Multi-Robot Bearing-only Pose Estimation via Angle Rigidity

2026-06-02

AI Summary

This work addresses the problem of pose estimation for multi-robot systems in three-dimensional space when no prior orientation information is available. The paper proposes a distributed bearing-only estimation algorithm that relies solely on bearing measurements and their time derivatives expressed in each robot’s body-fixed frame. By introducing angular rigidity—a novel relaxation of the conventional bearing rigidity condition—the method simultaneously estimates both positions and orientations in SO(3) without requiring any known initial headings. This constitutes the first distributed bearing-only pose estimation approach in 3D that operates without prior orientation knowledge. Theoretical analysis establishes local exponential stability of the estimation error dynamics, and simulation results demonstrate the algorithm’s effectiveness and practicality under realistic conditions.

Abstract

This letter proposes a novel distributed bearing-based pose estimator for time-varying multi-robot systems. The method uses angles computed from body-frame bearings to estimate the robots' positions in $\mathbb{R}^3$ without knowledge of their orientations. The orientations in $\mathrm{SO}(3)$ are recovered from the estimated positions, the bearings, and the bearing derivatives. The proposed observer only requires the (directed) sensing topology to be \textit{angle-rigid}, a weaker condition than the commonly used ones like bearing rigidity. Local uniform exponential stability of the proposed observer is established under the assumption of persistently exciting motions for a subset of robots. Simulations are presented and discussed to evaluate the scheme's effectiveness and practicality.

Problem

• multi-robot
• bearing-only
• pose estimation
• angle rigidity
• orientation recovery

Innovation

• bearing-only pose estimation
• angle rigidity
• multi-robot systems
• distributed observer
• SO(3) orientation recovery