R_sensor * sensor_omega_sensor = world_omega_sensor
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*
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*
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* - Common Quantity Types
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* P : pose/3d transformation
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* R : rotation
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* omega : angular velocity
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* t : translation
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* v : velocity
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* a : acceleration
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*
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* - Common Frames
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* sensor : the coordinate system attached to the sensor origin
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* body : the coordinate system attached to body/inertial frame.
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* Unless an optional frame transformation is provided, the
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* sensor frame and the body frame will be identical
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* world : the global/world coordinate frame. This is assumed to be
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* a tangent plane to the earth's surface somewhere near the
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* vehicle
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*/
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template<class POSE, class VELOCITY, class IMUBIAS>
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class InertialNavFactor_GlobalVelocity : public NoiseModelFactor5<POSE, VELOCITY, IMUBIAS, POSE, VELOCITY> {
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private:
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typedef InertialNavFactor_GlobalVelocity<POSE, VELOCITY, IMUBIAS> This;
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typedef NoiseModelFactor5<POSE, VELOCITY, IMUBIAS, POSE, VELOCITY> Base;
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Vector measurement_acc_;
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Vector measurement_gyro_;
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double dt_;
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Vector world_g_;
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Vector world_rho_;
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Vector world_omega_earth_;
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boost::optional<POSE> body_P_sensor_; // The pose of the sensor in the body frame
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public:
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// shorthand for a smart pointer to a factor
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typedef typename boost::shared_ptr<InertialNavFactor_GlobalVelocity> shared_ptr;
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/** default constructor - only use for serialization */
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InertialNavFactor_GlobalVelocity() {}
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/** Constructor */
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InertialNavFactor_GlobalVelocity(const Key& Pose1, const Key& Vel1, const Key& IMUBias1, const Key& Pose2, const Key& Vel2,
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const Vector& measurement_acc, const Vector& measurement_gyro, const double measurement_dt, const Vector world_g, const Vector world_rho,
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const Vector& world_omega_earth, const noiseModel::Gaussian::shared_ptr& model_continuous, boost::optional<POSE> body_P_sensor = boost::none) :
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Base(calc_descrete_noise_model(model_continuous, measurement_dt ),
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Pose1, Vel1, IMUBias1, Pose2, Vel2), measurement_acc_(measurement_acc), measurement_gyro_(measurement_gyro),
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dt_(measurement_dt), world_g_(world_g), world_rho_(world_rho), world_omega_earth_(world_omega_earth), body_P_sensor_(body_P_sensor) { }
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virtual ~InertialNavFactor_GlobalVelocity() {}
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/** implement functions needed for Testable */
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/** print */
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virtual void print(const std::string& s = "InertialNavFactor_GlobalVelocity", const KeyFormatter& keyFormatter = DefaultKeyFormatter) const {
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std::cout << s << "("
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<< keyFormatter(this->key1()) << ","
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<< keyFormatter(this->key2()) << ","
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<< keyFormatter(this->key3()) << ","
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<< keyFormatter(this->key4()) << ","
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<< keyFormatter(this->key5()) << "\n";
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std::cout << "acc measurement: " << this->measurement_acc_.transpose() << std::endl;
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std::cout << "gyro measurement: " << this->measurement_gyro_.transpose() << std::endl;
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std::cout << "dt: " << this->dt_ << std::endl;
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std::cout << "gravity (in world frame): " << this->world_g_.transpose() << std::endl;
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std::cout << "craft rate (in world frame): " << this->world_rho_.transpose() << std::endl;
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std::cout << "earth's rotation (in world frame): " << this->world_omega_earth_.transpose() << std::endl;
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if(this->body_P_sensor_)
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this->body_P_sensor_->print(" sensor pose in body frame: ");
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this->noiseModel_->print(" noise model");
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}
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/** equals */
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virtual bool equals(const NonlinearFactor& expected, double tol=1e-9) const {
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const This *e = dynamic_cast<const This*> (&expected);
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return e != NULL && Base::equals(*e, tol)
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&& (measurement_acc_ - e->measurement_acc_).norm() < tol
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&& (measurement_gyro_ - e->measurement_gyro_).norm() < tol
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&& (dt_ - e->dt_) < tol
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&& (world_g_ - e->world_g_).norm() < tol
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&& (world_rho_ - e->world_rho_).norm() < tol
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&& (world_omega_earth_ - e->world_omega_earth_).norm() < tol
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&& ((!body_P_sensor_ && !e->body_P_sensor_) || (body_P_sensor_ && e->body_P_sensor_ && body_P_sensor_->equals(*e->body_P_sensor_)));
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}
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POSE predictPose(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1) const {
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// Calculate the corrected measurements using the Bias object
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Vector GyroCorrected(Bias1.CorrectGyro(measurement_gyro_));
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const POSE& world_P1_body = Pose1;
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const VELOCITY& world_V1_body = Vel1;
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// Calculate the acceleration and angular velocity of the body in the body frame (including earth-related rotations)
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Vector body_omega_body;
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if(body_P_sensor_) {
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body_omega_body = body_P_sensor_->rotation().matrix() * GyroCorrected;
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} else {
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body_omega_body = GyroCorrected;
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}
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// Convert earth-related terms into the body frame
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Matrix body_R_world(world_P1_body.rotation().inverse().matrix());
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Vector body_rho = body_R_world * world_rho_;
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Vector body_omega_earth = body_R_world * world_omega_earth_;
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// Correct for earth-related terms
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body_omega_body -= body_rho + body_omega_earth;
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// The velocity is in the global frame, so composing Pose1 with v*dt is incorrect
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return POSE(Pose1.rotation() * POSE::Rotation::Expmap(body_omega_body*dt_), Pose1.translation() + typename POSE::Translation(world_V1_body*dt_));
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}
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VELOCITY predictVelocity(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1) const {
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// Calculate the corrected measurements using the Bias object
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Vector AccCorrected(Bias1.CorrectAcc(measurement_acc_));
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const POSE& world_P1_body = Pose1;
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const VELOCITY& world_V1_body = Vel1;
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// Calculate the acceleration and angular velocity of the body in the body frame (including earth-related rotations)
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Vector body_a_body, body_omega_body;
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if(body_P_sensor_) {
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Matrix body_R_sensor = body_P_sensor_->rotation().matrix();
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Vector GyroCorrected(Bias1.CorrectGyro(measurement_gyro_));
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body_omega_body = body_R_sensor * GyroCorrected;
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Matrix body_omega_body__cross = skewSymmetric(body_omega_body);
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body_a_body = body_R_sensor * AccCorrected - body_omega_body__cross * body_omega_body__cross * body_P_sensor_->translation().vector();
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} else {
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body_a_body = AccCorrected;
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}
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// Correct for earth-related terms
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Vector world_a_body = world_P1_body.rotation().matrix() * body_a_body + world_g_ - 2*skewSymmetric(world_rho_ + world_omega_earth_)*world_V1_body;
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// Calculate delta in the body frame
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VELOCITY VelDelta(world_a_body*dt_);
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// Predict
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return Vel1.compose(VelDelta);
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}
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void predict(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, POSE& Pose2, VELOCITY& Vel2) const {
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Pose2 = predictPose(Pose1, Vel1, Bias1);
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Vel2 = predictVelocity(Pose1, Vel1, Bias1);
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}
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POSE evaluatePoseError(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, const POSE& Pose2, const VELOCITY& Vel2) const {
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// Predict
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POSE Pose2Pred = predictPose(Pose1, Vel1, Bias1);
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// Calculate error
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return Pose2.between(Pose2Pred);
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}
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VELOCITY evaluateVelocityError(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, const POSE& Pose2, const VELOCITY& Vel2) const {
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// Predict
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VELOCITY Vel2Pred = predictVelocity(Pose1, Vel1, Bias1);
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// Calculate error
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return Vel2.between(Vel2Pred);
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}
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/** implement functions needed to derive from Factor */
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Vector evaluateError(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, const POSE& Pose2, const VELOCITY& Vel2,
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boost::optional<Matrix&> H1 = boost::none,
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boost::optional<Matrix&> H2 = boost::none,
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boost::optional<Matrix&> H3 = boost::none,
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boost::optional<Matrix&> H4 = boost::none,
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boost::optional<Matrix&> H5 = boost::none) const {
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// TODO: Write analytical derivative calculations
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// Jacobian w.r.t. Pose1
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if (H1){
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Matrix H1_Pose = gtsam::numericalDerivative11<POSE, POSE>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluatePoseError, this, _1, Vel1, Bias1, Pose2, Vel2), Pose1);
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Matrix H1_Vel = gtsam::numericalDerivative11<VELOCITY, POSE>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluateVelocityError, this, _1, Vel1, Bias1, Pose2, Vel2), Pose1);
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*H1 = stack(2, &H1_Pose, &H1_Vel);
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}
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// Jacobian w.r.t. Vel1
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if (H2){
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Matrix H2_Pose = gtsam::numericalDerivative11<POSE, VELOCITY>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluatePoseError, this, Pose1, _1, Bias1, Pose2, Vel2), Vel1);
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Matrix H2_Vel = gtsam::numericalDerivative11<VELOCITY, VELOCITY>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluateVelocityError, this, Pose1, _1, Bias1, Pose2, Vel2), Vel1);
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*H2 = stack(2, &H2_Pose, &H2_Vel);
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}
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// Jacobian w.r.t. IMUBias1
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if (H3){
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Matrix H3_Pose = gtsam::numericalDerivative11<POSE, IMUBIAS>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluatePoseError, this, Pose1, Vel1, _1, Pose2, Vel2), Bias1);
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Matrix H3_Vel = gtsam::numericalDerivative11<VELOCITY, IMUBIAS>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluateVelocityError, this, Pose1, Vel1, _1, Pose2, Vel2), Bias1);
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*H3 = stack(2, &H3_Pose, &H3_Vel);
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}
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// Jacobian w.r.t. Pose2
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if (H4){
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Matrix H4_Pose = gtsam::numericalDerivative11<POSE, POSE>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluatePoseError, this, Pose1, Vel1, Bias1, _1, Vel2), Pose2);
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Matrix H4_Vel = gtsam::numericalDerivative11<VELOCITY, POSE>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluateVelocityError, this, Pose1, Vel1, Bias1, _1, Vel2), Pose2);
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*H4 = stack(2, &H4_Pose, &H4_Vel);
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}
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// Jacobian w.r.t. Vel2
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if (H5){
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Matrix H5_Pose = gtsam::numericalDerivative11<POSE, VELOCITY>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluatePoseError, this, Pose1, Vel1, Bias1, Pose2, _1), Vel2);
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Matrix H5_Vel = gtsam::numericalDerivative11<VELOCITY, VELOCITY>(boost::bind(&InertialNavFactor_GlobalVelocity::evaluateVelocityError, this, Pose1, Vel1, Bias1, Pose2, _1), Vel2);
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*H5 = stack(2, &H5_Pose, &H5_Vel);
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}
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Vector ErrPoseVector(POSE::Logmap(evaluatePoseError(Pose1, Vel1, Bias1, Pose2, Vel2)));
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Vector ErrVelVector(VELOCITY::Logmap(evaluateVelocityError(Pose1, Vel1, Bias1, Pose2, Vel2)));
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return concatVectors(2, &ErrPoseVector, &ErrVelVector);
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}
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static inline noiseModel::Gaussian::shared_ptr CalcEquivalentNoiseCov(const noiseModel::Gaussian::shared_ptr& gaussian_acc, const noiseModel::Gaussian::shared_ptr& gaussian_gyro,
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const noiseModel::Gaussian::shared_ptr& gaussian_process){
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Matrix cov_acc = inverse( gaussian_acc->R().transpose() * gaussian_acc->R() );
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Matrix cov_gyro = inverse( gaussian_gyro->R().transpose() * gaussian_gyro->R() );
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Matrix cov_process = inverse( gaussian_process->R().transpose() * gaussian_process->R() );
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cov_process.block(0,0, 3,3) += cov_gyro;
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cov_process.block(6,6, 3,3) += cov_acc;
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return noiseModel::Gaussian::Covariance(cov_process);
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}
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static inline void Calc_g_rho_omega_earth_NED(const Vector& Pos_NED, const Vector& Vel_NED, const Vector& LatLonHeight_IC, const Vector& Pos_NED_Initial,
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Vector& g_NED, Vector& rho_NED, Vector& omega_earth_NED) {
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Matrix ENU_to_NED = Matrix_(3, 3,
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0.0, 1.0, 0.0,
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1.0, 0.0, 0.0,
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0.0, 0.0, -1.0);
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Matrix NED_to_ENU = Matrix_(3, 3,
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0.0, 1.0, 0.0,
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1.0, 0.0, 0.0,
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0.0, 0.0, -1.0);
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// Convert incoming parameters to ENU
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Vector Pos_ENU = NED_to_ENU * Pos_NED;
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Vector Vel_ENU = NED_to_ENU * Vel_NED;
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Vector Pos_ENU_Initial = NED_to_ENU * Pos_NED_Initial;
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// Call ENU version
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Vector g_ENU;
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Vector rho_ENU;
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Vector omega_earth_ENU;
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Calc_g_rho_omega_earth_ENU(Pos_ENU, Vel_ENU, LatLonHeight_IC, Pos_ENU_Initial, g_ENU, rho_ENU, omega_earth_ENU);
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// Convert output to NED
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g_NED = ENU_to_NED * g_ENU;
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rho_NED = ENU_to_NED * rho_ENU;
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omega_earth_NED = ENU_to_NED * omega_earth_ENU;
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}
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static inline void Calc_g_rho_omega_earth_ENU(const Vector& Pos_ENU, const Vector& Vel_ENU, const Vector& LatLonHeight_IC, const Vector& Pos_ENU_Initial,
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Vector& g_ENU, Vector& rho_ENU, Vector& omega_earth_ENU){
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double R0 = 6.378388e6;
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double e = 1/297;
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double Re( R0*( 1-e*(sin( LatLonHeight_IC(0) ))*(sin( LatLonHeight_IC(0) )) ) );
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// Calculate current lat, lon
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Vector delta_Pos_ENU(Pos_ENU - Pos_ENU_Initial);
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double delta_lat(delta_Pos_ENU(1)/Re);
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double delta_lon(delta_Pos_ENU(0)/(Re*cos(LatLonHeight_IC(0))));
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double lat_new(LatLonHeight_IC(0) + delta_lat);
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double lon_new(LatLonHeight_IC(1) + delta_lon);
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// Rotation of lon about z axis
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Rot3 C1(cos(lon_new), sin(lon_new), 0.0,
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-sin(lon_new), cos(lon_new), 0.0,
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0.0, 0.0, 1.0);
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// Rotation of lat about y axis
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Rot3 C2(cos(lat_new), 0.0, sin(lat_new),
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0.0, 1.0, 0.0,
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-sin(lat_new), 0.0, cos(lat_new));
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Rot3 UEN_to_ENU(0, 1, 0,
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0, 0, 1,
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1, 0, 0);
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Rot3 R_ECEF_to_ENU( UEN_to_ENU * C2 * C1 );
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Vector omega_earth_ECEF(Vector_(3, 0.0, 0.0, 7.292115e-5));
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omega_earth_ENU = R_ECEF_to_ENU.matrix() * omega_earth_ECEF;
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// Calculating g
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double height(LatLonHeight_IC(2));
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double EQUA_RADIUS = 6378137.0; // equatorial radius of the earth; WGS-84
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double ECCENTRICITY = 0.0818191908426; // eccentricity of the earth ellipsoid
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double e2( pow(ECCENTRICITY,2) );
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double den( 1-e2*pow(sin(lat_new),2) );
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double Rm( (EQUA_RADIUS*(1-e2))/( pow(den,(3/2)) ) );
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double Rp( EQUA_RADIUS/( sqrt(den) ) );
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double Ro( sqrt(Rp*Rm) ); // mean earth radius of curvature
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double g0( 9.780318*( 1 + 5.3024e-3 * pow(sin(lat_new),2) - 5.9e-6 * pow(sin(2*lat_new),2) ) );
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double g_calc( g0/( pow(1 + height/Ro, 2) ) );
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g_ENU = Vector_(3, 0.0, 0.0, -g_calc);
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// Calculate rho
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double Ve( Vel_ENU(0) );
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double Vn( Vel_ENU(1) );
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double rho_E = -Vn/(Rm + height);
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double rho_N = Ve/(Rp + height);
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double rho_U = Ve*tan(lat_new)/(Rp + height);
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rho_ENU = Vector_(3, rho_E, rho_N, rho_U);
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}
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static inline noiseModel::Gaussian::shared_ptr calc_descrete_noise_model(const noiseModel::Gaussian::shared_ptr& model, double delta_t){
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/* Q_d (approx)= Q * delta_t */
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/* In practice, square root of the information matrix is represented, so that:
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* R_d (approx)= R / sqrt(delta_t)
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* */
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return noiseModel::Gaussian::SqrtInformation(model->R()/std::sqrt(delta_t));
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}
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private:
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/** Serialization function */
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friend class boost::serialization::access;
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template<class ARCHIVE>
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void serialize(ARCHIVE & ar, const unsigned int version) {
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ar & boost::serialization::make_nvp("NonlinearFactor2",
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boost::serialization::base_object<Base>(*this));
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}
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}; // \class GaussMarkov1stOrderFactor
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} /// namespace aspn
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