Bearing-only solution for Fermat–Weber location problem: Generalized algorithms

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 current results address only the simple scenario where the beacons are stationary and the agent is modeled by a single integrator. In this paper, we present a number of bearing-only algorithms that let the agent follow the Fermat–Weber point of a group of stationary or moving beacons. Exponential and finite-time stability of the Fermat–Weber point are also established. The theoretical results are rigorously proven using Lyapunov theory and supported with simulation examples. © 2025 Elsevier Ltd