Related papers: Equivariant filter (EqF): A general filter design …

Radar-Inertial Odometry (RIO) based on the Extended Kalman Filter (EKF) relies on accurate extrinsic calibration between the radar and the Inertial Measurement Unit (IMU) and is sensitive to disturbances, as large linearization errors can…

This paper presents an Extended Kalman Filter (EKF) approach to localize a mobile robot with two quadrature encoders, a compass sensor, a laser range finder (LRF) and an omni-directional camera. The prediction step is performed by employing…

Aiming to enhance the consistency and thus long-term accuracy of Extended Kalman Filters for terrestrial vehicle localization, this paper introduces the Manifold Error State Extended Kalman Filter (M-ESEKF). By representing the robot's pose…

Generative modeling seeks to uncover the underlying factors that give rise to observed data that can often be modeled as the natural symmetries that manifest themselves through invariances and equivariances to certain transformation laws.…

Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this…

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…

The task of shape space learning involves mapping a train set of shapes to and from a latent representation space with good generalization properties. Often, real-world collections of shapes have symmetries, which can be defined as…

Invariant extended Kalman filter (InEKF) possesses excellent trajectory-independent property and better consistency compared to conventional extended Kalman filter (EKF). However, when applied to scenarios involving both global-frame and…

Autonomous mobile robot competitions judge based on a robot's ability to quickly and accurately navigate the game field. This means accurate localization is crucial for creating an autonomous competition robot. Two common localization…

In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are…

In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for…

Embodied systems experience the world as 'a symphony of flows': a combination of many continuous streams of sensory input coupled to self-motion, interwoven with the dynamics of external objects. These streams obey smooth,…

We demonstrate an object tracking method for 3D images with fixed computational cost and state-of-the-art performance. Previous methods predicted transformation parameters from convolutional layers. We instead propose an architecture that…

Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…

We present a novel spectral learning algorithm for simultaneous localization and mapping (SLAM) from range data with known correspondences. This algorithm is an instance of a general spectral system identification framework, from which it…

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they…

We introduce Equilibrium Matching (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models…

Inspired by constraints from physical law, equivariant machine learning restricts the learning to a hypothesis class where all the functions are equivariant with respect to some group action. Irreducible representations or invariant theory…

Spatial understanding is a critical aspect of most robotic tasks, particularly when generalization is important. Despite the impressive results of deep generative models in complex manipulation tasks, the absence of a representation that…