Sigma Point Kalman Filtering on Matrix Lie Groups Applied to the SLAM Problem

Forbes, James Richard; Zlotnik, David Evan

doi:10.1007/978-3-319-68445-1_37

Cited by 4 publications

(4 citation statements)

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“…This is exploited for state estimation in visual-inertial odometry with mobile robots. In [12], Kalman filtering adapted to data in SO (3) is used for estimating the attitude of robots that can rotate in space. The optimization problem in [13] uses sequential quadratic programming (SQP) working directly on the manifold SO(3) × R 3 .…”

Section: B Manifolds In Robot Applicationsmentioning

confidence: 99%

Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control

Calinon

2020

IEEE Robot. Automat. Mag.

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This paper presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. We first discuss the roles of Riemannian manifolds, geodesics and parallel transport in robotics. We then present several forms of manifolds that are already employed in robotics, by also listing manifolds that have been underexploited so far but that have potentials in future robot learning applications. A varied range of techniques employing Gaussian distributions on Riemannian manifolds are then introduced, including clustering, regression, information fusion, planning and control problems. Two examples of applications are presented, involving the control of a prosthetic hand from surface electromyography (sEMG) data, and the teleoperation of a bimanual underwater robot. Further perspectives are finally discussed with suggestions of promising research directions.

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Section: B Manifolds In Robot Applicationsmentioning

confidence: 99%

Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control

Calinon

2020

IEEE Robot. Automat. Mag.

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“…We define sigma points using (4) and the statistics of noise w n , and pass them through (12). Then, to findχ n one is faced with the optimization problem of computing a weighted mean on M. This route has already been advocated in [12]- [14,23]. However, to keep the implementation simple and analog to the EKF, we suggest to merely propagate the mean using the unnoisy state model, leading tô…”

Section: Unscented Kalman Filtering On Parallelizable Manifoldsmentioning

confidence: 99%

“…The idea is to make the EKF estimate an error instead of the state directly, leading to error state EKFs [4,9]- [11] and their UKF counterparts [12]- [14]. The set of orientations of a body in space is the Lie group SO(3) and efforts devoted to estimation on SO(3) have paved the way to EKF on Lie groups, see [1,15]- [19] and unscented Kalman filtering on Lie groups, see [7,8,13,20]- [23].…”

Section: Introductionmentioning

confidence: 99%

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A Code for Unscented Kalman Filtering on Manifolds (UKF-M)

Brossard

Barrau

Bonnabel

2020

2020 IEEE International Conference on Robotics and Automation (ICRA)

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The present paper introduces a novel methodology for Unscented Kalman Filtering (UKF) on manifolds that extends previous work by the authors on UKF on Lie groups. Beyond filtering performance, the main interests of the approach are its versatility, as the method applies to numerous state estimation problems, and its simplicity of implementation for practitioners not being necessarily familiar with manifolds and Lie groups. We have developed the method on two independent open-source Python and Matlab frameworks we call UKF-M, for quickly implementing and testing the approach. The online repositories contain tutorials, documentation, and various relevant robotics examples that the user can readily reproduce and then adapt, for fast prototyping and benchmarking. The code is available at

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