Article
Computer Science, Interdisciplinary Applications
Ziqi Ma, Zhuyong Liu, Pu You
Summary: A 3D corotational beam element formulated under the framework of special Euclidean group is proposed in this paper. The introduction of the special Euclidean group SE(3) to describe the rigid body motion ensures the invariance of the force vectors and tangent matrix. The reformulation of the element matrices through direct coordinate transformation demonstrates the advantages of the SE(3) framework in terms of computational efficiency compared with the original R3 x SO(3) framework.
COMPUTERS & STRUCTURES
(2023)
Article
Engineering, Mechanical
Ju Chen, Ziheng Huang, Qiang Tian
Summary: A multisymplectic Lie algebra variational integrator (MLAVI) is proposed for simulating the dynamics of a flexible multibody system. The method uses geometrically exact beam elements on the special Euclidean Lie group SE(3) to describe the flexible bodies, and derives a reduced Lagrangian density on the Lie algebra. A novel equality relation lemma is also proved, which simplifies the Jacobi matrix of the MLAVI. Numerical examples validate the accuracy and efficiency of the proposed method.
MECHANISM AND MACHINE THEORY
(2022)
Article
Engineering, Multidisciplinary
Teng Zhang, Cheng Liu, Huiying Tang
Summary: A new geometrically exact shell model is proposed in this study to address finite deformation and rotation issues, utilizing drilling rotations to eliminate geometric nonlinearity of rigid-body motion. Objectivity of discretized strain measures is ensured through interpolating relative motion, and locking alleviation techniques are employed for shear and membrane locking in dynamic analysis. The methodology showcases versatility and robustness in numerical examples presented.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Engineering, Electrical & Electronic
Kailong Li, Wenkui Li
Summary: This paper investigates the error model based on the Lie group, focusing on the construction and filtering comparison of the Special Euclidean group SE(3) based error model for the inertial navigation system (INS). The conventional theory only focuses on state error definition and uses Euler angles for attitude representation. In order to enrich the SE(3) based error model family, this paper proposes a theoretical bridge that connects attitude estimation to error model construction using Rodrigues parameter and modified Rodrigues parameter. Field tests are conducted to assess the comprehensive performance of the existing SE(3) based error model for INS under different conditions.
DIGITAL SIGNAL PROCESSING
(2023)
Article
Automation & Control Systems
Hashim A. Hashim, Lyndon J. Brown, Kenneth McIsaac
Summary: Two novel nonlinear pose filters have been proposed on the Special Euclidean Group SE(3), ensuring prescribed characteristics of transient and steady-state performance. The first filter requires preliminary pose reconstruction, while the second can directly perform its function using a set of vectorial measurements.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2021)
Article
Operations Research & Management Science
Sergey Kovalev, Isabelle Chalamon, Fabio J. Petani
Summary: This paper addresses the problem of maximizing diversity in the selection of a group of entities. The diversity is measured using either Euclidean or squared Euclidean distance. The proposed algorithms provide a time complexity of O(n + k log k) and can be used for both distance measures.
ANNALS OF OPERATIONS RESEARCH
(2023)
Article
Computer Science, Information Systems
Fuchun Huang, Dong Li
Summary: In this letter, a new technique called Jointing Permutation, Group, and Antenna Index Spatial Modulation (JPGA-ISM) is proposed to increase the information capacity by exploiting the Permutation Index (PI) domain. Two algorithm devices are designed to maximize the minimum Euclidean distance (MED) between transmit vectors. The use of a PI matrix and specific algorithm devices results in improved performance compared to other systems in terms of bit error probability (BEP).
IEEE WIRELESS COMMUNICATIONS LETTERS
(2023)
Article
Automation & Control Systems
Hashim A. Hashim, Frank L. Lewis
Summary: Two novel robust nonlinear stochastic full pose estimators are proposed on the Special Euclidean Group SE(3), utilizing the structure of deterministic pose estimators but adapting it to stochastic sense. The efficiency and robustness of the estimators are demonstrated through numerical results testing against high levels of noise and bias.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2021)
Article
Engineering, Electrical & Electronic
Yu Zheng, Jiantao Xin, Hui Wang, Shengli Zhang, Yongjie Qiao
Summary: In this article, a simplified SCMA codebook with a separable structure is proposed for implementing a low-complexity detector. The design scheme increases the minimum Euclidean distance (MED) of the codebook and enables independent recovery of transmitted signals over each resource element (RE), thus reducing the complexity of detection.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
(2022)
Article
Mathematics, Applied
Wei Hu, Xiaojuan Yin
Summary: This paper investigates the rigidity degree of a generator-cogenerator and its application in self-injective algebras, providing explicit formulas for the rigidity degrees of all indecomposable modules over representation-finite self-injective algebras using combinatorial methods. The rigidity dimensions of some algebras of types A and E are also given as an application.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Automation & Control Systems
Sidney Roberto Carvalho, Ubirajara Franco Moreno
Summary: The network structure is crucial for the success of strategies in distributed and cooperative systems; consensus algorithms mainly deal with continuous values, but many problems require distributed consensus over countable values; this study proposes an approach based on semidefinite programming to design optimal weights for control of convergence in a distributed random consensus protocol; utilizing Markov theory and biological inspiration, a dynamic spreading model is developed to predict information diffusion.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Robotics
Vincenzo Lippiello, Jonathan Cacace
Summary: This study proposes a pose tracking system based on a single camera sensor to localize an unmanned aerial vehicle operating over a pipe-rack for inspection activities. Numerical simulations are conducted to demonstrate the effectiveness of the proposed approach.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2022)
Article
Mathematics, Applied
Huikang Liu, Man-Chung Yue, Anthony Man-Cho So
Summary: This paper addresses the problem of estimating a collection of group elements in a group based on noisy observations of pairwise ratios. The paper proposes a unified approach for solving this problem and provides theoretical guarantees on the estimation error. It also formulates geometric conditions required by the approach and verifies them for various subgroups of the orthogonal group. Additionally, the paper develops a novel spectral-type estimator based on metric entropy and shows the superiority of the proposed approach through numerical experiments.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2023)
Article
Mathematics
Josef Dick, Martin Ehler, Manuel Graef, Christian Krattenthaler
Summary: By studying the spectral decomposition of discrepancy kernels when constrained to compact subsets of R-d, we can numerically approximate Borel probability measures using finite atomic measures. We calculate the kernels' Fourier coefficients and determine their asymptotics for restrictions to the Euclidean ball in odd dimensions, the rotation group SO(3), and the Grassmannian manifold G(2,4). The L-2 discrepancy is then expressed in the Fourier domain, allowing for efficient numerical minimization using the nonequispaced fast Fourier transform, which is publicly available for SO(3) and derived here for G(2,4). We also provide numerical experiments for SO(3) and G(2,4).
CONSTRUCTIVE APPROXIMATION
(2023)
Article
Engineering, Mechanical
Pu You, Zhuyong Liu, Ziqi Ma
Summary: This paper explores another coordinate projection method for two-dimensional corotational beam element and proposes the projection relationship between the element frame and the local frame in the framework of Lie algebra se(2). Based on the description of SE(2), the formulation of corotational beam element and integration algorithm is presented. The local frame description greatly reduces the nonlinearity of the formula by eliminating the effect of the rigid body motion on the projection matrix, internal force, and inertial force. Several examples are performed to verify the step-size convergence and iterative efficiency of SE(2) description compared with R3 description. Moreover, frame invariance brought by SE(2) is valuable for improving computing efficiency, as demonstrated by other examples.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2023)
Article
Robotics
David M. Rosen, Michael Kaess, John J. Leonard
IEEE TRANSACTIONS ON ROBOTICS
(2014)
Article
Robotics
Yulun Tian, Kasra Khosoussi, David M. Rosen, Jonathan P. How
Summary: This article introduces the first certified correct algorithm for distributed pose-graph optimization, which achieves globally optimal solutions and proposes the distributed Riemannian gradient framework and Riemannian block coordinate descent method. Extensive evaluations show that the proposed method can correctly recover globally optimal solutions under moderate noise.
IEEE TRANSACTIONS ON ROBOTICS
(2021)
Article
Robotics
Matthew Giamou, Filip Maric, David M. Rosen, Valentin Peretroukhin, Nicholas Roy, Ivan Petrovic, Jonathan Kelly
Summary: Inverse kinematics is the problem of finding robot joint configurations that satisfy constraints, which becomes more complicated with the presence of obstacles. This work introduces a convex feasibility problem formulation and proposes the CIDGIK algorithm, which achieves faster and more accurate convergence compared to traditional optimization-based approaches.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2022)
Article
Robotics
Qiangqiang Huang, Can Pu, Kasra Khosoussi, David M. Rosen, Dehann Fourie, Jonathan P. How, John J. Leonard
Summary: This paper introduces NF-iSAM, a novel algorithm for inferring the full posterior distribution in SLAM problems with nonlinear measurement models and non-Gaussian factors. NF-iSAM uses neural networks and normalizing flows to model and sample the full posterior. By leveraging the Bayes tree, NF-iSAM achieves efficient incremental updates in the non-Gaussian setting. Experimental results on range-only SLAM problems with data association ambiguity show that NF-iSAM outperforms state-of-the-art algorithms in accuracy of posterior beliefs for continuous and discrete variables.
IEEE TRANSACTIONS ON ROBOTICS
(2023)
Proceedings Paper
Automation & Control Systems
Kevin J. Doherty, David M. Rosen, John J. Leonard
Summary: In this work, a new initialization method is proposed for the pose-graph simultaneous localization and mapping (SLAM) and rotation averaging (RA) problems. Through the lens of spectral relaxation, the method utilizes classical linear-algebraic techniques to control the distance between the spectral estimate and the ground-truth. Experimental results demonstrate the effectiveness of the proposed method in producing high-quality initializations at a lower computational cost compared to existing techniques.
2022 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA 2022)
(2022)
Article
Robotics
David M. M. Rosen
Summary: Convex relaxation is a powerful method for robust machine perception systems, but solving large-scale semidefinite relaxations remains computationally challenging. This letter presents a method to accelerate the solution verification step, improving the overall speed of certifiable estimation methods.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2022)
Proceedings Paper
Automation & Control Systems
David M. Rosen, Julian Mason, John J. Leonard
2016 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA)
(2016)
Proceedings Paper
Computer Science, Artificial Intelligence
Luca Carlone, David M. Rosen, Giuseppe Calafiore, John J. Leonard, Frank Dellaert
2015 IEEE/RSJ INTERNATIONAL CONFERENCE ON INTELLIGENT ROBOTS AND SYSTEMS (IROS)
(2015)
Proceedings Paper
Automation & Control Systems
David M. Rosen, Charles DuHadway, John J. Leonard
2015 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA)
(2015)
Proceedings Paper
Automation & Control Systems
David M. Rosen, Michael Kaess, John J. Leonard
2013 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA)
(2013)
Proceedings Paper
Automation & Control Systems
David M. Rosen, Michael Kaess, John J. Leonard
2012 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA)
(2012)