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arxiv: 2606.24489 · v1 · pith:YFRGRMGHnew · submitted 2026-06-23 · 💻 cs.RO

Decentralized Pose Graph Riemannian Optimization for Object-based Multi-Robot SLAM

Yixian Zhao , Yan Huang , Yang Xu , Liang Li , Jinming Xu This is my paper

Pith reviewed 2026-06-26 00:01 UTC · model grok-4.3

classification 💻 cs.RO
keywords decentralized optimizationpose graph optimizationmulti-robot SLAMRiemannian manifold optimizationconsensus algorithmsobject-based mappingSE(d) group
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The pith

Consensus mechanism decouples joint trajectory and object pose estimation in multi-robot SLAM.

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

This paper introduces a decentralized optimization method for multi-robot SLAM involving shared objects that multiple robots observe. The approach separates the estimation of individual robot paths from the common object positions using consensus, which removes restrictions on how robots must communicate. As a result, the system functions with communication that is sparse, changes over time, or occurs only intermittently. An approximate second-order method on the manifold further cuts down the number of steps needed while keeping the geometric properties intact.

Core claim

The paper claims that object-based multi-robot pose graph optimization can be made fully decentralized by decoupling the coupled estimation problem through a consensus mechanism on the SE(d) manifold. This enables operation over arbitrary communication topologies, and a distributed approximate-Newton scheme achieves faster convergence to Riemannian first-order stationary points with lower communication cost, as shown by local condition-number analysis, without loss of accuracy.

What carries the argument

The consensus mechanism that decouples the joint estimation of robot trajectories and persistent object poses, combined with the distributed approximate-Newton scheme on the SE(d) manifold.

If this is right

  • The method works for any sparse, intermittent, or time-varying communication graphs.
  • It reduces the number of iterations and the amount of data exchanged between robots.
  • Convergence is guaranteed to first-order stationary points on the manifold.
  • Accuracy remains comparable to centralized solutions on benchmarks and real experiments.

Where Pith is reading between the lines

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

  • If the decoupling holds, teams could maintain consistent maps in settings where radio links are unreliable or blocked.
  • The local condition-number analysis points to possible further speedups by incorporating more curvature information locally.
  • Extensions might combine this with online object discovery rather than assuming persistent known objects.

Load-bearing premise

The consensus mechanism succeeds in decoupling the estimation even when the communication network is arbitrary and does not match the observation pattern.

What would settle it

Running the algorithm on a multi-robot dataset with highly disconnected or failing communication links and observing that the estimates diverge or have large errors compared to a centralized solver would disprove the decoupling claim.

Figures

Figures reproduced from arXiv: 2606.24489 by Jinming Xu, Liang Li, Yang Xu, Yan Huang, Yixian Zhao.

Figure 1
Figure 1. Figure 1: The real-life experiment system comprises six Dingo robots and nine objects. The colored solid lines and square dots in (b) and (c) refer to the estimated trajectories and object positions of robots, respectively. The colored dashed lines and dark blue square dots refer to the true values of the robot trajectories and the object positions, respectively. structure to build a communication-lean decentralized… view at source ↗
Figure 2
Figure 2. Figure 2: A pose graph illustration of the multi-robot SLAM problem. Robot 𝑖 (blue triangle) and robot 𝑗 (red triangle) collaboratively estimate the poses of shared objects {𝑦1 , …, 𝑦4 } (green circles) and their respective trajectories 𝑥𝑖 and 𝑥𝑗 . The graph includes intra-robot odometry (solid gray lines) and relative inter-robot/object measurements (colored dashed lines). where Log(⋅) maps the error from the manif… view at source ↗
Figure 3
Figure 3. Figure 3: visualizes the optimization results on the Sphere and Tours datasets obtained by our method. The results show that the five robots successfully reconstruct the over￾all pose graph by exchanging only separator variables at inter-robot boundaries. As reported in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Multi-UAV trajectory estimation and object local￾ization experiments. Colored lines: the trajectories of different UAVs. Star symbols: goal points of the robot. Colored polyhe￾dra: obstacle locations. its trajectory using odometry measurements and obtain the corresponding noisy observations when its distance to any obstacle gets below 5𝑚. All measurements are corrupted by Langevin rotation noise with 1 ◦ s… view at source ↗
Figure 5
Figure 5. Figure 5: Performance on large-scale simulation datasets in diverse communication topology [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The success rate of cost on large-scale simulation datasets in diverse communication topologies. (a) 𝜅 = 0.01 (b) 𝜏 = 0.001 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Success ratio of ATE from the multi-level noisy datasets. 6.2.3. Evaluations of the effectiveness of Schur complement To validate the effectiveness of using the Schur comple￾ment in our method, we performed several numerical experi￾ments focusing on both computation time and accuracy. The experiment was conducted on a predefined communication network with a network density of 𝜌 = 0.5, and the results were … view at source ↗
Figure 9
Figure 9. Figure 9: The success ratio of ATE under different degrees of connectivity for real-world dataset experiments. In terms of accuracy, the final optimized pose showed near￾identical results: an objective value of 0.0919 with the Schur complement and 0.0920 without it. These results confirm that the application of the Schur complement improves com￾putational efficiency without sacrificing optimization qual￾ity. 6.3. Re… view at source ↗
read the original abstract

Pose graph optimization (PGO) is a key back-end component for state estimation in networked multi-robot simultaneous localization and mapping (SLAM). In object-based multi-robot SLAM, the problem becomes more tightly coupled because robots must jointly estimate both their trajectories and the poses of persistent objects observed by multiple agents. Existing decentralized solutions often assume that the communication graph closely matches the physical interaction topology, which is restrictive in realistic deployments where communication is sparse, intermittent, or time-varying. This paper presents a fully decentralized Riemannian optimization framework for object-based multi-robot PGO that decouples the coupled estimation problem via a consensus mechanism, enabling flexible communication topologies. To improve convergence under limited communication budgets, we further develop a distributed approximate-Newton scheme that exploits local second-order information while operating directly on the SE(d) manifold to preserve geometric consistency, and we establish the convergence to Riemannian first-order stationary points and provide a local condition-number analysis explaining the benefit of approximate second-order information over first-order Riemannian descent. The resulting method reduces iteration count and communication overhead without sacrificing estimation accuracy. Extensive evaluations on public benchmarks, large-scale simulations, and real-world multi-robot experiments demonstrate improved accuracy, runtime efficiency, scalability across network topologies, and robustness to communication failures.

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

2 major / 2 minor

Summary. The paper presents a fully decentralized Riemannian optimization framework for object-based multi-robot pose graph optimization (PGO) in SLAM. It decouples the joint estimation of robot trajectories and persistent object poses via a consensus mechanism that supports sparse, intermittent, or time-varying communication topologies (unlike prior methods that require communication graphs to match physical interaction topologies). A distributed approximate-Newton scheme is developed that operates directly on the SE(d) manifold, with stated convergence to Riemannian first-order stationary points and a local condition-number analysis showing benefits over first-order Riemannian descent. The method is claimed to reduce iteration count and communication overhead without loss of accuracy. Extensive evaluations are reported on public benchmarks, large-scale simulations, and real-world multi-robot experiments demonstrating gains in accuracy, runtime, scalability, and robustness to communication failures.

Significance. If the decoupling and convergence claims hold, the work would meaningfully advance decentralized multi-robot SLAM by relaxing restrictive topology assumptions common in the literature, enabling more realistic deployments. The Riemannian formulation preserves manifold geometry, the approximate-Newton approach targets communication efficiency, and the combination of public benchmarks, simulations, and real experiments provides a solid empirical foundation. These elements (distributed second-order information on SE(d) plus explicit convergence analysis) are strengths that differentiate it from first-order decentralized baselines.

major comments (2)
  1. [Consensus mechanism and decoupling section] The central claim that the consensus mechanism decouples the coupled trajectory-object estimation problem for arbitrary (sparse, intermittent, time-varying) communication topologies is load-bearing; the manuscript must contain an explicit statement (likely a theorem or proposition) establishing that the local subproblems remain consistent with the global optimum under the stated communication model, including any minimum connectivity or dwell-time assumptions.
  2. [Distributed approximate-Newton scheme and analysis] The local condition-number analysis is invoked to explain why the distributed approximate-Newton scheme reduces iteration count relative to first-order Riemannian descent; this analysis must be stated with the precise local Hessian approximation used and the resulting bound on the condition number (or equivalent contraction factor) so that the claimed benefit can be verified.
minor comments (2)
  1. [Notation and problem formulation] Clarify the precise definition of the consensus variables and the update rule for object poses shared across robots; notation for the SE(d) retraction and the approximate Hessian should be introduced once and used consistently.
  2. [Evaluations] The experimental section should include an explicit statement of data exclusion criteria, number of Monte Carlo runs, and statistical significance tests for the reported accuracy and runtime improvements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address the two major comments point by point below and will revise the manuscript accordingly to strengthen the formal statements.

read point-by-point responses

  1. Referee: [Consensus mechanism and decoupling section] The central claim that the consensus mechanism decouples the coupled trajectory-object estimation problem for arbitrary (sparse, intermittent, time-varying) communication topologies is load-bearing; the manuscript must contain an explicit statement (likely a theorem or proposition) establishing that the local subproblems remain consistent with the global optimum under the stated communication model, including any minimum connectivity or dwell-time assumptions.

    Authors: We agree that an explicit formal statement is required to substantiate the decoupling claim under general communication topologies. The manuscript describes the consensus updates and their role in decoupling trajectory and object variables but does not isolate this property as a dedicated proposition. In the revised version we will insert Proposition 1 in Section III, which states that, under the assumption of T-periodic joint connectivity with minimum dwell time tau > 0, the distributed consensus iterates converge to the same fixed point as the centralized joint PGO problem. The proof will rely on a Lyapunov function defined on the product of SE(d) manifolds and standard results on time-varying consensus. revision: yes

  2. Referee: [Distributed approximate-Newton scheme and analysis] The local condition-number analysis is invoked to explain why the distributed approximate-Newton scheme reduces iteration count relative to first-order Riemannian descent; this analysis must be stated with the precise local Hessian approximation used and the resulting bound on the condition number (or equivalent contraction factor) so that the claimed benefit can be verified.

    Authors: We concur that the local condition-number argument must be stated with explicit definitions. Section IV-C currently invokes a block-diagonal Hessian approximation without writing the precise expression or the resulting bound. In the revision we will replace the paragraph with the following: the local Hessian approximation is H_i = sum_{j in N_i} (H_{ij} + lambda I), where H_{ij} are the second derivatives of the pairwise factors; under the local strong-convexity assumption with modulus mu and Lipschitz constant L we obtain the condition-number bound kappa <= (L + lambda)/(mu + lambda) <= kappa_first-order * (1 - c alpha), where alpha is the consensus gain. This explicit contraction factor will be used to explain the observed reduction in iteration count. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper's central claims rest on a consensus-based decoupling of the joint estimation problem followed by a distributed approximate-Newton scheme on the SE(d) manifold, with stated convergence to first-order stationary points and a local condition-number analysis. These steps invoke standard Riemannian optimization techniques and consensus mechanisms whose validity is independent of the target result; no equation reduces by construction to a fitted parameter, self-citation chain, or renamed input. The abstract and provided framing contain no self-definitional steps, fitted-input predictions, or load-bearing self-citations that would force the claimed benefits.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the described method appears to rely on standard Riemannian optimization and consensus algorithms from prior literature.

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