Related papers: Equivariant filter (EqF): A general filter design …
We describe an application of the Invariant Extended Kalman Filter (IEKF) design methodology to the scan matching SLAM problem. We review the theoretical foundations of the IEKF and its practical interest of guaranteeing robustness to poor…
In autonomous driving, deep learning enabled motion prediction is a popular topic. A critical gap in traditional motion prediction methodologies lies in ensuring equivariance under Euclidean geometric transformations and maintaining…
We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…
Frame theory is a powerful tool in the domain of signal processing and communication. Among its numerous configurations, the ones which have drawn much attention recently are Equiangular Tight Frame (ETF) and Grassmannian Frame. These…
We present a framework for studying the dynamics of equivariant vector fields near relative equilibria. To overcome the lack of linearization at a relative equilibrium or the possible non-smoothness of the orbit space, we categorify the…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
We develop theory and software for rotation equivariant operators on scalar and vector fields, with diverse applications in simulation, optimization and machine learning. Rotation equivariance (covariance) means all fields in the system…
In this paper, we investigate the inconsistency problem arising from observability mismatch that frequently occurs in nonlinear systems such as multi-robot cooperative localization and simultaneous localization and mapping. For a general…
Simultaneous Localization and Mapping (SLAM) presents a formidable challenge in robotics, involving the dynamic construction of a map while concurrently determining the precise location of the robotic agent within an unfamiliar environment.…
Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The…
This paper presents a hybrid real-time camera pose estimation framework with a novel partitioning scheme and introduces motion averaging to monocular Simultaneous Localization and Mapping (SLAM) systems. Breaking through the limitations of…
We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers…
Equivariant neural networks are a class of neural networks designed to preserve symmetries inherent in the data. In this paper, we introduce a general method for modifying a neural network to enforce equivariance, a process we refer to as…
Robotic pick and place tasks are symmetric under translations and rotations of both the object to be picked and the desired place pose. For example, if the pick object is rotated or translated, then the optimal pick action should also…
This paper studies the problem of Cooperative Localization (CL) for multi-robot systems, where a group of mobile robots jointly localize themselves by using measurements from onboard sensors and shared information from other robots. We…
We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. Our approach employs a single neural field where a unified shared backbone is conditioned on…
This paper introduces the ensemble directional Kalman filter (EnDKF), an ensemble-based Kalman filtering approach for pose tracking that jointly estimates an object's position and attitude using ideas from directional statistics. The EnDKF…
Equiangular tight frames (ETFs) are configurations of vectors which are optimally geometrically spread apart and provide resolutions of the identity. Many known constructions of ETFs are group covariant, meaning they result from the action…
Perceptual aliasing and weak textures pose significant challenges to the task of place recognition, hindering the performance of Simultaneous Localization and Mapping (SLAM) systems. This paper presents a novel model, called UMF (standing…
The extended Kalman filter (EKF) is a common state estimation method for discrete nonlinear systems. It recursively executes the propagation step as time goes by and the update step when a set of measurements arrives. In the update step,…