A Closed-Form 4-DoF Inter-Robot Pose Estimator using Bearing-only Measurements

2026-06-25

AI Summary

This work addresses the challenge that existing bearing-only 6-DOF cooperative localization methods often suffer from degraded observability under certain motion patterns, hindering rapid acquisition of reliable pose estimates. To overcome this limitation, the authors propose a closed-form 4-DOF relative pose estimation algorithm that relaxes rotational constraints and incorporates error projection to enable efficient translation estimation. Furthermore, they introduce a sliding-window-free observability analysis combined with an adaptive triggering mechanism to reduce reliance on motion excitation. Theoretical analysis identifies key degeneracy modes, while extensive simulations and real-world experiments demonstrate that the proposed method significantly lowers computational overhead and data collection time, while simultaneously improving estimation accuracy and robustness.

Abstract

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.

Problem

• cooperative localization
• inter-robot pose estimation
• observability degeneracy
• bearing-only measurements
• motion patterns

Innovation

• closed-form
• 4-DoF pose estimation
• bearing-only
• observability analysis
• cooperative localization