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Estimating SE(3) elements using a dual quaternion based linear Kalman filter

Rangaprasad Arun Srivatsan, Gillian T. Rosen, D. Feroze Naina Mohamed, Howie Choset
<i title="Robotics: Science and Systems Foundation"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gjhqqq6dgnaupkvp2ckhefvv6i" style="color: black;">Robotics: Science and Systems XII</a> </i> &nbsp;
Many applications in robotics such as registration, object tracking, sensor calibration, etc. use Kalman filters to estimate a time invariant SE(3) element by locally linearizing a non-linear measurement  ...  In this work, we use a dual quaternion to represent the SE(3) element and use multiple measurements simultaneously to rewrite the measurement model in a truly linear form with state dependent measurement  ...  Several researchers have noted that filters used for estimating SE(3) elements have non-linear update models [11] , and hence linear Kalman filters produce poor estimates of SE(3) elements.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15607/rss.2016.xii.013">doi:10.15607/rss.2016.xii.013</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/rss/SrivatsanRMC16.html">dblp:conf/rss/SrivatsanRMC16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bmcggaiufbbfxied7pqfxc2lce">fatcat:bmcggaiufbbfxied7pqfxc2lce</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180603132249/http://www.roboticsproceedings.org/rss12/p13.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2a/71/2a714c7dedec9e7a6a7103c46261845d52a8b390.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15607/rss.2016.xii.013"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

The SO(3) and SE(3) Lie Algebras of Rigid Body Rotations and Motions and their Application to Discrete Integration, Gradient Descent Optimization, and State Estimation [article]

Eduardo Gallo
<span title="2022-05-25">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Common mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter  ...  To do so, this article provides an in-depth review of the SO(3) and SE(3) Lie groups, known as the special orthogonal and special Euclidean groups of R3, which represent the rigid body rotations and motions  ...  Both approaches are combined in section 3.3.3, which describes the extended Kalman filter or EKF, the most widely used non linear state estimation algorithm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2205.12572v1">arXiv:2205.12572v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bjmlgi3vqzbrvgxod3bh6qmuom">fatcat:bjmlgi3vqzbrvgxod3bh6qmuom</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220527031706/https://arxiv.org/pdf/2205.12572v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/dc/f8/dcf80b5485ce13ad51f7a93d1f1ccba82cae594a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2205.12572v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Online Camera Registration for Robot Manipulation [chapter]

Neil Dantam, Heni Ben Amor, Henrik Christensen, Mike Stilman
<span title="2015-11-13">2015</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lirc5icuifhy7ln5rynpn4ak2e" style="color: black;">Springer Tracts in Advanced Robotics</a> </i> &nbsp;
We implement the approach on a Schunk LWA4 manipulator and Logitech C920 camera, servoing to target and pre-grasp configurations. Our filtering software is available under a permissive license.  ...  We register the camera online, converging in seconds, by visually tracking features on the robot and filtering the result.  ...  7) Kalman Filtering Next, we use an Extended Kalman filter (EKF) to attenuate noise over time, taking care to remain in the SE(3) manifold.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-23778-7_13">doi:10.1007/978-3-319-23778-7_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u7y5byep25g6fexwupdqhtew3q">fatcat:u7y5byep25g6fexwupdqhtew3q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160103075250/http://www.neil.dantam.name/papers/dantam2014online.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/31/a5/31a55a72c0d1e692f549074a0ceffc2804131ec3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-23778-7_13"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Camera Pose Filtering with Local Regression Geodesics on the Riemannian Manifold of Dual Quaternions [article]

Benjamin Busam and Tolga Birdal and Nassir Navab
<span title="2017-08-29">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We use a numerically stable Lie algebra of the dual quaternions together with and operators to locally linearize the 6D pose space.  ...  In this paper, we propose a novel principal component local regression filter acting directly on the Riemannian manifold of unit dual quaternions DH_1.  ...  in SE (3) which is done with an Extended Kalman Filter (EKF) for pose estimation by Filipe [12] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1704.07072v4">arXiv:1704.07072v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qup7lbp4czfhpptcxcaktidnme">fatcat:qup7lbp4czfhpptcxcaktidnme</a> </span>
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Camera Pose Filtering with Local Regression Geodesics on the Riemannian Manifold of Dual Quaternions

Benjamin Busam, Tolga Birdal, Nassir Navab
<span title="">2017</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6s36fqp6q5hgpdq2scjq3sfu6a" style="color: black;">2017 IEEE International Conference on Computer Vision Workshops (ICCVW)</a> </i> &nbsp;
We use a numerically stable Lie algebra of the dual quaternions together with exp and log operators to locally linearize the 6D pose space.  ...  In this paper, we propose a novel principal component local regression filter acting directly on the Riemannian manifold of unit dual quaternions DH 1 .  ...  in SE (3) which is done with an Extended Kalman Filter (EKF) for pose estimation by Filipe [12] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iccvw.2017.287">doi:10.1109/iccvw.2017.287</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iccvw/BusamBN17.html">dblp:conf/iccvw/BusamBN17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c7t4kbxacfeqxo53rl36qmdoki">fatcat:c7t4kbxacfeqxo53rl36qmdoki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200318224201/http://openaccess.thecvf.com/content_ICCV_2017_workshops/papers/w35/Busam_Camera_Pose_Filtering_ICCV_2017_paper.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ec/17/ec17f0c6b1d15607d18d61e675778768d08887d5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iccvw.2017.287"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

A Dual Quaternion Based Fusion Framework for IMU Data with 6 DOF Pose

<span title="">2016</span> <i title="Clausius Scientific Press, Inc."> Journal of Electronics and Information Science </i> &nbsp;
Based on the highly successful application of quaternions for attitude estimation, this paper proposes an approach to position, velocity and attitude estimation for Micro Aerial Vehicles(MAVs) using dual  ...  In this paper, the sensor fusion algorithm is pivoted around EKF(Extended Kalman Filter) and dual quaternion.  ...  This paper proposed a fusion framework using IMU with other sensors based on dual quaternion for MAVs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.23977/jeis.2016.11005">doi:10.23977/jeis.2016.11005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q3wvexxrvzdk3llzqi4rzbc4uq">fatcat:q3wvexxrvzdk3llzqi4rzbc4uq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721235732/http://www.clausiuspress.com/assets/default/article/2017/01/07/article_1483814010.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d2/27/d227664904d1d36b9e1cc95916fb7209babdfe06.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.23977/jeis.2016.11005"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Pose Estimation with Dual Quaternions and Iterative Closest Point

Aksel Sveier, Torstein A. Myhre, Olav Egeland
<span title="">2018</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lotzoejqpjhmjn2kywwcxlndie" style="color: black;">2018 Annual American Control Conference (ACC)</a> </i> &nbsp;
This paper presents a method for pose estimation of a rigid body using unit dual quaternions where pose measurements from point clouds are filtered with a multiplicative extended Kalman filter (MEKF).  ...  The unit constraint of the dual quaternion is ensured in the filtering process with the Dual Quaternion MEKF (DQ-MEKF), where the measurement updates are performed using the dual quaternion product so  ...  It was shown that the filter produced better results than ICP alone. The measurement update for estimating elements on the SE(3) and SO(3) group is nonlinear.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.23919/acc.2018.8431077">doi:10.23919/acc.2018.8431077</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/amcc/SveierME18.html">dblp:conf/amcc/SveierME18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cbi7bt6xlnfbjjggbkcant65vi">fatcat:cbi7bt6xlnfbjjggbkcant65vi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190501182128/https://ntnuopen.ntnu.no/ntnu-xmlui/bitstream/handle/11250/2585836/260218_v20_Pose_Estimation_using_Dual_Quaternions_and_ICP%28ACCEPTED%29.pdf?sequence=2" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/86/a9/86a95350354161301f9272d93448d3499e7c4c24.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.23919/acc.2018.8431077"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Online multi-camera registration for bimanual workspace trajectories

Neil T. Dantam, Heni Ben Amor, Henrik I. Christensen, Mike Stilman
<span title="">2014</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p2nw3ufilvbknotfq56xtvnhtq" style="color: black;">2014 IEEE-RAS International Conference on Humanoid Robots</a> </i> &nbsp;
Our filtering software is available under a permissive license. 1  ...  We demonstrate the approach using Schunk LWA4 and SDH manipulators and Logitech C920 cameras, showing accurate relative positioning for pen-capping and object hand-off tasks.  ...  SE(3) Median and Extended Kalman Filter We apply median and extended Kalman filtering in the special Euclidean group SE(3) to the measurements for wrist offset wi S w i and camera registration b S cj ,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/humanoids.2014.7041422">doi:10.1109/humanoids.2014.7041422</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/humanoids/DantamACS14.html">dblp:conf/humanoids/DantamACS14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3yskctybb5ft3fyzludk6ogs3a">fatcat:3yskctybb5ft3fyzludk6ogs3a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150912021423/http://www.neil.dantam.name/papers/dantam2014multi.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e1/78/e1789dc2ae8859c2f7a31c613c7ff513a59f4bf4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/humanoids.2014.7041422"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Bingham Distribution-Based Linear Filter for Online Pose Estimation

Arun Srivatsan Rangaprasad, Mengyun Xu, Nicolas Zevallos-Roberts, Howie Choset
<span title="2017-07-12">2017</span> <i title="Robotics: Science and Systems Foundation"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gjhqqq6dgnaupkvp2ckhefvv6i" style="color: black;">Robotics: Science and Systems XIII</a> </i> &nbsp;
A combination of Gaussian and Bingham distributions is used to develop a linear filter that accurately estimates the distribution of the pose parameters, in their true space.  ...  Such a description can be inadequate when using parameters such as unit-quaternions that are not unimodally distributed.  ...  [29] used dual-quaternions and developed a linear Kalman filter which is robust to initial pose errors.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15607/rss.2017.xiii.016">doi:10.15607/rss.2017.xiii.016</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/rss/RangaprasadXZC17.html">dblp:conf/rss/RangaprasadXZC17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kbb5h3gx6rhdjmevdpbxc74peq">fatcat:kbb5h3gx6rhdjmevdpbxc74peq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190728132911/http://www.roboticsproceedings.org:80/rss13/p16.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f7/83/f78353122c9980cada487b5d385ae279b08282ee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15607/rss.2017.xiii.016"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Dual Quaternion Particle Filtering for Pose Estimation

Aksel Sveier, Olav Egeland
<span title="">2020</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w55uhp5h3rdubpws6c5kic4vxm" style="color: black;">IEEE Transactions on Control Systems Technology</a> </i> &nbsp;
This article presents a particle filter for pose estimation using unit dual quaternion kinematics.  ...  Index Terms-Dual quaternions, kalman filters, nonlinear filters, particle filtters, pose estimation.  ...  Torstein A. Myhre for proofreading this paper and sharing his CUDA C++ software implementation of the particle filter, which they extended and altered to fit their own algorithms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tcst.2020.3026926">doi:10.1109/tcst.2020.3026926</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2rq74kgktrhznfcp67k5zqmluy">fatcat:2rq74kgktrhznfcp67k5zqmluy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201120183626/https://ieeexplore.ieee.org/ielx7/87/4389040/09223725.pdf?tp=&amp;arnumber=9223725&amp;isnumber=4389040&amp;ref=" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/80/bd/80bde412e0e7e49fa9d5cf715f6a826ce85f355f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tcst.2020.3026926"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Decentralized and Recursive Identification for Cooperative Manipulation of Unknown Rigid Body with Local Measurements [article]

Taosha Fan, Huan Weng, Todd Murphey
<span title="2018-02-22">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Dynamic consensus in different coordinates and a filter for dual quaternion are developed with which the identification problem can be solved in a distributed way.  ...  This paper proposes a fully decentralized and recursive approach to online identification of unknown kinematic and dynamic parameters for cooperative manipulation of a rigid body based on commonly used  ...  ACKNOWLDGEMENT This material is based upon work supported by the National Science Foundation under Grant CNS 1329891.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.01555v2">arXiv:1709.01555v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ta5dmzyrkrcrrickyyb5u367x4">fatcat:ta5dmzyrkrcrrickyyb5u367x4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191019192551/https://arxiv.org/pdf/1709.01555v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/70/dc/70dc02834f879f43978e10a60de47653f78ae2f3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.01555v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

6D Pose Uncertainty in Robotic Perception [chapter]

Wendelin Feiten, Pradeep Atwal, Robert Eidenberger, Thilo Grundmann
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> Advances in Robotics Research </i> &nbsp;
The projection of this Gaussian induces a distribution over 6D poses. One such base element is called a Projected Gaussian.  ...  The translation part is described either by a 3D vector (when we define the probability density function) or by a purely imaginary quaternion (which leads to a prepresentation of a transform by a dual  ...  Definition 2: Let SE(3) be the group of rigid transforms in R 3 , the rotation represented by a unit quaternion or equivalently a point on S 3 and the translation by a vector in R 3 , SE(3) ∼ S 3 × R 3  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-01213-6_9">doi:10.1007/978-3-642-01213-6_9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hg56loxjzfe6rhoyb4g6lg4wky">fatcat:hg56loxjzfe6rhoyb4g6lg4wky</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810213037/https://static.aminer.org/pdf/PDF/000/354/168/a_general_representation_for_orientational_uncertainty_using_random_unit_quarternions.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/aa/a7/aaa7e0293305f06bcae279e7b302ef798e2e4b27.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-01213-6_9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

MPG - A Framework for Reasoning on 6 DOF Pose Uncertainty [article]

Wendelin Feiten, Muriel Lang
<span title="2017-07-05">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
As parameterization of the 6D poses we select the dual quaternions, i.e. any pose is represented by two quaternions. The orientation part of a pose is described by a unit quaternion.  ...  The most frequently used approaches to describe the pdfs are sample based description and multivariate normal (Gaussian) distributions.  ...  This space can be interpreted as a linearization of SE(3) w.r.t. the dual quaternion representation at a rotation represented by a unit quaternion q 0 = [a, b, c, d] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1707.01941v1">arXiv:1707.01941v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5nrpibufobfibgpg5tsqqdfglm">fatcat:5nrpibufobfibgpg5tsqqdfglm</a> </span>
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Kalman Filter: Historical Overview and Review of Its Use in Robotics 60 Years after Its Creation

Claudio Urrea, Rayko Agramonte, Giovanni Diraco
<span title="2021-09-02">2021</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zlknqk4ahbcsthbafxw55emm7a" style="color: black;">Journal of Sensors</a> </i> &nbsp;
Sixty years after its creation, the Kalman filter is still used in autonomous navigation processes, robot control, and trajectory tracking, among other activities.  ...  Due to its widespread application in the robotics field, the Kalman filter has received increased attention from researchers.  ...  This variation has derived new filters, such as the DQEKF (Dual Quaternion Extended Kalman Filter) and the QVEKF (Quaternion Vector Extended Kalman Filter) presented in [20] ; the main difference between  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2021/9674015">doi:10.1155/2021/9674015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jpbjftwvjbcfzcr4i3j32epdru">fatcat:jpbjftwvjbcfzcr4i3j32epdru</a> </span>
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An EKF for Lie Groups with Application to Crane Load Dynamics

Alexander Meyer Sjøberg, Olav Egeland
<span title="">2019</span> <i title="Norwegian Society of Automatic Control"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b5wuwk3dqzchlhpuis7sqm4zje" style="color: black;">Modeling, Identification and Control</a> </i> &nbsp;
The filter is applied to estimation on SO(3) a case where a stereo camera setup tracks a crane wire with a payload.  ...  An extended Kalman filter (EKF) for systems with configuration given by matrix Lie groups is presented.  ...  can be linearized, and a simple Kalman filter can be used to estimate the system states as generalized coordinates.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4173/mic.2019.2.3">doi:10.4173/mic.2019.2.3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2nf2izbzwfdp5gkqmh4l5zywja">fatcat:2nf2izbzwfdp5gkqmh4l5zywja</a> </span>
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