A Decentralized LiDAR-SLAM System with Certifiably Optimal Pose Graph Optimization

Abstract: Decentralized multi-robot LiDAR-SLAM is essential for collaborative missions but faces significant challenges in maintaining global consistency. Existing frameworks predominantly rely on local-search optimization or one-time coordinate alignment, which are prone to suboptimal convergence and long-term inconsistency, especially in large-scale or degenerate environments. To address these limitations, this paper presents the first decentralized LiDAR-SLAM system that integrates a state-of-the-art certifiably optimal Pose Graph Optimization (PGO) backend. By leveraging the Riemannian Block Coordinate Descent (RBCD) algorithm, our system ensures globally consistent trajectory estimation without requiring accurate initial guesses. Experimental results demonstrate that the proposed framework achieves superior robustness, improving trajectory RMSE by up to 48.9% compared to the state-of-the-art DiSCo-SLAM.

• The paper proposes a decentralized LiDAR-SLAM system that integrates a certifiably optimal pose graph optimization backend using RBCD to ensure globally optimal trajectories.
• The paper validates its approach with split-trajectory experiments, demonstrating RMSE reductions of up to 48.9% compared to state-of-the-art systems.
• The paper shows that employing dual certificates effectively eliminates local minima, enhancing robustness in GNSS-denied and degenerate environments.

Decentralized LiDAR-SLAM with Certifiably Optimal Pose Graph Optimization

Introduction

Decentralized multi-robot LiDAR-SLAM is indispensable for collaborative mapping and localization tasks in GNSS-denied environments, particularly due to its scalability and robustness. However, accumulation of drift, especially in under-constrained directions, and suboptimal convergence in large-scale or degenerate operating environments present severe limitations for existing decentralized SLAM frameworks. Most notably, prevalent systems employ local search-based optimization or rely on one-off coordinate alignment strategies for inter-robot registration, which are structurally vulnerable to local minima and fail to guarantee global consistency. The paper "A Decentralized LiDAR-SLAM System with Certifiably Optimal Pose Graph Optimization" (2605.25051) addresses these issues by proposing a fully decentralized LiDAR-SLAM pipeline that, for the first time, incorporates a certifiably optimal PGO backend using the RBCD algorithm to ensure joint trajectory global optimality.

System Architecture

The framework is composed of a modular peer-to-peer architecture that processes point clouds and odometry from LIO-SAM frontends on each agent. Frontend modules employ Scan-Context descriptors for efficient loop closure detection and a P2P protocol for geometric constraint synchronization between agents. The core differentiator lies in the backend, where, instead of conventional local-search or rigid registration, the system formulates a continuous global PGO encompassing all intra- and inter-robot constraints. This optimization is cast as an SDP problem optimized on the Stiefel manifold via RBCD, which generates a dual certificate for verifying global optimality and detecting degenerate local minima.

Figure 1: Pipeline of the proposed system, highlighting the certifiably optimal PGO backend as the key innovation relative to DiSCo-SLAM.

This design maintains scalability and front-end efficiency while enabling robust, globally consistent batch PGO and volumetric mapping.

Certifiably Optimal Multi-Robot Trajectory Estimation

Local search-based backends, exemplified by DiSCo-SLAM, apply a one-time rigid transform alignment for inter-robot map merging but suffer from two primary flaws: (1) the single registration event is vulnerable to failure in ambiguous environments and (2) subsequent inter-robot constraints are ignored, causing irretrievable drift. In contrast, the proposed framework maintains a comprehensive pose graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ encapsulating all agents' poses and constraints. The backend objective jointly optimizes all robot poses over SE(3), with each new inter-robot encounter incrementally refining the global trajectory, thereby propagating corrections system-wide and eliminating the reliance on initial guess quality.

The non-convex PGO problem is recast as a semidefinite relaxation, solved with RBCD, which yields a dual certificate matrix $S^\ast$. If the relaxation is tight, certified by the $(d+1)$-th eigenvalue $\lambda_{d+1}(S^\ast) > 0$ for $d=3$, the solution is globally optimal. This certifiability addresses degenerate observability scenarios in a principled way: the system can automatically detect and discard non-global solutions, thereby ensuring structural trajectory integrity throughout operation.

Experimental Validation and Quantitative Results

To evaluate the system, the authors conduct split-trajectory experiments with overlapping LiDAR datasets, treating them as two agents in a decentralized setting. Deployments use high-density Ouster LiDAR, tactical-grade IMUs, and GNSS/IMU for ground-truth. Comparisons against DiSCo-SLAM and raw LIO-SAM odometry demonstrate the practical impact of certifiable PGO.

Figure 2: Quantitative localization trajectories computed by the proposed method, DiSCo-SLAM, and LIO-SAM odometry showing significant suppression of drift.

For Robot 1, the proposed method achieves a 3.62m RMSE versus 7.09m for DiSCo-SLAM and 7.01m for LIO-SAM, yielding a 48.9% reduction compared to DiSCo-SLAM. Robot 2 shows a 2.38m RMSE, a 13.4% improvement over DiSCo-SLAM and 51.4% over LIO-SAM. The mapping output aligns accurately with satellite ground-truth after trajectory fusion with the certifiable PGO solution.

Figure 3: Decentralized pipeline depicting Scan Context loop closures, P2P submap synchronization, certifiable PGO, and volumetric map fusion.

Theoretical and Practical Implications

The system demonstrates that integrating a certifiably optimal PGO backend removes the local-minima vulnerabilities inherent to local search-based decentralized SLAM, especially in challenging, weakly observable environments. The explicit verification of solution globality and the rejection of degenerate solutions establish a new robustness benchmark for large-scale multi-robot SLAM. From a theoretical perspective, the use of dual certificates and guarantees over SE(3) can serve as a foundation for further extensions, including tighter integration with heterogeneous sensors, dynamic environment robustness, and scalability to even larger fleets. Practically, this enables highly consistent volumetric mapping for real-world autonomous robots in infrastructure-constrained or GNSS-denied scenarios.

Conclusion

The proposed decentralized LiDAR-SLAM framework unifies every intra- and inter-robot geometric constraint into a certifiably globally optimal batch PGO. Empirical results show significant improvements in localization RMSE and trajectory consistency compared to state-of-the-art decentralized systems. The dual certificate-based approach eliminates local minima and non-global solutions, providing structural guarantees essential for real-world long-term deployment. Future work may include generalization to cross-modal sensor suites and operation in even more adverse environments, further extending the certifiable SLAM paradigm.