43 citations · 63 across the 21 of their papers we have counts for
23 papers
Tracking Control for a Dynamic Model of an Underwater Submersible
Matthew Hampsey, Pieter van Goor, Ravi Banavar +1
Underwater vehicles are naturally modelled as rigid bodies on SE(3) subjected to added mass effects. The passivity of the Hamiltonian structure of the system can be exploited to de…
Galilean State Estimation for Inertial Navigation Systems with Unknown Time Delay
Giulio Delama, Martin Scheiber, Yixiao Ge +3
Many Inertial Navigation Systems (INS) use Global Navigation Satellite System (GNSS) position as the primary measurement to drive filter performance and bound error growth. However…
Equivariant Observer Design on SL(3) for Image Intensity-Based Homography Estimation
Tarek Bouazza, Pieter van Goor, Robert Mahony +1
This paper addresses the problem of homography estimation using a nonlinear observer designed on the Lie group that exploits the full image information through dir…
Vision-Aided Relative State Estimation for Approach and Landing on a Moving Platform with Inertial Measurements
Tarek Bouazza, Alessandro Melis, Soulaimane Berkane +2
This paper tackles the problem of estimating the relative position, orientation, and velocity between a UAV and a planar platform undergoing arbitrary 3D motion during approach and…
Equivariant Tracking Control for Fully Actuated Mechanical Systems on Matrix Lie Groups
Matthew Hampsey, Pieter van Goor, Ravi Banavar +1
Mechanical control systems such as aerial, marine, space, and terrestrial robots often naturally admit a state-space that has the structure of a Lie group. The kinetic energy of su…
Galilean Symmetry in Robotics
Robert Mahony, Jonathan Kelly, Stephan Weiss
Galilean symmetry is the natural symmetry of inertial motion that underpins Newtonian physics. Although rigid-body symmetry is one of the most established and fundamental tools in…
The Difference between the Left and Right Invariant Extended Kalman Filter
Yixiao Ge, Giulio Delama, Martin Scheiber +4
The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The Invariant Extended Kalman Filter (IEKF) is a recent dev…
Maximum-likelihood reprojections for reliable Koopman predictors of parametric nonlinear dynamical systems
Pieter van Goor, Robert Mahony, Manuel Schaller +1
Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, system analysis, learning, and prediction are considered through the lens o…
The Geometry of Extended Kalman Filters on Manifolds with Affine Connection
Yixiao Ge, Pieter van Goor, Robert Mahony
The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The classical formulation of the EKF is posed for nonlinear…
Synchronous Models and Fundamental Systems in Observer Design
Pieter van Goor, Robert Mahony
This paper introduces the concept of a synchronous model as an extension of the internal model concept used in observer design for dynamical systems. A system is said to contain a…
Equivariant Filter Design for Range-only SLAM
Yixiao Ge, Arthur Pearce, Pieter van Goor +1
Range-only Simultaneous Localisation and Mapping (RO-SLAM) is of interest due to its practical applications in ultra-wideband (UWB) and Bluetooth Low Energy (BLE) localisation in t…
Equivariant IMU Preintegration with Biases: a Galilean Group Approach
Giulio Delama, Alessandro Fornasier, Robert Mahony +1
This letter proposes a new approach for Inertial Measurement Unit (IMU) preintegration, a fundamental building block that can be leveraged in different optimization-based Inertial…
Global Minimum Energy State Estimation for Embedded Nonlinear Systems with Symmetry
Pieter van Goor, Robert Mahony
Choosing a nonlinear state estimator for an application often involves a trade-off between local optimality (such as provided by an extended Kalman filter) and (almost-/semi-) glob…
Geometric Data Fusion for Collaborative Attitude Estimation
Yixiao Ge, Behzad Zamani, Pieter van Goor +2
In this paper, we consider the collaborative attitude estimation problem for a multi-agent system. The agents are equipped with sensors that provide directional measurements and re…
A Geometric Perspective on Fusing Gaussian Distributions on Lie Groups
Yixiao Ge, Pieter van Goor, Robert Mahony
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. A…
Exploiting polar symmetry in designing equivariant observers for vision-based motion estimation
Tarek Bouazza, Robert Mahony, Tarek Hamel
Accurately estimating camera motion from image sequences poses a significant challenge in computer vision and robotics. Many computer vision methods first compute the essential mat…
Exploiting Equivariance in the Design of Tracking Controllers for Euler-Poincare Systems on Matrix Lie Groups
Matthew Hampsey, Pieter van Goor, Ravi Banavar +1
The trajectory tracking problem is a fundamental control task in the study of mechanical systems. A key construction in tracking control is the error or difference between an actua…
MSCEqF: A Multi State Constraint Equivariant Filter for Vision-aided Inertial Navigation
Alessandro Fornasier, Pieter van Goor, Eren Allak +2
This letter re-visits the problem of visual-inertial navigation system (VINS) and presents a novel filter design we dub the multi state constraint equivariant filter (MSCEqF, in an…
Exploiting spatial group error and synchrony for a unicycle tracking controller
Matthew Hampsey, Pieter van Goor, Robert Mahony
Trajectory tracking for the kinematic unicycle has been heavily studied for several decades. The unicycle admits a natural $\SE(2)$ symmetry, a key structure exploited in many of t…
Synchronous Observer Design for Inertial Navigation Systems with Almost-Global Convergence
Pieter van Goor, Tarek Hamel, Robert Mahony
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…
A Note on the Extended Kalman Filter on a Manifold
Yixiao Ge, Pieter van Goor, Robert Mahony
The kinematics of many control systems, especially in the robotics field, naturally live on smooth manifolds. Most classical state-estimation algorithms, including the extended Kal…
Equivariant Symmetries for Inertial Navigation Systems
Alessandro Fornasier, Yixiao Ge, Pieter van Goor +2
This paper investigates the problem of inertial navigation system (INS) filter design through the lens of symmetry. The extended Kalman filter (EKF) and its variants have been the…
Equivariant Filter (EqF)
Pieter van Goor, Tarek Hamel, Robert Mahony
The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; that is, their state lies in a smooth manifold equippe…