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Found 19 papers, 3 papers with code
A Geometric Perspective on Fusing Gaussian Distributions on Lie Groups
Stochastic inference on Lie groups plays a key role in state estimation problems, such as inertial navigation, visual inertial odometry, pose estimation in virtual reality, etc.
Exploiting Equivariance in the Design of Tracking Controllers for Euler-Poincare Systems on Matrix Lie Groups
In this paper, we propose a group structure on the cotangent bundle of a Lie group and leverage this to define momentum and configuration errors for trajectory tracking drawing on recent work on equivariant observer design.
Exploiting spatial group error and synchrony for a unicycle tracking controller
Trajectory tracking for the kinematic unicycle has been heavily studied for several decades.
Synchronous Observer Design for Inertial Navigation Systems with Almost-Global Convergence
An Inertial Navigation System (INS) is a system that integrates acceleration and angular velocity readings from an Inertial Measurement Unit (IMU), along with other sensors such as GNSS position, GNSS velocity, and magnetometer, to estimate the attitude, velocity, and position of a vehicle.
A Note on the Extended Kalman Filter on a Manifold
With this structure, we show that a naive coordinate implementation of the EKF fails to account for geometry of the manifold in the update step and in the reset step.
Constructive Equivariant Observer Design for Inertial Navigation
Inertial Navigation Systems (INS) are algorithms that fuse inertial measurements of angular velocity and specific acceleration with supplementary sensors including GNSS and magnetometers to estimate the position, velocity and attitude, or extended pose, of a vehicle.
Event Blob Tracking: An Asynchronous Real-Time Algorithm
Event-based cameras have become increasingly popular for tracking fast-moving objects due to their high temporal resolution, low latency, and high dynamic range.
Nonlinear constructive observer design for direct homography estimation
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.
Tracking control on homogeneous spaces: the Equivariant Regulator (EqR)
Accurate tracking of planned trajectories in the presence of perturbations is an important problem in control and robotics.
Equivariant Filters are Equivariant
Observers for systems with Lie group symmetries are an active area of research that is seeing significant impact in a number of practical domains, including aerospace, robotics, and mechatronics.
Equivariant Filter Design for Discrete-time systems
The kinematics of many nonlinear control systems, especially in the robotics field, admit a transitive Lie-group symmetry, which is useful in high performance observer design.
Constructive Equivariant Observer Design for Inertial Velocity-Aided Attitude
Inertial Velocity-Aided Attitude (VAA) is an important problem in the control of Remotely Piloted Aerial Systems (RPAS), and involves estimating the velocity and attitude of a vehicle using gyroscope, accelerometer, and inertial-frame velocity (e. g. GPS velocity) measurements.
Observer Design for Nonlinear Systems with Equivariance
The equivariant filter exploits the symmetry and respects the geometry of an equivariant system model and yields high performance robust filters for a wide range of mechatronic and navigation systems.
Equivariant filter (EqF): A general filter design for systems on homogeneous spaces
The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry.
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 group with the inputs lying in the tangent of the tangent bundle known as the double tangent bundle.
Attitude Observation for Second Order Attitude Kinematics
This paper addresses the problem of estimating the attitude and angular velocity of a rigid object by exploiting its second order kinematic model.
Event Camera Calibration of Per-pixel Biased Contrast Threshold
Currently, most of the existing works use a single contrast threshold to estimate the intensity change of all pixels.
Equivariant Filter (EqF)
Simulation experiments of an example application show that the EqF significantly outperforms the extended Kalman filter and that the reduced linearisation error leads to a clear improvement in performance.
Constructive Observer Design for Visual Simultaneous Localisation and Mapping
Visual Simultaneous Localisation and Mapping (VSLAM) is a well-known problem in robotics with a large range of applications.
