A geometric nonlinear observer for simultaneous localisation and mapping

Abstract

The Simultaneous Localisation and Mapping (SLAM) problem involves estimating the pose of a robot relative to landmarks observed in the environment while at the same time estimating the location of those landmarks in the environment. This paper introduces a framework in which the landmarks and robot pose can be modelled in a single geometric structure, that of a homogeneous space obtained as the quotient of a novel Lie-group that we term the SLAM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> (3) group. Using this formulation we apply techniques from observer design for symmetric systems to derive a novel observer for the SLAM problem posed in continuous-time.