An Equivariant Observer Design for Visual Localisation and Mapping

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.Comment: 12 pages, 2 figures, published in 2019 IEEE CD

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

A distributed optimization framework for localization and formation control: applications to vision-based measurements

Multiagent systems have been a major area of research for the last 15 years. This interest has been motivated by tasks that can be executed more rapidly in a collaborative manner or that are nearly impossible to carry out otherwise. To be effective, the agents need to have the notion of a common goal shared by the entire network (for instance, a desired formation) and individual control laws to realize the goal. The common goal is typically centralized, in the sense that it involves the state of all the agents at the same time. On the other hand, it is often desirable to have individual control laws that are distributed, in the sense that the desired action of an agent depends only on the measurements and states available at the node and at a small number of neighbors. This is an attractive quality because it implies an overall system that is modular and intrinsically more robust to communication delays and node failures

PEBO-SLAM: Observer design for visual inertial SLAM with convergence guarantees

This paper introduces a new linear parameterization to the problem of visual inertial simultaneous localization and mapping (VI-SLAM) -- without any approximation -- for the case only using information from a single monocular camera and an inertial measurement unit. In this problem set, the system state evolves on the nonlinear manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully to generate invariant foliations, such that the problem can be reformulated into online \emph{constant parameter} identification, then interestingly with linear regression models obtained. It demonstrates that VI-SLAM can be translated into a linear least squares problem, in the deterministic sense, \emph{globally} and \emph{exactly}. Based on this observation, we propose a novel SLAM observer, following the recently established parameter estimation-based observer (PEBO) methodology. A notable merit is that the proposed observer enjoys almost global asymptotic stability, requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with provable stability but can hardly be assured in many practical scenarios

An almost globally convergent observer for visual SLAM without persistent excitation

In this paper we propose a novel observer to solve the problem of visual simultaneous localization and mapping (SLAM), only using the information from a single monocular camera and an inertial measurement unit (IMU). The system state evolves on the manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully in order to generate an invariant foliation, such that the problem is reformulated into online \emph{constant parameter} identification. Then, following the recently introduced parameter estimation-based observer (PEBO) and the dynamic regressor extension and mixing (DREM) procedure, we provide a new simple solution. A notable merit is that the proposed observer guarantees almost global asymptotic stability requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with guaranteed stability