Motor angular speed preintegration yields a new factor for factor-graph UAV odometry that, when fused with LiDAR, improves position accuracy 28% and velocity accuracy 65% over LIO-SAM while lowering measurement lag.
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A micro lie theory for state estimation in robotics
36 Pith papers cite this work. Polarity classification is still indexing.
36
Pith papers citing it
abstract
A Lie group is an old mathematical abstract object dating back to the XIX century, when mathematician Sophus Lie laid the foundations of the theory of continuous transformation groups. As it often happens, its usage has spread over diverse areas of science and technology many years later. In robotics, we are recently experiencing an important trend in its usage, at least in the fields of estimation, and particularly in motion estimation for navigation. Yet for a vast majority of roboticians, Lie groups are highly abstract constructions and therefore difficult to understand and to use. This may be due to the fact that most of the literature on Lie theory is written by and for mathematicians and physicists, who might be more used than us to the deep abstractions this theory deals with. In estimation for robotics it is often not necessary to exploit the full capacity of the theory, and therefore an effort of selection of materials is required. In this paper, we will walk through the most basic principles of the Lie theory, with the aim of conveying clear and useful ideas, and leave a significant corpus of the Lie theory behind. Even with this mutilation, the material included here has proven to be extremely useful in modern estimation algorithms for robotics, especially in the fields of SLAM, visual odometry, and the like. Alongside this micro Lie theory, we provide a chapter with a few application examples, and a vast reference of formulas for the major Lie groups used in robotics, including most jacobian matrices and the way to easily manipulate them. We also present a new C++ template-only library implementing all the functionality described here.
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representative citing papers
Triangle Splatting SLAM performs online tracking and mapping via differentiable rendering of triangle soups in RGB-D data, converts to connected meshes on-the-fly, and reports better 3D geometry than baselines on Replica and TUM-RGBD while matching tracking accuracy.
KiTe augments sampling-based kinodynamic planning with terminal costs in belief space, proving asymptotic optimality preservation and improved goal-reaching probability bounds via Wasserstein minimization, supported by learned uncertainty models and experiments.
ReActor jointly optimizes motion retargeting and RL policy training with an approximate gradient to generate physically consistent robot motions from human references using only sparse body correspondences.
Lie-group recursive dynamics algorithms are extended to higher-order time derivatives for floating-base robots, with quadratic computational scaling shown versus exponential for automatic differentiation on a 12-DoF aerial manipulator.
A factor graph framework estimates continuum robot shapes using Geometric Variable Strain coefficients constrained by Magnus expansion kinematics, achieving mean position errors below 2 mm in simulation.
GaussianFlow SLAM aligns projected Gaussian motion with optical flow to regularize monocular 3D Gaussian splatting SLAM, yielding better map quality and pose accuracy than prior methods.
Complementarity constraints are treated as a Lie group under relaxation to enable parameterization that satisfies them by construction in LCQP solvers.
Oriented per-voxel height images plus map-informed dual-resolution sampling yield robust real-time LiDAR-inertial odometry where standard LIO diverges.
Learned 2D data association and uncertainty—not recurrent architectures—drive the performance gains of deep visual SLAM, as shown by integrating them into classical ORB-SLAM3.
Anchored feature parameterizations in VINS make the unobservable subspace independent of landmark states, improving consistency over global representations in simulations and TUM-VI experiments.
EquiDexFlow is an SE(3)-equivariant flow-matching model for generating contact-grounded dexterous grasps that enforces surface contact and friction-cone compliance by architectural construction.
HOWTransfer recovers 3D hand motion from video, localizes contact intervals via hand-object cues, generates multi-modal grasp hypotheses, and edits trajectories to produce diverse robot-executable motions achieving 86% success.
G-solver combines Gaussian Belief Propagation and Gaussian Process priors into a fully Gaussian distributed solver for continuous-time SLAM that handles heterogeneous asynchronous sensors and multi-camera setups without explicit synchronization.
Self-supervised contact detection for legged robot odometry using joint encoders outperforms supervised methods that require force sensors.
A pixel-distributed direct visual odometry and depth estimation method using Gaussian Belief Propagation with keyframe anchoring for on-sensor consensus.
SFMDS learns multimodal dynamical systems via flow matching under soft or hard Lyapunov/positive-invariance constraints, including on Lie groups, and reports stable robot motion generation.
Lie Diffuser Actor corrects Euclidean representation of SE(3) poses in diffusion VLA policies via tangent-space score matching on left-invariant SDEs with exponential retraction, yielding +7.3% task length on CALVIN ABC→D.
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
LAST linearizes action manifolds with Lie-algebraic mapping and discretizes them into approximately isotropic charts to align with VL semantic geometry via Gromov-Wasserstein distance.
OCELOT fuses a debounced force GMM-FSM and kinematic GLRT into an ESEKF to produce accurate leg odometry from IMU, encoders and force sensors while explicitly detecting and rejecting slippage on diverse terrains.
FUSE introduces a unified interface for state estimation in SLAM that separates key design choices, with a LiDAR-IMU example showing 1.626m error on a 418m sequence, 7.9% better than Faster-LIO.
Hybrid analytical/AD method for SE(3) NLLs delivers exact Hessians 5x faster than finite-differencing while matching nested AD to machine precision, plus a fix for origin NaNs in the scalar basis.
Factor graphs and Chebyshev polynomials enable robust continuous-time state and trajectory estimation for tensegrity robots by fusing RGB-D camera and cable sensor data.
citing papers explorer
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Motor Angular Speed Preintegration for Multirotor UAV State Estimation
Motor angular speed preintegration yields a new factor for factor-graph UAV odometry that, when fused with LiDAR, improves position accuracy 28% and velocity accuracy 65% over LIO-SAM while lowering measurement lag.
-
Triangle Splatting SLAM
Triangle Splatting SLAM performs online tracking and mapping via differentiable rendering of triangle soups in RGB-D data, converts to connected meshes on-the-fly, and reports better 3D geometry than baselines on Replica and TUM-RGBD while matching tracking accuracy.
-
Terminal Matters: Kinodynamic Planning with a Terminal Cost and Learned Uncertainty in Belief State-Cost Space
KiTe augments sampling-based kinodynamic planning with terminal costs in belief space, proving asymptotic optimality preservation and improved goal-reaching probability bounds via Wasserstein minimization, supported by learned uncertainty models and experiments.
-
ReActor: Reinforcement Learning for Physics-Aware Motion Retargeting
ReActor jointly optimizes motion retargeting and RL policy training with an approximate gradient to generate physically consistent robot motions from human references using only sparse body correspondences.
-
Lie Group Formulation of Recursive Dynamics Algorithms of Higher Order for Floating-Base Robots
Lie-group recursive dynamics algorithms are extended to higher-order time derivatives for floating-base robots, with quadratic computational scaling shown versus exponential for automatic differentiation on a 12-DoF aerial manipulator.
-
Factor Graph-Based Shape Estimation for Continuum Robots via Magnus Expansion
A factor graph framework estimates continuum robot shapes using Geometric Variable Strain coefficients constrained by Magnus expansion kinematics, achieving mean position errors below 2 mm in simulation.
-
GaussianFlow SLAM: Monocular Gaussian Splatting SLAM Guided by GaussianFlow
GaussianFlow SLAM aligns projected Gaussian motion with optical flow to regularize monocular 3D Gaussian splatting SLAM, yielding better map quality and pose accuracy than prior methods.
-
Complementarity by Construction: A Lie-Group Approach to Solving Quadratic Programs with Linear Complementarity Constraints
Complementarity constraints are treated as a Lie group under relaxation to enable parameterization that satisfies them by construction in LCQP solvers.
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BIEVR-LIO: Robust LiDAR-Inertial Odometry through Bump-Image-Enhanced Voxel Maps
Oriented per-voxel height images plus map-informed dual-resolution sampling yield robust real-time LiDAR-inertial odometry where standard LIO diverges.
-
Why does Deep Learning Improve Visual SLAM?
Learned 2D data association and uncertainty—not recurrent architectures—drive the performance gains of deep visual SLAM, as shown by integrating them into classical ORB-SLAM3.
-
Observability and Consistency Analysis for Visual-Inertial Navigation with Anchored Feature Parameterizations
Anchored feature parameterizations in VINS make the unobservable subspace independent of landmark states, improving consistency over global representations in simulations and TUM-VI experiments.
-
EquiDexFlow: Contact-Grounded SE(3)-Equivariant Dexterous Grasp Generative Flows
EquiDexFlow is an SE(3)-equivariant flow-matching model for generating contact-grounded dexterous grasps that enforces surface contact and friction-cone compliance by architectural construction.
-
Hand-centric Human-to-Robot Trajectory Transfer from Video Demonstrations via Open-World Contact Localization
HOWTransfer recovers 3D hand motion from video, localizes contact intervals via hand-object cues, generates multi-modal grasp hypotheses, and edits trajectories to produce diverse robot-executable motions achieving 86% success.
-
Breaking Time: A Fully Gaussian Framework for Distributed and Continuous-Time SLAM
G-solver combines Gaussian Belief Propagation and Gaussian Process priors into a fully Gaussian distributed solver for continuous-time SLAM that handles heterogeneous asynchronous sensors and multi-camera setups without explicit synchronization.
-
Learning Contact Representation for Leg Odometry
Self-supervised contact detection for legged robot odometry using joint encoders outperforms supervised methods that require force sensors.
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PixVOD: Pixel-Distributed Direct Visual Odometry and Depth Estimation
A pixel-distributed direct visual odometry and depth estimation method using Gaussian Belief Propagation with keyframe anchoring for on-sensor consensus.
-
Let the Dynamics Flow: Stable Flow Matching Dynamical Systems
SFMDS learns multimodal dynamical systems via flow matching under soft or hard Lyapunov/positive-invariance constraints, including on Lie groups, and reports stable robot motion generation.
-
The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space
Lie Diffuser Actor corrects Euclidean representation of SE(3) poses in diffusion VLA policies via tangent-space score matching on left-invariant SDEs with exponential retraction, yielding +7.3% task length on CALVIN ABC→D.
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Operator-norm bounds and a quadratic lower-growth example for the special Euclidean algebra se(3)
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
-
LAST: Bridging Vision-Language and Action Manifolds via Gromov-Wasserstein Alignment
LAST linearizes action manifolds with Lie-algebraic mapping and discretizes them into approximately isotropic charts to align with VL semantic geometry via Gromov-Wasserstein distance.
-
OCELOT: Odometry and Contact Estimation for Legged Robots
OCELOT fuses a debounced force GMM-FSM and kinematic GLRT into an ESEKF to produce accurate leg odometry from IMU, encoders and force sensors while explicitly detecting and rejecting slippage on diverse terrains.
-
FUSE: A Framework for Unified State Estimation in Vehicular and Robotic SLAM Systems
FUSE introduces a unified interface for state estimation in SLAM that separates key design choices, with a LiDAR-IMU example showing 1.626m error on a 418m sequence, 7.9% better than Faster-LIO.
-
Exact Higher-Order Derivatives for SE(3) via Analytical/AD Methods
Hybrid analytical/AD method for SE(3) NLLs delivers exact Hessians 5x faster than finite-differencing while matching nested AD to machine precision, plus a fix for origin NaNs in the scalar basis.
-
State and Trajectory Estimation of Tensegrity Robots via Factor Graphs and Chebyshev Polynomials
Factor graphs and Chebyshev polynomials enable robust continuous-time state and trajectory estimation for tensegrity robots by fusing RGB-D camera and cable sensor data.
-
A Robust Approach for LiDAR-Inertial Odometry Without Sensor-Specific Modeling
A sensor-agnostic LiDAR-inertial odometry method using simplified IMU integration and novel regularization on scan-to-map registration that maintains consistent performance across diverse sensors and platforms.
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Bundle Adjustment in the Eager Mode
Introduces an eager-mode PyTorch BA library with GPU-accelerated sparse ops claiming 18.5-23x speedups over GTSAM, g2o, and Ceres.
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Iterated Invariant EKF for 3D Landmark-Aided Inertial Navigation
IterIEKF applied to landmark-aided 3D inertial navigation outperforms SO(3)-EKF, IterSO(3)-EKF and IEKF by ~80% in position/velocity MAE and yields better NEES consistency in simulation.
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D-CLIPSE: Distributed Consensus-based Localization with Passive Listening on Shared State Exchange
D-CLIPSE reaches near-centralized multi-robot localization accuracy and consistency by consensus on shared states only, plus passive listening of preintegrated odometry exchanges.
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CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts
Lifting non-conservative, actuated, and contact-constrained robot dynamics into an exactly symplectic phase-space map yields state-of-the-art out-of-distribution autoregressive rollout error at low parameter and FLOP cost.
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Improved Representation of Matrix Lie Group Operations through Tensor Notation
Introduces tensor notation with Einstein summation to clarify matrix Lie group derivatives and operations in gradient-based estimation frameworks.
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Temporally Consistent Object 6D Pose Estimation for Robot Control
A factor graph that fuses motion models with uncertainty-aware pose measurements improves temporal consistency and benchmark scores for vision-based robot control.
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Iterated Invariant EKF for Quadruped Robot Odometry
An IterIEKF algorithm for quadruped odometry, relying on proprioceptive kinematic constraints, outperforms vanilla IEKF and SO(3) Kalman filters in accuracy and consistency on simulations and real datasets.
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Adapting Neural Robot Dynamics on the Fly for Predictive Control
A hybrid offline-online approach adapts neural robot dynamics models via low-rank second-order updates to enable robust predictive tracking control on quadrotors in novel conditions.
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SCC-Loc: A Unified Semantic Cascade Consensus Framework for UAV Thermal Geo-Localization
SCC-Loc claims SOTA UAV thermal geo-localization (9.37 m mean error, 7.6× better at 5 m) via a shared-DINOv2 semantic cascade consensus pipeline and a new Thermal-UAV dataset.
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Landscape-Awareness for Geometric View Diffusion Model
A score-based method is introduced to guide optimization in geometric view diffusion models toward correct viewpoints, improving convergence and sample efficiency over naive multistart strategies.
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Joint Magnetometer-IMU Calibration via Maximum A Posteriori Estimation
A MAP-based joint calibration method for magnetometer-IMU pairs achieves 20-30% lower RMSE in parameters than two state-of-the-art methods, calibrates 30 pairs in under two minutes, and supports comparable navigation performance.