Lie Group Methods

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Overview

Lie group methods study transformations such as rotations and rigid-body motions using groups and their tangent Lie algebras, preserving composition and geometric constraints. They support robotics, state estimation, trajectory optimization, simulation, and symmetry-aware learning through tools such as exponential and logarithm maps, invariant metrics, geometric integrators, and manifold optimization. Current approaches also incorporate group structure into neural operators, attention, diffusion models, and symmetry discovery, with tests spanning robot control, pose graphs, physical dynamics, and molecular conformations. A central challenge is to preserve geometric guarantees and global validity while keeping derivatives, optimization, and sampling efficient, particularly near singularities or on complex groups.

Latest papers

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42 papers3 papers in the last four weeks, down 50% on the four weeks before. 0.0% of all new papers.

  1. Lie Group Formulation of Recursive Dynamics Algorithms of Higher Order for Floating-Base Robots

    May 7, 2026Ahmed Ali, Chiara Gabellieri, Antonio FranchiMultibody DynamicsRobotics

    Robotics and Mechatronics Department, Electrical Engineering, Mathematics, and Computer Science (EEMCS) Faculty, University of Twente, 7500 AE Enschede, The Netherlands. · Department of Computer, Control and Management Engineering, Sapienza University of Rome, 00185 Rome, Italy.

  2. Exact Higher-Order Derivatives for SE(3) via Analytical/AD Methods

    May 4, 2026Frank O. KuehnelAutomatic DifferentiationLie Group Methods

    Sigma Point Labs, Denver, CO, USA

  3. Closed Form Relations and Higher-Order Approximations of First and Second Derivatives of the Tangent Operator on SE(3)

    Apr 24, 2026Andreas MuellerRepresentation GeometryLie Group Methods

    Institute of Robotics, Johannes Kepler University Linz, Austria

  4. Natural Gradient Gaussian Approximation Filter on Lie Groups for Robot State Estimation

    Apr 11, 2026Tianyi Zhang, Wenhan Cao, Chang Liu +2Robot State EstimationBayesian Filtering

    School of Vehicle and Mobility, Tsinghua University, Beijing, China · College of Engineering, Peking University, Beijing, China · School of Vehicle and Mobility and College of Artificial Intelligence, Tsinghua University, Beijing, China

  5. NS-RGS: Newton-Schulz based Riemannian gradient method for orthogonal group synchronization

    Apr 7, 2026Haiyang Peng, Deren Han, Xin Chen +1Lie Group MethodsRiemannian Optimization

  6. Schrödinger Bridge Over A Compact Connected Lie Group

    Mar 14, 2026Hamza Mahmood, Abhishek Halder, Adeel AkhtarSchrödinger BridgesStochastic Optimal Control

    Department of Mechanical & Industrial Engineering at the New Jersey Institute of Technology, Newark, NJ 07102, USA · Department of Aerospace Engineering at Iowa State University, Ames, IA 50011, USA

  7. A Diffeomorphism Groupoid and Algebroid Framework for Discontinuous Image Registration

    Mar 12, 2026Lili Bao, Bin Xiao, Shihui Ying +1Deformable Image RegistrationLie Group Methods

    Department of Computer Science, University of Copenhagen, Universitetsparken 1, Copenhagen 2100, Denmark · Institute for Medical Imaging Technology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai 201800, China · Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200444, China +1

  8. A General Lie-Group Framework for Continuum Soft Robot Modeling

    Mar 9, 2026Lingxiao Xun, Benoît Rosa, Jérôme Szewczyk +1Soft RoboticsLie Group Methods

    Sorbonne Université, CNRS UMR 7222, Inserm U1150, ISIR, F-75005, Paris, France. · Université de Strasbourg, CNRS, INSERM, ICube, UMR7357, Strasbourg, France.

  9. Spectral Discovery of Continuous Symmetries via Generalized Fourier Transforms

    Mar 7, 2026Pavan Karjol, Kumar Shubham, Prathosh APSymmetry DiscoverySpectral Methods

    Department of Electrical Communication Engineering , Indian Institute of Science , Bengaluru, Karnataka

  10. Vector Fields for Path Following on Lie Groups with Application in Robot Control

    Feb 25, 2026Felipe Bartelt, Luciano C. A. Pimenta, Weijia Yao +1Robotic ControlLie Group Methods

  11. Geometric Neural Operators via Lie Group-Constrained Latent Dynamics

    Feb 18, 2026Jiaquan Zhang, Fachrina Dewi Puspitasari, Songbo Zhang +7Neural PDE SolversPDE Operator Learning

    School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China · Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China · Institute of Software Chinese Academy of Sciences, Beijing, China +2

  12. Making Space for Time: The Special Galilean Group and Its Application to Some Robotics Problems

    Sep 22, 2024Jonathan KellyLie Group MethodsSpatiotemporal Reasoning

    Space & Terrestrial Autonomous Robotic Systems (STARS) Laboratory, University of Toronto Institute for Aerospace Studies (UTIAS), Toronto, Canada