Bearing-Only Solution to the Fermat-Weber Location Problem for Unicycle Agent

TL;DR

This paper develops bearing-only control algorithms for unicycle robots to solve the Fermat-Weber Location Problem, accounting for nonholonomic constraints, with validation through simulations and experiments.

Contribution

It introduces novel bearing-only control laws for unicycle agents tackling stationary and moving beacons, extending existing FWLP solutions to nonholonomic robots.

Findings

Control laws successfully track Fermat-Weber points in simulations.

Algorithms effectively handle stationary and moving beacons.

Experimental results validate the proposed methods.

Abstract

This paper addresses bearing-only algorithms for solving the Fermat-Weber Location Problem (FWLP) with a unicycle agent. Unlike existing FWLP solutions for single- or double-integrator agents, our approach accounts for the nonholonomic constraints of wheeled robots. We first develop a bearing-only control law for the case with stationary beacons. Next, we consider saturated control inputs and propose a corresponding bearing-only control law. Finally, we address moving beacons with constant velocities and develop a control law that enables the unicycle agent to track the moving Fermat-Weber point. Both simulations and experiments are provided to demonstrate the effectiveness of the proposed methods.