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arxiv: 2605.11210 · v1 · submitted 2026-05-11 · 💻 cs.RO

Recognition: 2 theorem links

· Lean Theorem

Distributed Pose Graph Optimization via Continuous Riemannian Dynamics

Jaeho Shin, Maani Ghaffari, Yulun Tian

Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:55 UTC · model grok-4.3

classification 💻 cs.RO
keywords pose graph optimizationdistributed optimizationRiemannian dynamicsLie groupsmulti-robot SLAMgeometric integrationdamped dynamics
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The pith

By modeling pose variables as massive particles subject to damping, equilibria of the Riemannian dynamics coincide with critical points of the pose graph optimization problem.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that pose graph optimization can be recast as a continuous-time motion on curved spaces in which each pose acts like a heavy particle that slows down due to damping. The places where this motion stops are exactly the points where no small adjustment improves the match between measured relative poses and the estimated configuration. In multi-robot cases the motion equations split along block-diagonal mass and damping terms so each robot integrates only its own poses while exchanging little data; the velocity part of the state also lets robots forecast where neighbors will be when messages are late. Different choices of particle mass and friction recover standard methods such as Riemannian gradient descent and Gauss-Newton as special cases.

Core claim

The central claim is that the equilibrium points of the Riemannian dynamics obtained by modeling pose variables as massive particles subject to damping coincide with first-order critical points of the original PGO problem. The governing damped Euler-Poincaré equations together with a semi-implicit geometric integrator produce a discrete algorithm that generalizes existing first- and second-order methods; when mass and damping matrices are block-diagonal the same integrator yields a fully distributed scheme in which each robot solves an ordinary differential equation for its own variables with low communication cost and with neighbor prediction to tolerate delays.

What carries the argument

Damped Euler-Poincaré equations on Lie groups that drive the modeled particles to rest precisely at the critical points of the PGO objective.

If this is right

  • Riemannian gradient descent and Gauss-Newton arise as special cases by appropriate choice of mass and damping.
  • Each robot can integrate its own ordinary differential equation independently once block-diagonal mass and damping matrices are used.
  • Velocity variables enable explicit prediction of neighboring poses, improving convergence when communication is delayed or asynchronous.
  • Convergence to first-order critical points is guaranteed whenever the chosen integrator satisfies the energy-dissipation condition.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The particle-dynamics view may allow natural addition of extra forces or constraints that represent physical limits in robotic mapping.
  • The velocity estimates produced during integration could serve as a built-in measure of local uncertainty around the final poses.
  • The same continuous formulation might be combined with discrete steps in hybrid solvers that adapt to problem scale or noise level.

Load-bearing premise

The semi-implicit geometric integrator must dissipate energy so that the discrete updates still converge to critical points of the PGO objective.

What would settle it

A numerical run on a standard PGO benchmark in which the algorithm stops at a configuration whose gradient norm in the original cost function is clearly nonzero.

Figures

Figures reproduced from arXiv: 2605.11210 by Jaeho Shin, Maani Ghaffari, Yulun Tian.

Figure 1
Figure 1. Figure 1: The proposed approach formulates pose graph optimization [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Trajectory estimates returned by the proposed algorithm on [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Performance profiles of synchronous methods over 1,000 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Optimality gap for varying delay steps in asynchronous [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relative mass variation and energy convergence (state-dependent, [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

We present a framework for distributed Pose Graph Optimization (PGO) by formulating the problem as a second-order continuous-time dynamical system evolving on Lie groups. By modeling pose variables as massive particles subject to damping, the equilibrium points of the resulting Riemannian dynamics coincide with first-order critical points of the original PGO problem. Using the governing damped Euler--Poincar\'e equations and a semi-implicit geometric integrator, we design an optimization algorithm that generalizes existing algorithms such as Riemannian gradient descent and Gauss--Newton. In multi-robot settings, we present a fully distributed and parallel method based on block-diagonal mass and damping matrices, where each robot solves an ordinary differential equation for its own poses with minimal communication overhead. Moreover, modeling both state and velocity enables principled neighbor prediction that significantly improves convergence under delayed communication. Theoretically, we present an analysis and establish sufficient condition that ensures energy dissipation under the employed geometric discretization scheme. Experiments on benchmark PGO datasets demonstrate that the proposed solver achieves superior performance compared to state-of-the-art distributed baselines in both synchronous and asynchronous regimes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes formulating distributed pose graph optimization (PGO) as a second-order continuous-time Riemannian dynamical system on Lie groups, modeling pose variables as massive particles subject to damping. Equilibria of the resulting dynamics coincide with first-order critical points of the PGO objective by construction. A semi-implicit geometric integrator discretizes the damped Euler-Poincaré equations, generalizing Riemannian gradient descent and Gauss-Newton; the distributed version uses block-diagonal mass/damping matrices with neighbor prediction for asynchronous communication. A sufficient condition is stated to guarantee energy dissipation under the discretization, and experiments on benchmark datasets are claimed to show superior performance over distributed baselines in synchronous and asynchronous regimes.

Significance. If the sufficient condition for discrete energy dissipation is rigorously established and holds under block-diagonal approximations and delayed inexact coupling, the approach could offer a principled way to incorporate inertia and damping into distributed PGO solvers, potentially improving convergence rates and robustness to communication delays in multi-robot SLAM. The continuous-time modeling naturally supports neighbor prediction, which is a conceptual strength if the discrete guarantees are confirmed.

major comments (3)
  1. [Theoretical analysis] Theoretical analysis section: The sufficient condition for energy dissipation of the semi-implicit geometric integrator is stated but neither derived nor proved; no verification is provided that it holds for the chosen mass/damping matrices on benchmark graphs, especially under the block-diagonal structure and delayed neighbor predictions required for the distributed asynchronous case. This condition is load-bearing for the central convergence claim.
  2. [Distributed algorithm] Distributed algorithm and discretization sections: The energy-dissipation analysis does not address survival of the sufficient condition when mass and damping matrices are block-diagonal, coupling forces become inexact due to delays, and neighbor prediction is employed; without this, the guarantee that the discrete algorithm converges to PGO critical points does not extend to the multi-robot asynchronous regime.
  3. [Experiments] Experiments section: The abstract asserts superior performance on benchmark PGO datasets relative to state-of-the-art distributed baselines, yet the manuscript supplies no quantitative metrics, error bars, iteration counts, final costs, or ablation studies on the effect of the sufficient-condition parameters, preventing assessment of the practical claims.
minor comments (2)
  1. [Modeling section] Clarify the precise definition of the Riemannian gradient and the mapping from the PGO cost to the forcing term in the Euler-Poincaré equations to make the first-principles construction more transparent.
  2. [Experiments] Add explicit statements of the mass and damping matrix choices used in the experiments and confirm they satisfy the sufficient condition for the reported step sizes.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and will revise the manuscript to strengthen the theoretical foundations, extend the distributed analysis, and improve the experimental reporting.

read point-by-point responses

  1. Referee: [Theoretical analysis] Theoretical analysis section: The sufficient condition for energy dissipation of the semi-implicit geometric integrator is stated but neither derived nor proved; no verification is provided that it holds for the chosen mass/damping matrices on benchmark graphs, especially under the block-diagonal structure and delayed neighbor predictions required for the distributed asynchronous case. This condition is load-bearing for the central convergence claim.

    Authors: We agree that the derivation of the sufficient condition for energy dissipation should be fully presented. The current manuscript states the condition but condenses the proof. In the revised version, we will expand the theoretical analysis section with a complete step-by-step derivation of the energy dissipation property for the semi-implicit geometric integrator. We will also add numerical verification confirming that the condition holds for the chosen block-diagonal mass and damping matrices on the benchmark graphs, and we will discuss the effect of delayed neighbor predictions on the dissipation property. revision: yes

  2. Referee: [Distributed algorithm] Distributed algorithm and discretization sections: The energy-dissipation analysis does not address survival of the sufficient condition when mass and damping matrices are block-diagonal, coupling forces become inexact due to delays, and neighbor prediction is employed; without this, the guarantee that the discrete algorithm converges to PGO critical points does not extend to the multi-robot asynchronous regime.

    Authors: We acknowledge that the energy-dissipation analysis in the manuscript is developed primarily for the exact synchronous case and does not explicitly treat the block-diagonal approximation, inexact delayed couplings, or neighbor prediction. In the revision, we will add a dedicated subsection extending the analysis to these distributed settings, deriving conditions under which the sufficient condition remains valid or providing relaxed bounds that account for bounded communication delays. Where a complete guarantee cannot be established without further assumptions, we will clearly delineate the limitations and support the claims with the existing empirical results from the asynchronous experiments. revision: partial

  3. Referee: [Experiments] Experiments section: The abstract asserts superior performance on benchmark PGO datasets relative to state-of-the-art distributed baselines, yet the manuscript supplies no quantitative metrics, error bars, iteration counts, final costs, or ablation studies on the effect of the sufficient-condition parameters, preventing assessment of the practical claims.

    Authors: We agree that additional quantitative detail is required for a thorough assessment. Although the manuscript reports comparative performance, we will revise the experiments section to include explicit tables with final objective values, iteration counts to convergence, wall-clock times, and error bars computed over multiple runs with varied initializations. We will also add ablation studies examining the sensitivity of performance to the mass and damping parameters tied to the sufficient condition. revision: yes

Circularity Check

1 steps flagged

The claimed coincidence between equilibria of the damped Riemannian dynamics and PGO critical points holds by construction of the modeling choice.

specific steps
  1. self definitional [Abstract]
    "By modeling pose variables as massive particles subject to damping, the equilibrium points of the resulting Riemannian dynamics coincide with first-order critical points of the original PGO problem."

    The dynamics are explicitly constructed with a damping term that vanishes at zero velocity, leaving the equations to reduce exactly to the Riemannian gradient equaling zero. The stated coincidence is therefore true by definition of the chosen second-order system rather than a non-trivial consequence of the PGO objective.

full rationale

The paper's central first-principles result is obtained directly from the chosen formulation rather than derived independently. The discrete convergence analysis relies on a stated sufficient condition for energy dissipation whose verification details for the distributed asynchronous setting are not exhibited as reducing to prior inputs. No fitted parameters, self-citations, or renaming of known results appear in the provided text. This produces partial circularity confined to the continuous-time modeling step.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the modeling assumption that damped particle dynamics on the pose manifold share the same critical points as the PGO objective, plus the existence of a discretization that dissipates a suitable energy function.

free parameters (1)
  • damping and mass matrices
    Block-diagonal mass and damping matrices are chosen to enable per-robot ODE solving; their specific scaling is not derived from first principles in the abstract.
axioms (2)
  • domain assumption Equilibrium points of the damped Riemannian dynamics coincide with first-order critical points of the PGO cost function.
    This is the load-bearing link between the continuous dynamical system and the original optimization problem.
  • ad hoc to paper A sufficient condition exists that guarantees energy dissipation for the chosen semi-implicit geometric integrator.
    The abstract invokes this condition to ensure the discrete algorithm inherits convergence properties from the continuous dynamics.

pith-pipeline@v0.9.0 · 5482 in / 1368 out tokens · 45741 ms · 2026-05-13T01:55:21.794902+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Reference graph

Works this paper leans on

111 extracted references · 111 canonical work pages · 2 internal anchors

  1. [1]

    Shin, Sungho , month = may, year =. Graph-. 2023. doi:10.23919/ACC55779.2023.10155947 , language =

    work page doi:10.23919/acc55779.2023.10155947 2023

  2. [2]

    Overlapping

    Shin, Sungho and Anitescu, Mihai and Zavala, Victor , pages =. Overlapping. 2020 59th. doi:10.1109/CDC42340.2020.9304139 , abstract =

    work page doi:10.1109/cdc42340.2020.9304139 2020

  3. [3]

    Na, Sen and Shin, Sungho and Anitescu, Mihai and Zavala, Victor , journal=. On the. 2022 , month=mar, volume=

    work page 2022

  4. [4]

    Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs

    Shin, Sungho and Anitescu, Mihai and Zavala, Victor , month = dec, year =. Exponential. doi:10.48550/arXiv.2101.03067 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2101.03067

  5. [5]

    IEEE Trans.\ on Control of Network Systems , author =

    Decentralized. IEEE Trans.\ on Control of Network Systems , author =. 2020 , keywords =. doi:10.1109/TCNS.2020.2967805 , abstract =

    work page doi:10.1109/tcns.2020.2967805 2020

  6. [6]

    IEEE Int

    McGann, Daniel and Lassak, Kyle and Kaess, Michael , file =. IEEE Int. Conf. on Robotics and Automation , title =

    work page

  7. [7]

    McGann and M

    D. McGann and M. Kaess , fullauthor =. Proc. Robotics: Science and Systems (RSS) , address =

    work page

  8. [11]

    and Dellaert, Frank , month = sep, year =

    Choudhary, Siddharth and Carlone, Luca and Christensen, Henrik I. and Dellaert, Frank , month = sep, year =. Exactly sparse memory efficient. 2015. doi:10.1109/IROS.2015.7353543 , abstract =

    work page doi:10.1109/iros.2015.7353543 2015

  9. [12]

    2023 IEEE International Conference on Robotics and Automation (ICRA) , pages=

    Cross-agent relocalization for decentralized collaborative SLAM , author=. 2023 IEEE International Conference on Robotics and Automation (ICRA) , pages=. 2023 , organization=

    work page 2023

  10. [13]

    Distributed Pose Graph Optimization via Contractive Belief Sharing , year=

    Liu, Xiangyu and Chli, Margarita , journal=. Distributed Pose Graph Optimization via Contractive Belief Sharing , year=

    work page

  11. [14]

    doi:10.48550/arXiv.2010.00156 , abstract =

    Cristofalo, Eric and Montijano, Eduardo and Schwager, Mac , month = oct, year =. doi:10.48550/arXiv.2010.00156 , abstract =

    work page doi:10.48550/arxiv.2010.00156 2010

  12. [15]

    Initialization techniques for

    Carlone, Luca and Tron, Roberto and Daniilidis, Kostas and Dellaert, Frank , pages =. Initialization techniques for. 2015. doi:10.1109/ICRA.2015.7139836 , abstract =

    work page doi:10.1109/icra.2015.7139836 2015

  13. [16]

    Generalized

    Fan, Taosha and Murphey, Todd , editor =. Generalized. Robotics. 2022 , doi =

    work page 2022

  14. [17]

    Decentralization and

    Fan, Taosha and Ortiz, Joseph and Hsiao, Ming and Monge, Maurizio and Dong, Jing and Murphey, Todd and Mukadam, Mustafa , month = jul, year =. Decentralization and. Robotics:. doi:10.15607/RSS.2023.XIX.111 , abstract =

    work page doi:10.15607/rss.2023.xix.111 2023

  15. [18]

    Efficient

    Konolige, K and Grisetti, G and Kümmerle, Rainer and Burgard, W and Limketkai, B and Vincent, R , pages =. Efficient. 2010. doi:10.1109/IROS.2010.5649043 , abstract =

    work page doi:10.1109/iros.2010.5649043 2010

  16. [19]

    A fast and accurate approximation for planar pose graph optimization , volume =. The Int. Journal of Robotics Research , author =. 2014 , pages =. doi:10.1177/0278364914523689 , abstract =

    work page doi:10.1177/0278364914523689 2014

  17. [20]

    Wei, Ermin and Ozdaglar, Asuman , month = dec, year =. On the. 2013. doi:10.1109/GlobalSIP.2013.6736937 , language =

    work page doi:10.1109/globalsip.2013.6736937 2013

  18. [21]

    Distributed

    Wei, Ermin and Ozdaglar, Asuman , month = dec, year =. Distributed. 2012. doi:10.1109/CDC.2012.6425904 , language =

    work page doi:10.1109/cdc.2012.6425904 2012

  19. [23]

    Halsted, Trevor and Shorinwa, Ola and Yu, Javier and Schwager, Mac , month = mar, year =. A. doi:10.48550/arXiv.2103.12840 , abstract =

    work page doi:10.48550/arxiv.2103.12840

  20. [24]

    and Kumar, V

    Karypis, G. and Kumar, V. , month = nov, year =. Multilevel. doi:10.1109/SC.1998.10018 , abstract =

    work page doi:10.1109/sc.1998.10018 1998

  21. [25]

    Iterative

    Saad, Yousef , year =. Iterative

    work page

  22. [27]

    SlideSLAM : Sparse , Lightweight , Decentralized Metric - Semantic SLAM for Multi - Robot Navigation , July 2024

    Liu, Xu and Lei, Jiuzhou and Prabhu, Ankit and Tao, Yuezhan and Spasojevic, Igor and Chaudhari, Pratik and Atanasov, Nikolay and Kumar, Vijay , month = jul, year =. doi:10.48550/arXiv.2406.17249 , abstract =

    work page doi:10.48550/arxiv.2406.17249

  23. [32]

    Learning Feature Maps of the Koopman Operator: A Subspace Viewpoint,

    Cristofalo, Eric and Montijano, Eduardo and Schwager, Mac , month = dec, year =. Consensus-based. 2019. doi:10.1109/CDC40024.2019.9029792 , abstract =

    work page doi:10.1109/cdc40024.2019.9029792 2019

  24. [34]

    Journal of Intelligent & Robotic Systems , author =

    Distributed. Journal of Intelligent & Robotic Systems , author =. 2025 , pages =. doi:10.1007/s10846-025-02257-w , abstract =

    work page doi:10.1007/s10846-025-02257-w 2025

  25. [35]

    , month = may, year =

    Chang, Yun and Tian, Yulun and How, Jonathan P. and Carlone, Luca , keywords =. Kimera-. 2021. doi:10.1109/ICRA48506.2021.9561090 , abstract =

    work page doi:10.1109/icra48506.2021.9561090 2021

  26. [36]

    on Robotics , author =

    IEEE Trans. on Robotics , author =. 2021 , keywords =. doi:10.1109/TRO.2021.3075644 , abstract =

    work page doi:10.1109/tro.2021.3075644 2021

  27. [37]

    2020 , keywords =

    IEEE Robotics and Automation Letters , author =. 2020 , keywords =. doi:10.1109/LRA.2020.2967681 , abstract =

    work page doi:10.1109/lra.2020.2967681 2020

  28. [38]

    Field Robotics , author =

    Towards. Field Robotics , author =. 2022 , keywords =. doi:10.55417/fr.2022032 , abstract =

    work page doi:10.55417/fr.2022032 2022

  29. [39]

    IEEE Trans

    Streaming. IEEE Trans. on Signal Processing , author =. 2022 , keywords =. doi:10.1109/TSP.2022.3188208 , abstract =

    work page doi:10.1109/tsp.2022.3188208 2022

  30. [40]

    Zhang, Yetong and Hsiao, Ming and Dong, Jing and Engel, Jakob and Dellaert, Frank , keywords =. 2021. doi:10.1109/IROS51168.2021.9636687 , abstract =

    work page doi:10.1109/iros51168.2021.9636687 2021

  31. [41]

    Decentralised cooperative localisation for heterogeneous teams of mobile robots , doi =

    Bailey, Tim and Bryson, Mitch and Mu, Hua and Vial, John and McCalman, Lachlan and Durrant-Whyte, Hugh , keywords =. Decentralised cooperative localisation for heterogeneous teams of mobile robots , doi =. 2011

    work page 2011

  32. [42]

    Andersson, Lars A. A. and Nygards, Jonas , pages =. C-. 2008. doi:10.1109/ROBOT.2008.4543634 , abstract =

    work page doi:10.1109/robot.2008.4543634 2008

  33. [43]

    IEEE Trans

    Spectral. IEEE Trans. on Robotics , author =. 2024 , pages =. doi:10.1109/TRO.2023.3327635 , abstract =

    work page doi:10.1109/tro.2023.3327635 2024

  34. [44]

    2022 , keywords =

    IEEE Robotics and Automation Letters , author =. 2022 , keywords =. doi:10.1109/LRA.2022.3191204 , abstract =

    work page doi:10.1109/lra.2022.3191204 2022

  35. [46]

    Collaborative

    Li, Fu and Yang, Shaowu and Yi, Xiaodong and Yang, Xuejun , year =. Collaborative. doi:10.1007/978-3-030-00916-8_45 , abstract =

    work page doi:10.1007/978-3-030-00916-8_45

  36. [47]

    Rotation. Int. Journal of Computer Vision , author =. 2013 , pages =. doi:10.1007/s11263-012-0601-0 , abstract =

    work page doi:10.1007/s11263-012-0601-0 2013

  37. [48]

    IEEE Trans

    Communication- and. IEEE Trans. on Robotics , author =. 2025 , pages =. doi:10.1109/TRO.2025.3567540 , abstract =

    work page doi:10.1109/tro.2025.3567540 2025

  38. [49]

    IEEE Transactions on Robotics , volume=

    Kimera-multi: Robust, distributed, dense metric-semantic slam for multi-robot systems , author=. IEEE Transactions on Robotics , volume=. 2022 , publisher=

    work page 2022

  39. [50]

    The invariant extended

    Barrau, Axel and Bonnabel, Silvere , journal=. The invariant extended. 2016 , publisher=

    work page 2016

  40. [51]

    borglab/gtsam , year =

    Frank Dellaert and. borglab/gtsam , month = May, year = 2022, publisher =. doi:10.5281/zenodo.5794541 , url =

    work page doi:10.5281/zenodo.5794541 2022

  41. [53]

    IEEE Robotics and Automation Letters , volume=

    Cartan-sync: Fast and global SE (d)-synchronization , author=. IEEE Robotics and Automation Letters , volume=. 2017 , publisher=

    work page 2017

  42. [54]

    Journal of Machine Learning Research , year=

    A differential equation for modeling Nesterov's accelerated gradient method: Theory and insights , author=. Journal of Machine Learning Research , year=

    work page

  43. [55]

    Soviet Mathematics Doklady , year=

    A method for solving the convex programming problem with convergence rate O (1/k2) , author=. Soviet Mathematics Doklady , year=

    work page

  44. [56]

    proceedings of the National Academy of Sciences , volume=

    A variational perspective on accelerated methods in optimization , author=. proceedings of the National Academy of Sciences , volume=. 2016 , publisher=

    work page 2016

  45. [57]

    Journal of Machine Learning Research , pages=

    A Lyapunov analysis of accelerated methods in optimization , author=. Journal of Machine Learning Research , pages=

    work page

  46. [59]

    Advances in Neural Information Processing Systems , volume=

    Acceleration via symplectic discretization of high-resolution differential equations , author=. Advances in Neural Information Processing Systems , volume=

    work page

  47. [60]

    Optimization Methods and Software , volume=

    Practical perspectives on symplectic accelerated optimization , author=. Optimization Methods and Software , volume=. 2023 , publisher=

    work page 2023

  48. [61]

    Geometric numerical integration , volume=

    Structure-preserving algorithms for ordinary differential equations , author=. Geometric numerical integration , volume=. 2006 , publisher=

    work page 2006

  49. [62]

    2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , year=

    Projected gradient descent on Riemannian manifolds with applications to online power system optimization , author=. 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , year=

    work page 2016

  50. [63]

    Journal of Nonlinear Science , volume=

    Accelerated optimization on Riemannian manifolds via discrete constrained variational integrators , author=. Journal of Nonlinear Science , volume=. 2022 , publisher=

    work page 2022

  51. [64]

    Proceedings of the IEEE conference on computer vision and pattern recognition , year=

    Gravitational approach for point set registration , author=. Proceedings of the IEEE conference on computer vision and pattern recognition , year=

    work page

  52. [65]

    Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

    Accelerated gravitational point set alignment with altered physical laws , author=. Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

    work page

  53. [66]

    IEEE Transactions on Image Processing , volume=

    GraphReg: Dynamical point cloud registration with geometry-aware graph signal processing , author=. IEEE Transactions on Image Processing , volume=. 2022 , publisher=

    work page 2022

  54. [67]

    2018 International Conference on 3D Vision (3DV) , pages=

    Nrga: Gravitational approach for non-rigid point set registration , author=. 2018 International Conference on 3D Vision (3DV) , pages=. 2018 , organization=

    work page 2018

  55. [68]

    IEEE transactions on pattern analysis and machine intelligence , volume=

    Efficient registration of high-resolution feature enhanced point clouds , author=. IEEE transactions on pattern analysis and machine intelligence , volume=. 2018 , publisher=

    work page 2018

  56. [69]

    Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

    Dynamical pose estimation , author=. Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

    work page

  57. [70]

    The Euler-Poincar

    Bloch, Anthony and Krishnaprasad, PS and Marsden, Jerrold E and Ratiu, Tudor S , journal=. The Euler-Poincar. 1996 , publisher=

    work page 1996

  58. [71]

    IMA Journal of Numerical Analysis , volume=

    Global rates of convergence for nonconvex optimization on manifolds , author=. IMA Journal of Numerical Analysis , volume=. 2019 , publisher=

    work page 2019

  59. [72]

    SIAM Journal on Optimization , volume=

    Asynchronous stochastic coordinate descent: Parallelism and convergence properties , author=. SIAM Journal on Optimization , volume=. 2015 , publisher=

    work page 2015

  60. [73]

    International conference on machine learning , pages=

    Asynchronous decentralized parallel stochastic gradient descent , author=. International conference on machine learning , pages=. 2018 , organization=

    work page 2018

  61. [74]

    Georgia Institute of Technology, Tech

    Factor graphs and GTSAM: A hands-on introduction , author=. Georgia Institute of Technology, Tech. Rep , volume=

    work page

  62. [75]

    Mathematical programming , volume=

    Benchmarking optimization software with performance profiles , author=. Mathematical programming , volume=. 2002 , publisher=

    work page 2002

  63. [76]

    2018 , publisher=

    Global formulations of Lagrangian and Hamiltonian dynamics on manifolds , author=. 2018 , publisher=

    work page 2018

  64. [77]

    The International Journal of Robotics Research , volume=

    Convex geometric motion planning of multi-body systems on lie groups via variational integrators and sparse moment relaxation , author=. The International Journal of Robotics Research , volume=. 2025 , publisher=

    work page 2025

  65. [78]

    IEEE Transactions on Robotics , year=

    Port-Hamiltonian neural ODE networks on Lie groups for robot dynamics learning and control , author=. IEEE Transactions on Robotics , year=

    work page

  66. [79]

    2008 , publisher=

    Optimization algorithms on matrix manifolds , author=. 2008 , publisher=

    work page 2008

  67. [81]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Lie group variational integrators for the full body problem , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2007 , publisher=

    work page 2007

  68. [82]

    Kamak Ebadi, Lukas Bernreiter, Harel Biggie, Gavin Catt, Yun Chang, Arghya Chatterjee, Christopher E. Denniston, Simon-Pierre Deschênes, Kyle Harlow, Shehryar Khattak, Lucas Nogueira, Matteo Palieri, Pavel Petráček, Matěj Petrlík, Andrzej Reinke, Vít Krátký, Shibo Zhao, Ali-akbar Agha-mohammadi, Kostas Alexis, Christoffer Heckman, Kasra Khosoussi, Navinda...

    work page doi:10.1109/tro.2023.3323938 2024

  69. [83]

    Kimera-multi: Robust, distributed, dense metric-semantic slam for multi-robot systems

    Yulun Tian, Yun Chang, Fernando Herrera Arias, Carlos Nieto-Granda, Jonathan P How, and Luca Carlone. Kimera-multi: Robust, distributed, dense metric-semantic slam for multi-robot systems. IEEE Transactions on Robotics, 38 0 (4), 2022

    work page 2022

  70. [84]

    SlideSLAM : Sparse , Lightweight , Decentralized Metric - Semantic SLAM for Multi - Robot Navigation , July 2024

    Xu Liu, Jiuzhou Lei, Ankit Prabhu, Yuezhan Tao, Igor Spasojevic, Pratik Chaudhari, Nikolay Atanasov, and Vijay Kumar. SlideSLAM : Sparse , Lightweight , Decentralized Metric - Semantic SLAM for Multi - Robot Navigation , July 2024. arXiv:2406.17249

    work page arXiv 2024

  71. [85]

    Swarm- SLAM : Sparse Decentralized Collaborative Simultaneous Localization and Mapping Framework for Multi - Robot Systems

    Pierre-Yves Lajoie and Giovanni Beltrame. Swarm- SLAM : Sparse Decentralized Collaborative Simultaneous Localization and Mapping Framework for Multi - Robot Systems . IEEE Robotics and Automation Letters, 9(1): 0 475--482, January 2024. ISSN 2377-3766, 2377-3774. doi:10.1109/LRA.2023.3333742

    work page doi:10.1109/lra.2023.3333742 2024

  72. [86]

    COVINS : Visual - Inertial SLAM for Centralized Collaboration

    Patrik Schmuck, Thomas Ziegler, Marco Karrer, Jonathan Perraudin, and Margarita Chli. COVINS : Visual - Inertial SLAM for Centralized Collaboration . In 2021 IEEE Int. Symposium on Mixed and Augmented Reality Adjunct , pages 171--176, October 2021. doi:10.1109/ISMAR-Adjunct54149.2021.00043

    work page doi:10.1109/ismar-adjunct54149.2021.00043 2021

  73. [87]

    Rosen, and Jonathan P

    Yulun Tian, Kasra Khosoussi, David M. Rosen, and Jonathan P. How. Distributed Certifiably Correct Pose - Graph Optimization . IEEE Trans. on Robotics, 37(6): 0 2137--2156, December 2021. ISSN 1941-0468. doi:10.1109/TRO.2021.3072346

    work page doi:10.1109/tro.2021.3072346 2021

  74. [88]

    Asynchronous Distributed Smoothing and Mapping via On - Manifold Consensus ADMM

    Daniel McGann, Kyle Lassak, and Michael Kaess. Asynchronous Distributed Smoothing and Mapping via On - Manifold Consensus ADMM . In IEEE Int. Conf. on Robotics and Automation, pages 4577--4583, 2024

    work page 2024

  75. [89]

    Taosha Fan and Todd D. Murphey. Majorization Minimization Methods for Distributed Pose Graph Optimization . IEEE Trans.\ on Robotics, 40: 0 22--42, 2024. ISSN 1941-0468. doi:10.1109/TRO.2023.3324818

    work page doi:10.1109/tro.2023.3324818 2024

  76. [90]

    Riku Murai, Joseph Ortiz, Sajad Saeedi, Paul H. J. Kelly, and Andrew J. Davison. A Robot Web for Distributed Many - Device Localization . IEEE Trans. on Robotics, 40: 0 121--138, 2024. ISSN 1941-0468. doi:10.1109/TRO.2023.3324127

    work page doi:10.1109/tro.2023.3324127 2024

  77. [91]

    Yulun Tian, Alec Koppel, Amrit Singh Bedi, and Jonathan P. How. Asynchronous and Parallel Distributed Pose Graph Optimization . IEEE Robotics and Automation Letters, 5(4): 0 5819--5826, October 2020. ISSN 2377-3766. doi:10.1109/LRA.2020.3010216

    work page doi:10.1109/lra.2020.3010216 2020

  78. [92]

    The euler-poincar \'e equations and double bracket dissipation

    Anthony Bloch, PS Krishnaprasad, Jerrold E Marsden, and Tudor S Ratiu. The euler-poincar \'e equations and double bracket dissipation. Communications in mathematical physics, 175 0 (1): 0 1--42, 1996

    work page 1996

  79. [93]

    Port-hamiltonian neural ode networks on lie groups for robot dynamics learning and control

    Thai Duong, Abdullah Altawaitan, Jason Stanley, and Nikolay Atanasov. Port-hamiltonian neural ode networks on lie groups for robot dynamics learning and control. IEEE Transactions on Robotics, 2024

    work page 2024

  80. [94]

    Convex geometric motion planning of multi-body systems on lie groups via variational integrators and sparse moment relaxation

    Sangli Teng, Ashkan Jasour, Ram Vasudevan, and Maani Ghaffari. Convex geometric motion planning of multi-body systems on lie groups via variational integrators and sparse moment relaxation. The International Journal of Robotics Research, 44 0 (10-11): 0 1784--1813, 2025

    work page 2025

Showing first 80 references.