Lie++

Maintainer: Alessandro Fornasier

• Description
• Installation
• Usage
  • Base groups usage
  • Composition of groups
• Credit
  • License
  • Usage for academic purposes

Description

Lie++ is a header-only C++ library based on Eigen for Lie groups. It provides a set of classes and functions for working with common Lie groups encountered in robotics application.

Installation

This is a header-only C++ library meant to be used within other projects. Either copy the content of include folder within the external project's include folder or use cmake's FetchContent_Declare as follows

FetchContent_Declare(
    LiePlusPlus
    GIT_REPOSITORY  
    GIT_TAG         main
    GIT_SHALLOW     TRUE
    GIT_PROGRESS    TRUE
)
list(APPEND external LiePlusPlus) 
list(APPEND include_dirs ${LIEPLUSPLUS_INCLUDE_DIR})
list(APPEND libs LiePlusPlus Eigen3::Eigen)

Usage

Two mini examples on how to use the base groups of the library and how to compose them to create new groups. For usage of Lie++ in the context of filter design have a look at MSCEqF

Base groups usage

#include <groups/SEn.hpp>

int main(int argc, char **argv)
{
  using SO3d = group::SO3<double>;
  using SE23d = group::SEn3<double, 2>;
  using Vector3d = Eigen::Matrix<double, 3, 1>;
  using Vector9d = Eigen::Matrix<double, 9, 1>;
  using Matrix9d = Eigen::Matrix<double, 9, 9>;
  
  # Define random extended pose X via exponential map
  Vector9d x = Vector9d::Random();
  SE23d X = SE23d::exp(x);
  
  # Define Extended pose Y with identity rotation, and given velocity and position
  Vector3d p = Vector3d(1, 2, 3);
  Vector3d v = Vector3d(0.1, 0.1, 0.3);
  SO3d R = SO3d();
  SE23d Y = SE23d(R, {v, p});
  
  # Get extended pose composition Z = XY
  SE23d Z = X*Y;
  
  # print Z as matrix
  std::cout << Z.asMatrix() << std::endl;
  
  # print Rotational component of Z as quaternion, position and velocity
  std::cout << Z.q() << '\n' << Z.p() << '\n'<< Z.v() << '\n' std::endl;
  
  # get Adjoint matrix of SE23
  Matrix9d AdZ = Z.Adjoint();
}

Composition of groups

#include <groups/SEn.hpp>

/**
 * @brief Composition of SO(3) and SE(3) via direct product
 */
template <typename FPType>
class ComposedGroup
{
  public:
    using SO3 = group::SO3<FPType>;
    using SE3 = group::SEn3<FPType, 1>;
    using Vector3 = Eigen::Matrix<FPType, 3, 1>;
    using Vector6 = Eigen::Matrix<FPType, 6, 1>;
    using Vector9 = Eigen::Matrix<FPType, 9, 1>;
  
    ComposedGroup() : C_(), P_() {};
    
    ComposedGroup(const SO3& C, const SE3& P) : C_(C), P_(P) {};
    
    // other constructors ...
    
    [[nodiscard]] static const ComposedGroup exp(const Vector9& u)
    {
      return ComposedGroup(SO3::exp(u.template block<3, 1>(0, 0)), SE3::exp(u.template block<6, 1>(3, 0)));
    }

    [[nodiscard]] static const Vector9 log(const ComposedGroup& X)
    {
      Vector6 u = Vector9::Zero();
      u.template block<3, 1>(0, 0) = SO3::log(X.C_);
      u.template block<6, 1>(3, 0) = SE3::log(X.P_);
      return u;
    }
    
    [[nodiscard]] const ComposedGroup operator*(const ComposedGroup& other) const
    {
      return ComposedGroup(C_ * other.C_, P_ * other.P_);
    }
    
    // other methods ...
    
  private:
    SO3 C_;
    SE3 P_;
    
}

Credit

This code was written within the Control of Networked System (CNS), University of Klagenfurt.

License

This software is made available to the public to use (source-available), licensed under the terms of the BSD-2-Clause-License with no commercial use allowed, the full terms of which are made available in the LICENSE file. No license in patents is granted.

Usage for academic purposes

If you use this software in an academic research setting, please cite the corresponding paper.

@article{fornasier2023equivariant,
  title={Equivariant Symmetries for Inertial Navigation Systems},
  author={Fornasier, Alessandro and Ge, Yixiao and van Goor, Pieter and Mahony, Robert and Weiss, Stephan},
  journal={arXiv preprint arXiv:2309.03765},
  year={2023}
}

@article{fornasier2023msceqf,
  title={MSCEqF: A Multi State Constraint Equivariant Filter for Vision-aided Inertial Navigation},
  author={Fornasier, Alessandro and van Goor, Pieter and Allak, Eren and Mahony, Robert and Weiss, Stephan},
  journal={arXiv preprint arXiv:2311.11649},
  year={2023}
}