List
- https://github.com/vikashg/Geometry-Reading-list
- A Comprehensive Introduction to Differential Geometry (5 vols), Michael Spivak
- Introduction to Differential Geometry, Lecture Notes, Joel W. Robbin, Dietmar A. Salamon
- Riemannian Geometry, Manfredo P. do Carmo
- Differential Geometry of Curves and Surfaces, Manfredo P. doCarmo
- Differential Geometry, Erwin Kreyszig
- Differential Geometry: Curves, Surfaces and Manifold, Wolfgang Kuhnel
- Introduction to Smooth Manifolds by John M Lee
- Naive Lie Theory, John Stillwell
- Manifolds and Differential Geometry, Jeffrey M. Lee
- Differential Geometry and Lie Groups: A Computational Perspective, Gallier & Quaintance
- Topology & Geometry - LECTURE 01 Part 01/02, Tadashi Tokieda
- 3Blue1Brown
- https://thebrightsideofmathematics.com/courses/manifolds/overview - Manifolds-Dark - Manifolds-Light
- https://www.linkedin.com/pulse/math-geometric-deep-learning-made-simple-patrick-nicolas-sxl4c
- Mathematical Foundations of Geometric Deep Learning, Haitz Sáez de Ocáriz Borde, Michael Bronstein
- https://www.matematik.lu.se/matematiklu/personal/sigma/index.html
List
- https://www.matematik.lu.se/matematiklu/personal/sigma/DG-Applications
- Topologists and Roboticists Explore an ‘Inchoate World’, Dana Mackenzie
- Geometric Fundamentals of Robotics, Selig
- Manifolds, Geometry, and Robotics, Frank C. Park -Talk
- Geometric Algorithms for Robot Dynamics: A Tutorial Review, Frank C. Park
- Discussion of “Geometric Algorithms for Robot Dynamics: A Tutorial Review”, Frank C. Park
- Research statement, Sylvain Calinon
- Is it worth learning differential geometric methods for modelling and control of mechanical systems, Andrew Lewis
- What Can Algebraic Topology and Differential Geometry Teach Us About Intrinsic Dynamics and Global Behavior of Robots?, Albu-Schäffer, Sachtler
- Some applications of differential geometry in the theory of mechanical systems, M.P. Kharlamov
- Structured Robotics and Optimization, Nathan Ratliff
- Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures, Papillon, Sanborn, Mathe et al
Please refer to F.2 Lie for repositories!
List
- A micro Lie theory for state estimation in robotics_Solà - Cheatsheet
- Lie Groups and Lie Algebras in Robotics, Selig
- SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey_Joohwan Seo
- A tutorial on SE(3) transformation parameterizations and on-manifold optimization in MRPT C++
- pinocchio: Dealing with Lie group geometry
- A Mathematical Introduction to Robotic Manipulation_Murray_Chapter3
- A Math Cookbook for Robot Manipulation, Calinon
- State Estimation for Robotics_Barfoot
- Geometry of interaction: Port-based and energy-aware robotics, Stefano Stramigioli
- A tutorial on SE(3) transformation parameterizations and on-manifold optimization, José Luis Blanco-Claraco
Please refer to F.4 Riemannian for repositories, also to A.11 Manifold Learning!
List
- Introduction to Riemannian Geometry and Geometric Statistics: from basic theory to implementation with Geomstats, Guigui, Miolane, Pannec
- Riemannian geometry as a unifying theory for robot motion learning and control, Jaquier, Asfour
- A Riemannian Take on Distance Fields and Geodesic Flows in Robotics, Li, Qiu, Calinon
- Pulling back symmetric Riemannian geometry for data analysis, Willem Diepeveen - Github
- Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning, Jaquier, Rozo, Tamim Asfour - Good practices to use geometric methods, Leonel Rozo
List
List
Please refer to F.6 Information Geometry for repositories!
List
- An elementary introduction to information geometry, Frank Nielsen
- Information Geometry and Its Applications, Shun-ichi Amari
- Information theory on Lie groups and mobile robotics applications
- CMAES on Riemannian Manifolds for Optimizing Robotic Manipulation Tasks
- https://patricknicolas.substack.com/p/geometry-of-closed-form-statistical
List
List
- Gradient systems in view of information geometry, Akio Fujiwara, Shun-ichi Amari
- https://agustinus.kristia.de/blog/natural-gradient
- https://franknielsen.github.io/NaturalGradient/NaturalGradient.html
- Natural gradient, The Bayesian Learning Rule, Mohammad Emtiyaz Khan, Håvard Rue
- New insights and perspectives on the natural gradient method, James Martens
- Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Models, Hugh Salimbeni, Stefanos Eleftheriadis, James Hensman
- https://towardsdatascience.com/its-only-natural-an-excessively-deep-dive-into-natural-gradient-optimization-75d464b89dbb
- https://gebob19.github.io/natural-gradient
List
- Differential Geometric Approach to Optimization Problems and Its Applications to Robotics, 2023, Journal of the Robotics Society of Japan, № 6, p. 530-535
- An introduction to Optimization on smooth manifolds, Nicolas Boumal - Slides
- Optimization Algorithms on Matrix Manifolds, P.-A. Absil , R. Mahony, Rodolphe Sepulchre
- Riemannian Optimization and Its Applications, Hiroyuki Sato
- Manopt.jl: Optimisation on Riemannian Manifolds, Ronny Bergmann, JuliaCon 2022
- Introduction to Riemannian Optimization, Benyamin Ghojogh
- A tutorial on SE(3) transformation parameterizations and on-manifold optimization, José Luis Blanco-Claraco
- Minimization on the Lie Group SO(3) and Related Manifolds, Camillo J. Taylor and David J. Kriegman
- 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, Eduardo Gallo
List
- Prof. Melvin Leok, Computational geometric mechanics
- Geometric Dynamics, Udrişte
- Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, Lee, Leok & McClamroch
- Geometric Dynamics on Riemannian Manifolds, Udrişte, Tevy
- Differential Geometry and Dynamics: Two Examples. Narc Chaperon
- Differential Geometry Applied to Dynamical Systems, Jean-Marc Ginoux
- Geometric approach to Hamiltonian dynamics and statistical mechanics, Casetti, Pettini & Cohen
- Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics, Marco Pettini
- Geometry from Dynamics, Classical and Quantum, Cariñena, Ibort, Marmo & Morandi
- Some applications of differential geometry in the theory of mechanical systems, Kharlamov
- Robot Model Identification and Learning: A Modern Perspective, Taeyoon Lee, Jaewoon Kwon, Patrick M. Wensing, Frank C. Park
Books
- Prof. Francesco Bullo
- Introduction to Differential Geometry for Engineers, 2012, Brian F. Doolin, Clyde F. Martin, Dover
- Differential Geometric Control Theory, Proceedings, Michigan Technological University, 28.6.-2.7.82 (1983), Brockett, Millman, Sussmann
- Geometric Control Theory, Velimir Jurdjevic
- Introduction to geometric control, Sachkov - Book
- An Introduction to Aspects of Geometric Control Theory, Bloch
- A short introduction to geometric control theory, Simic
- Geometric Control of Mechanical Systems, Bullo & Lewis
- Optimal Control on Riemannian Manifolds, Andras Kupcsik, IROS'22 Tutorial
- Introduction to geometric control theory, KTH Not DG
- https://www.researchgate.net/publication/356455577_Note_on_geometric_algebras_and_control_problems_with_SO3-symmetries
Geometric Integrators
List
- Viacheslav Borovitskiy
- Manifold learning: what, how, and why, Meilă, Zhang
- Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures, Papillon et al
- Deep Regression on Manifolds: A 3D Rotation Case Study - Code
- Introduction to Geometric Learning in Python with Geomstats, Miolane et al
- Riemannian Geometry in Machine Learning, Isay Katsman
- A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty
- SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey_Joohwan Seo
- Learning with 3D rotations, a hitchhiker's guide to SO(3), Geist et al
- Geometric Methods for Manifold Representation Learning, Yonghyeon Lee
- A Unified Formulation of Geometry-aware Dynamic Movement Primitives, Fares J. Abu-Dakka, et al - Code
List
- https://mohitd.github.io/lie-groups-part-1.html
- https://mohitd.github.io/lie-groups-part-2.html
- https://patricknicolas.substack.com
- https://johnwlambert.github.io/lie-groups
- https://roebenack.de/lie-derivatives
- https://ethaneade.com
- https://arwilliams.github.io
- https://marksaroufim.medium.com/how-to-move-lie-group-robotics-67fc4f3959d1
- https://andbloch.github.io
- https://agustinus.kristia.de
- https://gebob19.github.io
List
- IROS'20 Bringing geometric methods to robot learning, optimization and control - Live session
- RSS 2021 Geometry and Topology in Robotics - Live session
- IROS'22 Tutorial "Riemann and Gauss meet Asimov: A tutorial on Geometric methods in robot learning, optimization, and control"
- ICRA'24 Tutorial "Riemann and Gauss meet Asimov: 2nd Tutorial on Geometric Methods in Robot Learning, Optimization, and Control" - Tutorial
- RSS 2024 Geometric and Algebraic Structure in Robot Learning - Videos - OpenReview
List
- Riemannian Optimization Algorithms for Applications and Their Theoretical Properties, Lai Zhijian, 2024
- Leveraging the geometric structure of robotic tasks for motion design, Andrew Bylard, 2021 - Talk
- Geometric control of underactuated mechanical systems with application focus on bipedal robots, Tan Chen, 2021
- Geometric Control and Learning for Dynamic Legged Robots, Avinash Siravuru, 2019
- Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control_Jacquier, 2020
- Orthogonal Manifold Foliations for Impedance Control of Redundant Kinematic Structures Arne Sachtler, 2020
- Geometric Control Methods for Nonlinear Systems and Robotic Applications, Claudio Altafini, 2001
Please refer to F.2 Lie for repositories!
List
- Continuous-Time State Estimation Methods in Robotics: A Survey
- Lie-algebra Adaptive Tracking Control for Rigid Body Dynamics
- Geometric Impedance Control on SE(3) for Robotic Manipulators
- GUFIC Geometric Formulation of Unified Force-Impedance Control on SE(3) for Robotic Manipulators
- A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control
List
- Contact-Rich SE(3)-Equivariant Robot Manipulation Task Learning via Geometric Impedance Control
- Physics-guided Learning-based Adaptive Control on the SE(3) Manifold
- RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation
- EquAct: An SE(3)-Equivariant Multi-Task Transformer for Open-Loop Robotic Manipulation
- EquiGraspFlow: SE(3)-Equivariant 6-DoF Grasp Pose Generative Flows
- OrbitGrasp: SE(3)-Equivariant Grasp Learning
- Towards Feasible Dynamic Grasping: Leveraging Gaussian Process Distance Field, SE(3) Equivariance, and Riemannian Mixture Models
- SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion
- Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation
- Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objects
Please refer to F.4 Riemannian for repositories!
List
- https://docs.omniverse.nvidia.com/isaacsim/latest/concepts/motion_generation/rmpflow.html
- Understanding the Geometry of Workspace Obstacles in Motion Optimization
- Riemannian Motion Policies
- Riemannian Motion Policy Fusion through Learnable Lyapunov Function Reshaping
- RMPs for Safe Impedance Control in Contact-Rich Manipulation
- Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning
- RMP for legged robots
- Obstacle avoidance using raycasting and Riemannian Motion Policies at kHz rates for MAVs
- An Efficient Locally Reactive Controller for Safe Navigation in Visual Teach and Repeat Missions
- Control of Nonholonomic Systems: From Sub-Riemannian Geometry to Motion Planning
- Neural RMP
- Mesh Manifold Based Riemannian Motion Planning for Omnidirectional Micro Aerial Vehicles
- Neural reactive path planning with Riemannian motion policies for robotic silicone sealing
- Integration of RMP and Whole-Body Control for Dynamic Legged Locomotion
- Nonprehensile Riemannian Motion Predictive Control
E.4 Fabrics
Please refer to F.5 Finsler for repositories!
List
- IROS22 Nathan Ratliff - Generalized Nonlinear Geometries and Geometric Fabrics
- Geometric fabrics: Transparent tools for behavior engineering_Nathan Ratliff
- CoRL 2020 Tutorial 3_Nathan Ratliff
- Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior, Nathan Ratliff
- MLPC2020: Nathan Ratliff, Optimization Over a Geometric Fabrics
- Generalized Nonlinear and Finsler Geometry for Robotics, Nathan Ratliff
- Optimization Fabrics
- Optimization Fabrics for Behavioral Design
- Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior
- Geometric Fabrics for the Acceleration-based Design of Robotic Motion
- Geometric Fabrics: a Safe Guiding Medium for Policy Learning
- Fabrics: A Foundationally Stable Medium for Encoding Prior Experience
- Neural Geometric Fabrics: Efficiently Learning High-Dimensional Policies from Demonstration
- Dynamic Optimization Fabrics for Motion Generation - Dynamic Optimization Fabrics for Motion Generation
- Autotuning Symbolic Optimization Fabrics for Trajectory Generation
- Fabrics Reactive grasp and motion planning for adaptive mobile manipulation among obstacles_Michael Pantic
- DextrAH-G: Pixels-to-Action Dexterous Arm-Hand Grasping with Geometric Fabrics
- Neural Geometric Fabrics: Efficiently Learning High-Dimensional Policies from Demonstration, Mandy Xie et al
Please refer to F.1 Optimization on Manifold for repositories!
List
- Learning to Optimize on SPD Manifolds, Zhi Gao et al
- Understanding the Geometry of Workspace Obstacles in Motion Optimization, Nathan Ratliff
- Optimization Methods on Riemannian Manifolds and Their Application to Shape Space, Wolfgang Ring and Benedikt Wirth
- Reduction by Symmetry and Optimal Control with Broken Symmetries on Riemannian Manifolds, Goodman, Colombo
- https://agustinus.kristia.de/blog/optimization-riemannian-manifolds
- https://andbloch.github.io/Stochastic-Gradient-Descent-on-Riemannian-Manifolds
- https://docs.yaoquantum.org/dev/generated/examples/8.riemannian-gradient-flow/index.html
- Inverse Kinematics as Low-Rank Euclidean Distance Matrix Completion, Filip Marić, Matthew Giamou, Ivan Petrović, Jonathan Kelly
- Riemannian Optimization Algorithms for Applications and Their Theoretical Properties, Lai Zhijian, 2024
List
- Theoretical foundation for CMA-ES from information geometric perspective, Akimoto et al
- Information-Geometric Optimization Algorithms: A Unifying Picture via Invariance Principles, Ollivier et al
- The Natural Gradient as a control signal for a humanoid robot, Stollenga et al
- FAdam: Adam is a natural gradient optimizer using diagonal empirical Fisher information, Dongseong Hwang
List
- A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints, Arimoto
- EigenMPC: An Eigenmanifold-Inspired Model-Predictive Control Framework for Exciting Efficient Oscillations in Mechanical Systems
- Geometric Impedance Control on SE(3) for Robotic Manipulators
- Geometric Formulation of Unified Force-Impedance Control on SE(3) for Robotic Manipulators
- A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control
- Contact-Rich SE(3)-Equivariant Robot Manipulation Task Learning via Geometric Impedance Control
- A Geometric Optimal Control Approach for Imitation and Generalization of Manipulation Skills, Boyang Ti, Calinon et al
- A contact covariant approach to optimal control with applications to sub-Riemannian geometry, Michał Jóźwikowski, Witold Respondek - Geometry of the Pontryagin Maximum Principle Talk 1 - Talk 2
- Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groups, Wotte et al
- Adaptive Control of SE(3) Hamiltonian Dynamics with Learned Disturbance Features, Duong et al
List
List
List
- https://github.com/pymanopt/pymanopt
- https://github.com/JuliaManifolds/Manopt.jl
- https://github.com/JuliaNLSolvers/Optim.jl
- https://github.com/zhigao2017/Learning-to-optimize-on-SPD-manifolds
- https://github.com/FreemanTheMaverick/Maniverse
- https://github.com/lezcano/geotorch
- https://github.com/mctorch/mctorch
- https://github.com/david-m-rosen/Optimization
- https://github.com/pdebus/MTVMTL
- https://github.com/dalab/matrix-manifolds
- https://github.com/andyjm3/AI-vs-BW
List
- https://github.com/NxRLab/ModernRobotics
- https://github.com/kevinzakka/mink
- https://github.com/martantoine/Minc
- https://github.com/based-robotics/mjinx
- https://github.com/stephane-caron/pink
- https://github.com/chungmin99/pyroki
- https://github.com/bdaiinstitute/spatialmath-python
- https://github.com/naver/roma
- https://github.com/kornia/kornia
- https://github.com/utiasASRL/pylgmath
- https://github.com/pypose/pypose
- https://github.com/artivis/manif
- https://github.com/farm-ng/farm-ng-core/tree/main?tab=readme-ov-file#sophus-2-building-blocks-for-2d-and-3d-geometry
- https://github.com/pettni/smooth - https://pettni.github.io/smooth
- https://github.com/dfki-ric/pytransform3d
- https://github.com/brentyi/jaxlie
- https://github.com/AlexanderFabisch/jaxtransform3d
- https://github.com/ami-iit/liecasadi
- https://github.com/junggon/gear
- https://github.com/jgerstmayr/EXUDYN/blob/master/main/pythonDev/exudyn/lieGroupBasics.py
- https://github.com/ami-iit/lie-group-controllers
- https://github.com/StanfordASL/Adaptive-Control-Oriented-Meta-Learning
- https://github.com/vkotaru/nonlinear_controls/blob/master/src/SO3_control.cpp
- https://github.com/UMich-CURLY/Lie-MPC-AMVs
- https://github.com/coin-or/ADOL-C/blob/master/ADOL-C/examples/additional_examples/lie/GantryCrane.cpp
- https://github.com/borglab/gtsam/blob/develop/gtsam/base/Lie.h
- https://github.com/decargroup/navlie
- https://github.com/Joohwan-Seo/GUFIC_mujoco
- https://github.com/Joohwan-Seo/GIC_Learning_public
- https://github.com/Joohwan-Seo/Geometric_Impedance_Control_Comparison
- https://github.com/Joohwan-Seo/Geometric-Impedance-Control-Public
- https://github.com/Danfoa/MorphoSymm
List
- https://github.com/wildart/ManifoldLearning.jl
- https://github.com/patnicolas/geometriclearning
- https://github.com/HeegerGao/RiEMann
- https://github.com/bdlim99/EquiGraspFlow
- https://github.com/ZXP-S-works/SE2-equivariant-grasp-learning
- https://github.com/robotgradient/grasp_diffusion
- https://github.com/BoceHu/orbitgrasp
- https://github.com/utiasSTARS/bingham-rotation-learning
- https://github.com/martius-lab/hitchhiking-rotations
- https://github.com/NoemieJaquier/hyperbolic-gplvms
- https://github.com/boschresearch/GeodesicMotionSkills
- https://github.com/psh117/ljcmp
- https://github.com/StanfordASL/LSBMP
- https://github.com/JiangengDong/CoMPNetX
List
List
List
- https://github.com/GitZH-Chen/Awesome-Riemannian-Deep-Learning
- https://github.com/humans-to-robots-motion/pyrieef
- https://github.com/gtrll/multi-robot-rmpflow
- https://github.com/NVlabs/motion-policy-networks
- https://github.com/StanfordASL/PBDS.jl
- https://github.com/ethz-asl/geodetic_utils
- https://github.com/rortiz9/rmp-ros
- https://github.com/xymeng/rmp_nav
- https://github.com/ethz-asl/reactive_avoidance
- https://github.com/UWRobotLearning/rmp2
List
- https://github.com/andyjm3/Awesome-Riemannian-Optimization
- https://github.com/whuang08/ROPTLIB
- https://sourceforge.net/projects/rieoptpack
- https://github.com/SaitejaUtpala/rieoptax
- https://github.com/kisungyou/RiemBase
- https://github.com/andyjm3/RiemNA
- https://github.com/master/tensorflow-riemopt
- https://github.com/Hideki105/riemannian-optimization
- https://github.com/SaitejaUtpala/rieoptax
- https://github.com/Gabe-YHLee/RiemGeomCurves
- https://github.com/jychen18/RPMG
- https://github.com/changliu00/Riem-SVGD
- https://github.com/hiroyuki-kasai/RSOpt
Fabrics
List
- https://github.com/geomstats/geomstats/tree/main/geomstats/information_geometry
- https://github.com/cranmer/play/tree/master/manifoldLearning
- https://github.com/patnicolas/geometriclearning/tree/main/python/geometry/information_geometry
- https://github.com/Noeloikeau/information_geometry
- https://github.com/HANDSOMEJACKANDY/improved-empirical-fisher
- https://github.com/muellerjohannes/geometry-natural-policy-gradients
- https://github.com/Abdoulaye-Koroko/natural-gradients
- https://github.com/hujiangpku/RNGD
- https://github.com/MariusZeinhofer/Natural-Gradient-PINNs-ICML23
- https://github.com/wiseodd/natural-gradients
- https://github.com/lessw2020/FAdam_PyTorch
- https://github.com/tachukao/mgplvm-pytorch