Globally Asymptotically Stable Attitude Observer on SO(3)

Wu, Tse-Huai; Kaufman, Evan; Lee, Taeyoung

doi:10.1109/cdc.2015.7402527

Cited by 30 publications

(15 citation statements)

References 13 publications

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“…Hence, the best stability result one can achieve with the continuous timeinvariant observers, for inertial navigation, is almost global asymptotic stability. Motivated by the hybrid observers designed on the Lie groups SO(3) and SE(3) in [6], [32], [38], [39], observer ( 14)-( 15) can be hybridized by introducing a resetting mechanism that prevents the state variables from converging to or getting stuck at the undesired equilibrium points of the closed-loop system [19]. Applying the framework of hybrid dynamical systems [40]- [42], the equilibrium point ( R = I 3 , p = ṽ = 0) for the hybrid version of the observer ( 17)-( 19) (with both fixed-gain and variable-gain approaches) is uniformly globally exponentially stable [19, Theorem 1 and Theorem 2].…”

Section: Motivated By the Geometric Nonlinear Observers On Se(3)mentioning

confidence: 99%

Observers Design for Inertial Navigation Systems: A Brief Tutorial

Wang

Tayebi

2020

Preprint

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The design of navigation observers able to simultaneously estimate the position, linear velocity and orientation of a vehicle in a three-dimensional space is crucial in many robotics and aerospace applications. This problem was mainly dealt with using the extended Kalman filter and its variants which proved to be instrumental in many practical applications. Although practically efficient, the lack of strong stability guarantees of these algorithms motivated the emergence of a new class of geometric navigation observers relying on Riemannian geometry tools, leading to provable strong stability properties. The objective of this brief tutorial is to provide an overview of the existing estimation schemes, as well as some recently developed geometric nonlinear observers, for autonomous navigation systems relying on inertial measurement unit (IMU) and landmark measurements.

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Section: Motivated By the Geometric Nonlinear Observers On Se(3)mentioning

confidence: 99%

Observers Design for Inertial Navigation Systems: A Brief Tutorial

Wang

Tayebi

2020

Preprint

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“…Most of the attitude estimation literature addresses the case of magnetic heading attitude estimation using MEMS IMUs (Crassidis et al, 2007; Guo et al, 2008; Hamel and Mahony, 2006; Metni et al, 2005, 2006; Wu et al, 2015). Mahony et al (2008) reported an attitude nonlinear complementary filter on SO ( 3 ) .…”

Section: Literature Reviewmentioning

confidence: 99%

“…as a low-frequency estimate of (23). This approximation (25) is used in Costanzi et al (2016), Mahony et al (2008), Pflimlin et al (2007), and Wu et al (2015). Figure 2 presents the vehicle acceleration experienced by the JHU ROV in the vehicle trial.…”

Section: Preliminariesmentioning

confidence: 99%

Adaptive bias and attitude observer on the special orthogonal group for true-north gyrocompass systems: Theory and preliminary results

Spielvogel

Whitcomb

2019

The International Journal of Robotics Research

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This article reports an adaptive sensor bias observer and attitude observer operating directly on [Formula: see text] for true-north gyrocompass systems that utilize six-degree-of-freedom inertial measurement units (IMUs) with three-axis accelerometers and three-axis angular rate gyroscopes (without magnetometers). Most present-day low-cost robotic vehicles employ attitude estimation systems that employ microelectromechanical system (MEMS) magnetometers, angular rate gyros, and accelerometers to estimate magnetic attitude (roll, pitch, and magnetic heading) with limited heading accuracy. Present-day MEMS gyros are not sensitive enough to dynamically detect the Earth’s rotation, and thus cannot be used to estimate true-north geodetic heading. Relying on magnetic compasses can be problematic for vehicles that operate in environments with magnetic anomalies and those requiring high-accuracy navigation as the limited accuracy ([Formula: see text] error) of magnetic compasses is typically the largest error source in underwater vehicle navigation systems. Moreover, magnetic compasses need to undergo time-consuming recalibration for hard-iron and soft-iron errors every time a vehicle is reconfigured with a new instrument or other payload, as very frequently occurs on oceanographic marine vehicles. In contrast, the gyrocompass system reported herein utilizes fiber optic gyroscope (FOG) IMU angular rate gyro and MEMS accelerometer measurements (without magnetometers) to dynamically estimate the instrument’s time-varying true-north attitude (roll, pitch, and geodetic heading) in real-time while the instrument is subject to a priori unknown rotations. This gyrocompass system is immune to magnetic anomalies and does not require recalibration every time a new payload is added to or removed from the vehicle. Stability proofs for the reported bias and attitude observers, preliminary simulations, and a full-scale vehicle trial are reported that suggest the viability of the true-north gyrocompass system to provide dynamic real-time true-north heading, pitch, and roll utilizing a comparatively low-cost FOG IMU.

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“…The attitude can be estimated through Gaussian filters which often consider unit-quaternion in the representation, such as Kalman filter (KF) [6], extended KF (EKF) [7], and multiplicative EKF (MEKF) [8]. However, to successfully address the nonlinear nature of the attitude problem a nonlinear deterministic filter evolved directly on the Special Orthogonal Group SO (3) can be used [3][4][5][9][10][11][12]. As a matter of fact, nonlinear deterministic attitude filters are simpler in derivation, require less computational power, and demonstrate better tracking performance in comparison with Gaussian filters [3].…”

Section: Introductionmentioning

confidence: 99%

“…Consider the pose kinematics in(10) and the group of noise-free velocity measurements in(11) where Y m = Ω + b, in addition to other vector measurements given in(8) and(9)coupled with the filter in (26), (27), (28), (29), and (30). Let Assumption 1 hold.…”

mentioning

confidence: 99%

Guaranteed Performance of Nonlinear Pose Filter on SE(3)

Hashim¹,

Brown²,

McIsaac³

2019

2019 American Control Conference (ACC)

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This paper presents a novel nonlinear pose filter evolved directly on the Special Euclidean Group SE (3) with guaranteed characteristics of transient and steady-state performance. The above-mention characteristics can be achieved by trapping the position error and the error of the normalized Euclidean distance of the attitude in a given large set and guiding them to converge systematically to a small given set. The error vector is proven to approach the origin asymptotically from almost any initial condition. The proposed filter is able to provide a reliable pose estimate with remarkable convergence properties such that it can be fitted with measurements obtained from low-cost measurement units. Simulation results demonstrate high convergence capabilities and robustness considering large error in initialization and high level of uncertainties in measurements.

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Globally Asymptotically Stable Attitude Observer on SO(3)

Cited by 30 publications

References 13 publications

Observers Design for Inertial Navigation Systems: A Brief Tutorial

Observers Design for Inertial Navigation Systems: A Brief Tutorial

Adaptive bias and attitude observer on the special orthogonal group for true-north gyrocompass systems: Theory and preliminary results

Guaranteed Performance of Nonlinear Pose Filter on SE(3)

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