An Equivariant Observer Design for Visual Localisation and Mapping

Abstract

This paper builds on recent work on Simultaneous Localisation and Mapping (SLAM) in the non-linear observer community, by framing the visual localisation and mapping problem as a continuous-time equivariant observer design problem on the symmetry group of a kinematic system. The state-space is a quotient of the robot pose expressed on SE(3) and multiple copies of real projective space, used to represent both points in space and bearings in a single unified framework. An observer with decoupled Riccati-gains for each landmark is derived and we show that its error system is almost globally asymptotically stable and exponentially stable in-the-large.

arXiv comment12 pages, 2 figures, published in 2019 IEEE CDC

References in corpus (3)

• Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age
• Symmetry-preserving Observers
• An EKF-SLAM algorithm with consistency properties

Cited by in corpus (7)

• Observer Design for Nonlinear Systems with Equivariance
• Equivariant Systems Theory and Observer Design
• Constructive Observer Design for Visual Simultaneous Localisation and Mapping
• Invariant Kalman Filtering with Noise-Free Pseudo-Measurements
• A Global Asymptotic Convergent Observer for SLAM
• A Minimum Energy Filter for Localisation of an Unmanned Aerial Vehicle
• Equivariant Filter Design for Range-only SLAM