Manif: A micro Lie theory library for state estimation in robotics applications
Jérémie Deray, Joan Solà
Abstract
There has been a remarkable effort in the last years in the robotics community to formulate\nestimation problems properly (Eade, 2013)(Barfoot, 2017). This is motivated by an increasing\ndemand for precision, consistency, and stability of the solutions. Indeed, proper modeling of\nthe states and measurements, the functions relating them, and their uncertainties, is crucial\nto achieve these goals. This has led to problem formulations involving what has been known\nas ‘manifolds’, which in this context are no less than the smooth topologic surfaces of the Lie\ngroups where the state representations evolve (Chirikjian, 2011).\nmanif (Deray & Solà, 2019) is a micro Lie theory library targeted at state estimation in\nrobotics applications. With a single dependency on Eigen (Guennebaud, Jacob, & others,\n2010) and a requirement on C++11 only, it is developed as a header-only library, making it\neasy to integrate to existing projects.\nThe manif library provides simple interfaces to the most common operations on Lie groups\nin state estimation. Its design is similar to Eigen, in that all Lie group classes inherit from a\ntemplated base class using static polymorphism. This allows for writing generic code without\npaying the price of pointer arithmetic. Thanks to this polymorphism, the library is open to\nextensions to Lie groups beyond the currently implemented: the Special Orthogonal groups\nSO(2) and SO(3) and the Special Euclidean groups SE(2) and SE(3).\nThe mathematical foundations of the library are given in (Solà, Deray, & Atchuthan, 2018),\nwhich is often referred to in the documentation, especially for providing references for the\nmathematical formulae.