Bearing-Only Solution for Fermat-Weber Location Problem: Generalized Algorithms

TL;DR

This paper introduces new bearing-only algorithms enabling autonomous agents, modeled as single or double integrators, to locate the Fermat-Weber point among stationary or moving beacons, with rigorous proofs and simulations.

Contribution

It extends Fermat-Weber location solutions to dynamic scenarios using bearing-only measurements and diverse agent models, with proven stability.

Findings

Algorithms successfully guide agents to Fermat-Weber points.

Theoretical proofs confirm convergence and stability.

Simulations demonstrate effectiveness in dynamic environments.

Abstract

This paper presents novel algorithms for the Fermat-Weber Location Problem, guiding an autonomous agent to the point that minimizes the weighted sum of Euclidean distances to some beacons using only bearing measurements. The existing results address only the simple scenario where the beacons are stationary and the agent is modeled by a single integrator. In this paper, we propose a number of bearing-only algorithms that let the agent, which can be modeled as either a single-integrator or a double-integrator, follow the Fermat-Weber point of a group of stationary or moving beacons. The theoretical results are rigorously proven using Lyapunov theory and supported with simulation examples.