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This paper considers the design of nonlinear observers for invariant systems posed on finite-dimensional connected Lie groups with measurements generated by a transitive group action on an associated homogeneous space. We consider the case…

In this paper we give a geometrical framework for the design of observers on finite-dimensional Lie groups for systems which possess some specific symmetries. The design and the error (between true and estimated state) equation are explicit…

Visual Simultaneous Localisation and Mapping (VSLAM) is a well-known problem in robotics with a large range of applications. This paper presents a novel approach to VSLAM by lifting the observer design to a novel Lie group on which the…

A geometric nonlinear observer algorithm for Simultaneous Localization and Mapping (SLAM) developed on the Lie group of \mathbb{SLAM}_{n}\left(3\right) is proposed. The presented novel solution estimates the vehicle's pose (i.e. attitude…

This paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown…

A method of designing observers and observer-based tracking controllers is proposed for nonlinear systems on manifolds via embedding into Euclidean space and transversal stabilization. Given a system on a manifold, we first embed the…

This paper presents the equivariant systems theory and observer design for second order kinematic systems on matrix Lie groups. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of…

This paper addresses the problem of Simultaneous Localization and Mapping (SLAM) for rigid body systems in three-dimensional space. We introduce a new matrix Lie group SE_{3+n}(3), whose elements are composed of the pose, gravity, linear…

This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of…

Nonlinear observer design for systems whose state space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model…

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…

A robust nonlinear stochastic observer for simultaneous localization and mapping (SLAM) is proposed using the available uncertain measurements of angular velocity, translational velocity, and features. The proposed observer is posed on the…

This paper deals with the design of globally exponentially stable invariant observers on the Special Euclidian group SE(3). First, we propose a generic hybrid observer scheme (depending on a generic potential function) evolving on…

A nonlinear observer on the Special Euclidean group $\mathrm{SE(3)}$ for full pose estimation, that takes the system outputs on the real projective space directly as inputs, is proposed. The observer derivation is based on a recent advanced…

Feature-based homography estimation approaches rely on extensive image processing for feature extraction and matching, and do not adequately account for the information provided by the image. Therefore, developing efficient direct…

Linear observed systems on groups encode the geometry of a variety of practical state estimation problems. In this paper, we propose an observer framework for a class of linear observed systems by restricting a bi-invariant system on a Lie…

The process of simultaneously mapping the environment in three dimensional (3D) space and localizing a moving vehicle's pose (orientation and position) is termed Simultaneous Localization and Mapping (SLAM). SLAM is a core task in robotics…

This paper addresses the problem of Visual-Inertial Odometry (VIO) for rigid body systems evolving in three-dimensional space. We introduce a novel matrix Lie group structure, denoted SE_{3+n}(3), that unifies the pose, gravity, linear…

A symmetry-preserving, reduced-order state observer is presented for the unmeasured part of a system's state, where the nonlinear system dynamics exhibit symmetry under the action of a Lie group. Leveraging this symmetry with a moving…

In this paper, we introduce the framework of a generalized design, which represents any linear operator as a finite sum of local linear maps attached to finitely many points, thereby abstracting the core of design theory without employing…