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include/msckf_vio/feature.hpp
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include/msckf_vio/feature.hpp
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/*
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* COPYRIGHT AND PERMISSION NOTICE
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* Penn Software MSCKF_VIO
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* Copyright (C) 2017 The Trustees of the University of Pennsylvania
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* All rights reserved.
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*/
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#ifndef MSCKF_VIO_FEATURE_H
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#define MSCKF_VIO_FEATURE_H
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#include <iostream>
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#include <map>
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#include <vector>
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#include <Eigen/Dense>
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#include <Eigen/Geometry>
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#include <Eigen/StdVector>
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#include "math_utils.hpp"
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#include "imu_state.h"
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#include "cam_state.h"
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namespace msckf_vio {
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/*
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* @brief Feature Salient part of an image. Please refer
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* to the Appendix of "A Multi-State Constraint Kalman
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* Filter for Vision-aided Inertial Navigation" for how
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* the 3d position of a feature is initialized.
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*/
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struct Feature {
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW
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typedef long long int FeatureIDType;
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/*
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* @brief OptimizationConfig Configuration parameters
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* for 3d feature position optimization.
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*/
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struct OptimizationConfig {
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double translation_threshold;
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double huber_epsilon;
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double estimation_precision;
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double initial_damping;
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int outer_loop_max_iteration;
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int inner_loop_max_iteration;
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OptimizationConfig():
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translation_threshold(0.2),
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huber_epsilon(0.01),
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estimation_precision(5e-7),
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initial_damping(1e-3),
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outer_loop_max_iteration(10),
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inner_loop_max_iteration(10) {
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return;
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}
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};
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// Constructors for the struct.
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Feature(): id(0), position(Eigen::Vector3d::Zero()),
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is_initialized(false) {}
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Feature(const FeatureIDType& new_id): id(new_id),
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position(Eigen::Vector3d::Zero()),
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is_initialized(false) {}
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/*
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* @brief cost Compute the cost of the camera observations
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* @param T_c0_c1 A rigid body transformation takes
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* a vector in c0 frame to ci frame.
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* @param x The current estimation.
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* @param z The ith measurement of the feature j in ci frame.
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* @return e The cost of this observation.
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*/
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inline void cost(const Eigen::Isometry3d& T_c0_ci,
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const Eigen::Vector3d& x, const Eigen::Vector2d& z,
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double& e) const;
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/*
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* @brief jacobian Compute the Jacobian of the camera observation
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* @param T_c0_c1 A rigid body transformation takes
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* a vector in c0 frame to ci frame.
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* @param x The current estimation.
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* @param z The actual measurement of the feature in ci frame.
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* @return J The computed Jacobian.
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* @return r The computed residual.
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* @return w Weight induced by huber kernel.
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*/
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inline void jacobian(const Eigen::Isometry3d& T_c0_ci,
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const Eigen::Vector3d& x, const Eigen::Vector2d& z,
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Eigen::Matrix<double, 2, 3>& J, Eigen::Vector2d& r,
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double& w) const;
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/*
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* @brief generateInitialGuess Compute the initial guess of
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* the feature's 3d position using only two views.
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* @param T_c1_c2: A rigid body transformation taking
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* a vector from c2 frame to c1 frame.
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* @param z1: feature observation in c1 frame.
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* @param z2: feature observation in c2 frame.
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* @return p: Computed feature position in c1 frame.
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*/
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inline void generateInitialGuess(
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const Eigen::Isometry3d& T_c1_c2, const Eigen::Vector2d& z1,
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const Eigen::Vector2d& z2, Eigen::Vector3d& p) const;
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/*
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* @brief checkMotion Check the input camera poses to ensure
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* there is enough translation to triangulate the feature
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* positon.
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* @param cam_states : input camera poses.
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* @return True if the translation between the input camera
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* poses is sufficient.
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*/
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inline bool checkMotion(
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const CamStateServer& cam_states) const;
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/*
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* @brief InitializePosition Intialize the feature position
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* based on all current available measurements.
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* @param cam_states: A map containing the camera poses with its
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* ID as the associated key value.
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* @return The computed 3d position is used to set the position
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* member variable. Note the resulted position is in world
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* frame.
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* @return True if the estimated 3d position of the feature
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* is valid.
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*/
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inline bool initializePosition(
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const CamStateServer& cam_states);
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// An unique identifier for the feature.
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// In case of long time running, the variable
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// type of id is set to FeatureIDType in order
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// to avoid duplication.
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FeatureIDType id;
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// id for next feature
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static FeatureIDType next_id;
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// Store the observations of the features in the
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// state_id(key)-image_coordinates(value) manner.
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std::map<StateIDType, Eigen::Vector4d, std::less<StateIDType>,
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Eigen::aligned_allocator<
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std::pair<const StateIDType, Eigen::Vector2d> > > observations;
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// 3d postion of the feature in the world frame.
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Eigen::Vector3d position;
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// A indicator to show if the 3d postion of the feature
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// has been initialized or not.
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bool is_initialized;
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// Noise for a normalized feature measurement.
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static double observation_noise;
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// Optimization configuration for solving the 3d position.
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static OptimizationConfig optimization_config;
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};
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typedef Feature::FeatureIDType FeatureIDType;
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typedef std::map<FeatureIDType, Feature, std::less<int>,
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Eigen::aligned_allocator<
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std::pair<const FeatureIDType, Feature> > > MapServer;
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void Feature::cost(const Eigen::Isometry3d& T_c0_ci,
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const Eigen::Vector3d& x, const Eigen::Vector2d& z,
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double& e) const {
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// Compute hi1, hi2, and hi3 as Equation (37).
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const double& alpha = x(0);
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const double& beta = x(1);
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const double& rho = x(2);
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Eigen::Vector3d h = T_c0_ci.linear()*
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Eigen::Vector3d(alpha, beta, 1.0) + rho*T_c0_ci.translation();
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double& h1 = h(0);
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double& h2 = h(1);
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double& h3 = h(2);
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// Predict the feature observation in ci frame.
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Eigen::Vector2d z_hat(h1/h3, h2/h3);
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// Compute the residual.
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e = (z_hat-z).squaredNorm();
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return;
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}
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void Feature::jacobian(const Eigen::Isometry3d& T_c0_ci,
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const Eigen::Vector3d& x, const Eigen::Vector2d& z,
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Eigen::Matrix<double, 2, 3>& J, Eigen::Vector2d& r,
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double& w) const {
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// Compute hi1, hi2, and hi3 as Equation (37).
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const double& alpha = x(0);
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const double& beta = x(1);
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const double& rho = x(2);
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Eigen::Vector3d h = T_c0_ci.linear()*
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Eigen::Vector3d(alpha, beta, 1.0) + rho*T_c0_ci.translation();
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double& h1 = h(0);
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double& h2 = h(1);
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double& h3 = h(2);
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// Compute the Jacobian.
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Eigen::Matrix3d W;
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W.leftCols<2>() = T_c0_ci.linear().leftCols<2>();
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W.rightCols<1>() = T_c0_ci.translation();
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J.row(0) = 1/h3*W.row(0) - h1/(h3*h3)*W.row(2);
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J.row(1) = 1/h3*W.row(1) - h2/(h3*h3)*W.row(2);
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// Compute the residual.
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Eigen::Vector2d z_hat(h1/h3, h2/h3);
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r = z_hat - z;
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// Compute the weight based on the residual.
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double e = r.norm();
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if (e <= optimization_config.huber_epsilon)
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w = 1.0;
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else
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w = optimization_config.huber_epsilon / (2*e);
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return;
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}
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void Feature::generateInitialGuess(
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const Eigen::Isometry3d& T_c1_c2, const Eigen::Vector2d& z1,
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const Eigen::Vector2d& z2, Eigen::Vector3d& p) const {
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// Construct a least square problem to solve the depth.
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Eigen::Vector3d m = T_c1_c2.linear() * Eigen::Vector3d(z1(0), z1(1), 1.0);
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Eigen::Vector2d A(0.0, 0.0);
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A(0) = m(0) - z2(0)*m(2);
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A(1) = m(1) - z2(1)*m(2);
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Eigen::Vector2d b(0.0, 0.0);
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b(0) = z2(0)*T_c1_c2.translation()(2) - T_c1_c2.translation()(0);
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b(1) = z2(1)*T_c1_c2.translation()(2) - T_c1_c2.translation()(1);
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// Solve for the depth.
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double depth = (A.transpose() * A).inverse() * A.transpose() * b;
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p(0) = z1(0) * depth;
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p(1) = z1(1) * depth;
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p(2) = depth;
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return;
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}
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bool Feature::checkMotion(
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const CamStateServer& cam_states) const {
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const StateIDType& first_cam_id = observations.begin()->first;
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const StateIDType& last_cam_id = (--observations.end())->first;
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Eigen::Isometry3d first_cam_pose;
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first_cam_pose.linear() = quaternionToRotation(
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cam_states.find(first_cam_id)->second.orientation).transpose();
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first_cam_pose.translation() =
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cam_states.find(first_cam_id)->second.position;
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Eigen::Isometry3d last_cam_pose;
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last_cam_pose.linear() = quaternionToRotation(
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cam_states.find(last_cam_id)->second.orientation).transpose();
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last_cam_pose.translation() =
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cam_states.find(last_cam_id)->second.position;
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// Get the direction of the feature when it is first observed.
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// This direction is represented in the world frame.
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Eigen::Vector3d feature_direction(
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observations.begin()->second(0),
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observations.begin()->second(1), 1.0);
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feature_direction = feature_direction / feature_direction.norm();
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feature_direction = first_cam_pose.linear()*feature_direction;
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// Compute the translation between the first frame
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// and the last frame. We assume the first frame and
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// the last frame will provide the largest motion to
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// speed up the checking process.
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Eigen::Vector3d translation = last_cam_pose.translation() -
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first_cam_pose.translation();
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double parallel_translation =
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translation.transpose()*feature_direction;
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Eigen::Vector3d orthogonal_translation = translation -
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parallel_translation*feature_direction;
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if (orthogonal_translation.norm() >
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optimization_config.translation_threshold)
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return true;
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else return false;
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}
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bool Feature::initializePosition(
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const CamStateServer& cam_states) {
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// Organize camera poses and feature observations properly.
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std::vector<Eigen::Isometry3d,
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Eigen::aligned_allocator<Eigen::Isometry3d> > cam_poses(0);
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std::vector<Eigen::Vector2d,
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Eigen::aligned_allocator<Eigen::Vector2d> > measurements(0);
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for (auto& m : observations) {
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// TODO: This should be handled properly. Normally, the
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// required camera states should all be available in
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// the input cam_states buffer.
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auto cam_state_iter = cam_states.find(m.first);
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if (cam_state_iter == cam_states.end()) continue;
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// Add the measurement.
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measurements.push_back(m.second.head<2>());
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measurements.push_back(m.second.tail<2>());
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// This camera pose will take a vector from this camera frame
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// to the world frame.
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Eigen::Isometry3d cam0_pose;
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cam0_pose.linear() = quaternionToRotation(
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cam_state_iter->second.orientation).transpose();
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cam0_pose.translation() = cam_state_iter->second.position;
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Eigen::Isometry3d cam1_pose;
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cam1_pose = cam0_pose * CAMState::T_cam0_cam1.inverse();
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cam_poses.push_back(cam0_pose);
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cam_poses.push_back(cam1_pose);
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}
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// All camera poses should be modified such that it takes a
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// vector from the first camera frame in the buffer to this
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// camera frame.
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Eigen::Isometry3d T_c0_w = cam_poses[0];
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for (auto& pose : cam_poses)
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pose = pose.inverse() * T_c0_w;
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// Generate initial guess
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Eigen::Vector3d initial_position(0.0, 0.0, 0.0);
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generateInitialGuess(cam_poses[cam_poses.size()-1], measurements[0],
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measurements[measurements.size()-1], initial_position);
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Eigen::Vector3d solution(
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initial_position(0)/initial_position(2),
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initial_position(1)/initial_position(2),
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1.0/initial_position(2));
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// Apply Levenberg-Marquart method to solve for the 3d position.
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double lambda = optimization_config.initial_damping;
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int inner_loop_cntr = 0;
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int outer_loop_cntr = 0;
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bool is_cost_reduced = false;
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double delta_norm = 0;
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// Compute the initial cost.
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double total_cost = 0.0;
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for (int i = 0; i < cam_poses.size(); ++i) {
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double this_cost = 0.0;
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cost(cam_poses[i], solution, measurements[i], this_cost);
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total_cost += this_cost;
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}
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// Outer loop.
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do {
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Eigen::Matrix3d A = Eigen::Matrix3d::Zero();
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Eigen::Vector3d b = Eigen::Vector3d::Zero();
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for (int i = 0; i < cam_poses.size(); ++i) {
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Eigen::Matrix<double, 2, 3> J;
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Eigen::Vector2d r;
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double w;
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jacobian(cam_poses[i], solution, measurements[i], J, r, w);
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if (w == 1) {
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A += J.transpose() * J;
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b += J.transpose() * r;
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} else {
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double w_square = w * w;
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A += w_square * J.transpose() * J;
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b += w_square * J.transpose() * r;
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}
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}
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// Inner loop.
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// Solve for the delta that can reduce the total cost.
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do {
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Eigen::Matrix3d damper = lambda * Eigen::Matrix3d::Identity();
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Eigen::Vector3d delta = (A+damper).ldlt().solve(b);
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Eigen::Vector3d new_solution = solution - delta;
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delta_norm = delta.norm();
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double new_cost = 0.0;
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for (int i = 0; i < cam_poses.size(); ++i) {
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double this_cost = 0.0;
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cost(cam_poses[i], new_solution, measurements[i], this_cost);
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new_cost += this_cost;
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}
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if (new_cost < total_cost) {
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is_cost_reduced = true;
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solution = new_solution;
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total_cost = new_cost;
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lambda = lambda/10 > 1e-10 ? lambda/10 : 1e-10;
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} else {
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is_cost_reduced = false;
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lambda = lambda*10 < 1e12 ? lambda*10 : 1e12;
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}
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} while (inner_loop_cntr++ <
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optimization_config.inner_loop_max_iteration && !is_cost_reduced);
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inner_loop_cntr = 0;
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} while (outer_loop_cntr++ <
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optimization_config.outer_loop_max_iteration &&
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delta_norm > optimization_config.estimation_precision);
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// Covert the feature position from inverse depth
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// representation to its 3d coordinate.
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Eigen::Vector3d final_position(solution(0)/solution(2),
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solution(1)/solution(2), 1.0/solution(2));
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// Check if the solution is valid. Make sure the feature
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// is in front of every camera frame observing it.
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bool is_valid_solution = true;
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for (const auto& pose : cam_poses) {
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Eigen::Vector3d position =
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pose.linear()*final_position + pose.translation();
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if (position(2) <= 0) {
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is_valid_solution = false;
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break;
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}
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}
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// Convert the feature position to the world frame.
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position = T_c0_w.linear()*final_position + T_c0_w.translation();
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if (is_valid_solution)
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is_initialized = true;
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return is_valid_solution;
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}
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} // namespace msckf_vio
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#endif // MSCKF_VIO_FEATURE_H
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