Attitude Observation for Second Order Attitude Kinematics

Ng, Yonhon; Goor, Pieter van; Mahony, Robert; Hamel, Tarek

doi:10.1109/cdc40024.2019.9029785

Cited by 11 publications

(10 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…for U ≡ 0 similar to the drift considered in the authors earlier work on second order attitude kinematics [22]. This is characteristic of all second order kinematic systems.…”

Section: Problem Formulationsupporting

confidence: 63%

Equivariant Systems Theory and Observer Design for Second Order Kinematic Systems on Matrix Lie Groups

Goor²,

Hamel³

et al. 2020

2020 59th IEEE Conference on Decision and Control (CDC)

Self Cite

View full text Add to dashboard Cite

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 group with the inputs lying in the tangent of the tangent bundle known as the double tangent bundle. We provide a simple parameterization of both the tangent bundle state space and the input space (the fiber space of the double tangent bundle) and then introduce a semi-direct product group and group actions onto both the state and input spaces. We show that with the proposed group actions the second order kinematics are equivariant. An equivariant lift of the kinematics onto the symmetry group is defined and used to design a nonlinear observer on the lifted state space using nonlinear constructive design techniques. A simple hovercraft simulation verifies the performance of our observer.

show abstract

“…for U ≡ 0 similar to the drift considered in the authors earlier work on second order attitude kinematics [22]. This is characteristic of all second order kinematic systems.…”

Section: Problem Formulationsupporting

confidence: 63%

Equivariant Systems Theory and Observer Design for Second Order Kinematic Systems on Matrix Lie Groups

Goor²,

Hamel³

et al. 2020

2020 59th IEEE Conference on Decision and Control (CDC)

Self Cite

View full text Add to dashboard Cite

show abstract

“…The gauge invariance inherent in the SLAM problem induces a homogeneous space structure that underlies recent work by the authors [vHM20,vMHT20,vMHT19,vM21]. This perspective is critically important for the visual SLAM problem where cameras are the primary exteroceptive sensor and the SLAM problem can no longer be modelled [vGHM20] using the SE n+1 (3) geometry introduced by Barrau et [NvMH19,NvHM20] for second order kinematics, while Phogat et al considered a direct product structure for general second order systems on Matrix Lie groups [PC20].…”

Section: Literature Reviewmentioning

confidence: 99%

Observer Design for Nonlinear Systems with Equivariance

Mahony,

van Goor,

Hamel

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high performance observers. A key insight is to pose the observer state to lie in the symmetry group rather than on the system state space. This allows one to define a globally defined intrinsic equivariant error but poses a challenge in defining internal dynamics for the observer. By choosing an equivariant lift of the system dynamics for the observer internal model we show that the error dynamics have a particularly nice form. Applying the methodology of Extended Kalman Filtering (EKF) to the equivariant error state yields the Equivariant Filter (EqF). The geometry of the state-space manifold appears naturally as a curvature modification to the classical EKF Riccati equation. 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.

show abstract

“…non-biased inertial navigation problem, nonlinear geometric deterministic [6] [7] and stochastic [8] observers for second order kinematic systems have been considered. Different from these approaches, Barrau and Bonnabel [2] proposed the Invariant Extended Kalman Filter (IEKF), a geometric EKFlike observer for kinematic systems posed on a matrix Lie group with invariance properties.…”

Section: Introductionmentioning

confidence: 99%

Equivariant Filter Design for Inertial Navigation Systems with Input Measurement Biases

Fornasier¹,

Ng²,

Mahony³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Inertial Navigation Systems (INS) are a key technology for autonomous vehicles applications. Recent advances in estimation and filter design for the INS problem have exploited geometry and symmetry to overcome limitations of the classical Extended Kalman Filter (EKF) approach that formed the mainstay of INS systems since the mid-twentieth century. The industry standard INS filter, the Multiplicative Extended Kalman Filter (MEKF), uses a geometric construction for attitude estimation coupled with classical Euclidean construction for position, velocity and bias estimation. The recent Invariant Extended Kalman Filter (IEKF) provides a geometric framework for the full navigation states, integrating attitude, position and velocity, but still uses the classical Euclidean construction to model the bias states. In this paper, we use the recently proposed Equivariant Filter (EqF) framework to derive a novel observer for biased inertial-based navigation in a fully geometric framework. The introduction of virtual velocity inputs with associated virtual bias leads to a full equivariant symmetry on the augmented system. The resulting filter performance is evaluated with both simulated and realworld data, and demonstrates increased robustness to a wide range of erroneous initial conditions, and improved accuracy when compared with the industry standard Multiplicative EKF (MEKF) approach.

show abstract

Attitude Observation for Second Order Attitude Kinematics

Cited by 11 publications

References 24 publications

Equivariant Systems Theory and Observer Design for Second Order Kinematic Systems on Matrix Lie Groups

Equivariant Systems Theory and Observer Design for Second Order Kinematic Systems on Matrix Lie Groups

Observer Design for Nonlinear Systems with Equivariance

Equivariant Filter Design for Inertial Navigation Systems with Input Measurement Biases

Contact Info

Product

Resources

About