The Fermat-Weber location problem in single integrator dynamics using only local bearing angles

This paper proposes a modified gradient control law to solve the Fermat-Weber location problem. The control law may guide an autonomous agent to the point that minimizes the weighted sum distance with regard to some stationary beacons using only bearing measurements. Based on previous results from Fermat-Weber location problem and Lyapunov stability theory, we prove that the agent will globally asymptotically reach the destination only using local bearing measurements. We also consider a scenario when the beacons are not stationary. Simulation results are provided to verify the mathematical analysis.