# Multi-agent Localization of A Common Reference Coordinate Frame: An Extrinsic Approach

## TL;DR

This paper proposes two cooperative localization schemes for multi-agent systems to determine their global frame transformations using local measurements, achieving almost global convergence with stability guarantees.

## Contribution

It introduces two novel frame localization algorithms with asymptotic and finite-time stability for multi-agent systems, ensuring convergence up to an unknown bias.

## Key findings

- Estimates converge almost globally to true transformations.
- Algorithms achieve asymptotic and finite-time stability.
- Simulation validates the effectiveness of the proposed methods.

## Abstract

This paper studies the problem of multi-agent cooperative localization of a common reference coordinate frame in $\mathbb{R}^3$. Each agent in a system maintains a body-fixed coordinate frame and its actual \textit{frame transformation} (translation and rotation) from the global coordinate system is unknown. The mobile agents aim to determine their \textit{trajectories of rigid-body motions} (or the frame transformations, i.e., rotations and translations) with respect to the global coordinate frame up to a common frame transformation by using local measurements and information exchanged with neighbors. We present two frame localization schemes which compute the rigid-body motions of the agents with asymptotic stability and finite-time stability properties, respectively. Under both localization laws, the estimates of the frame transformations of the agents converge to the actual frame transformations almost globally and up to an unknown constant transformation bias. Finally, simulation results are provided.