Hybrid Attitude and Gyro-Bias Observer Design on $SO(3)$

Berkane, Soulaimane; Abdessameud, Abdelkader; Tayebi, Abdelhamid

doi:10.1109/tac.2017.2705558

Cited by 44 publications

(35 citation statements)

References 19 publications

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“…Note that the parameters λ F and κ depend on the initial conditions, which is different from Theorem 1. This nonuniform type of exponential stability is a consequence of the angular velocity bias (see, for instance, the hybrid observers on SO(3) in [35] and the hybrid observers on SE(3) in [21]).…”

Section: Hybrid Observers Design Using Biased Angular Velocitymentioning

confidence: 99%

Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements

Wang

Tayebi

2020

IEEE Trans. Automat. Contr.

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This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group SE2(3), leading to global exponential stability. The first observer relies on fixed gains, while the second one uses variable gains depending on the solution of a continuous Riccati equation (CRE). These observers are then extended to handle biased angular velocity measurements. Both simulation and experimental results are presented to illustrate the performance of the proposed observers.

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Section: Hybrid Observers Design Using Biased Angular Velocitymentioning

confidence: 99%

Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements

Wang

Tayebi

2020

IEEE Trans. Automat. Contr.

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“…Moreover, for any distinct non-negative scalars ρ i , i = 1, 2, 3, the matrix M is positive semi-definite with three distinct eigenvalues. From (15), one can notice that σ R has two terms: the first term k R ψ a (MR) is commonly used for the establishment of the stability proofs of the attitude estimation subsystem; see for instance [6], [17]. The second term depending on the estimation errorx is an asymptotically vanishing perturbation term as it will be shown later.…”

Section: B Error Dynamics and Stability Analysismentioning

confidence: 99%

“…A local Riccati-based nonlinear observer, inspired from [16], has been proposed in [14]. Motivated by the work in [17], [18], hybrid nonlinear observers, with global exponential stability guarantees, have been proposed in [15].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Observers for Stereo-Vision-Aided Inertial Navigation

Wang

Tayebi

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on SO(3) × R 15 relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame. Unlike the existing local Kalman-type observers, our proposed nonlinear observer guarantees almost global asymptotic stability and local exponential stability. A detailed uniform observability analysis has been conducted and sufficient conditions are derived. Moreover, a hybrid version of the proposed observer is provided to handle the intermittent nature of the measurements in practical applications. Simulation and experimental results are provided to illustrate the effectiveness of the proposed state observer.

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“…A large body of works on nonlinear observers has been devoted to attitude observer design on the Special Orthogonal group SO(3) (see (Mahony et al 2008, Berkane, Abdessameud & Tayebi 2017, Trumpf, Mahony, Hamel & Lageman 2012, Khosravian, Trumpf, Mahony & Hamel 2016, Zlotnik & Forbes 2017, Batista, Silvestre & Oliveira 2014 and the references therein) and to pose observer design on the Special Euclidean group SE(3) (see (Baldwin, Mahony, Trumpf, Hamel & Cheviron 2007, Izadi & Sanyal 2016, Hua, Zamani, Trumpf, Mahony & Hamel 2011, Wang & Tayebi 2017, Vasconcelos, Cunha, Silvestre & Oliveira 2010 and the references therein). Various refinements have been carried out to take particularities of the considered system and available sensors into account.…”

Section: Introductionmentioning

confidence: 99%

“…Time delay in output measurements is considered in (Khosravian et al 2016) for velocity-aided attitude observer design. Hybrid nonlinear attitude and pose observers are proposed in (Berkane et al 2017, Wang & Tayebi 2019 to overcome topological obstructions of Lie groups containing rotations (Bhat & Bernstein 2000) so that global asymptotical stability can be achieved. These are just a very nonexhaustive list of examples.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear observer design on SL(3) for homography estimation by exploiting point and line correspondences with application to image stabilization

et al. 2020

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Although homography estimation from correspondences of mixed-type features, namely points and lines, has been relatively well studied with algebraic approaches by the computer vision community, this problem has never been addressed with nonlinear observer paradigms. In this paper, a novel nonlinear observer on the Special Linear group SL(3) applied to homography estimation is developed. The key advance with respect to similar works on the topic is the formulation of observer innovation that exploits directly point and line correspondences as input without requiring prior algebraic reconstruction of individual homographies. Rigourous observability and stability analysis is provided. A potential application to image stabilization in presence of very fast camera motion, severe occlusion, specular reflection, image blur, and light saturation is demonstrated with very encouraging results.

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Hybrid Attitude and Gyro-Bias Observer Design on $SO(3)$

Cited by 44 publications

References 19 publications

Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements

Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements

Nonlinear Observers for Stereo-Vision-Aided Inertial Navigation

Nonlinear observer design on SL(3) for homography estimation by exploiting point and line correspondences with application to image stabilization

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