Multi-Robot Bearing-only Pose Estimation via Angle Rigidity

Bearing-odometry-based cooperative localization has attracted increasing research interest due to its minimal infrastructure requirements, low communication bandwidth and broad applicability in complex environments. However, existing 6-DoF approaches still face challenges in rapidly obtaining accurate and reliable inter-robot pose estimation, as the system is prone to observability degeneracy under specific motion patterns. To address these issues, we first propose a closed-form 4-DoF inter-robot pose estimator, which relaxes nonlinear constraints for rotations estimation and employs error projection for translations estimation. We then conduct a theoretical analysis of the system's observability, identifying degeneracy under two typical motion patterns: collinear and shape-preserving formations. The analysis further shows that the proposed 4-DoF system requires less stringent motion excitation for observability, enabling reliable estimation under a broader range of cooperative maneuvers. Furthermore, an observability test module is introduced to autonomously determine the optimal estimation instant, eliminating reliance on a predefined fixed-length sliding window. Extensive simulations and real-world experiments demonstrate that the proposed algorithm achieves higher estimation accuracy with significantly low computational cost, and the observability test module ensures estimation reliability while minimizing the data collection interval.

Relative localization is essential for cooperation in autonomous multi-robot systems. Existing approaches either rely on shared environmental features or inertial assumptions, or they degrade under pairwise non-line-of-sight conditions and outliers in complex environments. Robustly and efficiently fusing inter-robot bearings, distances, and inertial measurements for tens of robots remains challenging. We present CREPES-X (Cooperative RElative Pose Estimation System with multiple eXtended features), a hierarchical relative localization framework that enhances speed, accuracy, and robustness under challenging conditions, without requiring any global information. The hardware packs infrared (IR) LEDs, an IR camera, an ultra-wideband module, and an IMU into a cube no larger than $6\,\text{cm}$ on each side. On this hardware, a two-stage hierarchical estimator meets different latency, accuracy, and robustness requirements. The single-frame estimator returns instantaneous relative poses from a closed-form solution with bearing outlier rejection. The multi-frame estimator then refines these poses with IMU pre-integration under robocentric relative kinematics, using loosely- and tightly-coupled optimization. Extensive simulations and real-world experiments validate the effectiveness of CREPES-X, demonstrating robustness of up to $90\%$ bearing outliers, resilience in challenging conditions, and RMSE of $7.0\,\text{cm}$ and $2.2^\circ$ in real-world datasets.

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.