# Target Approaching Control Under a GPS-Denied Environment with Range-Only Measurements

## TL;DR

This paper presents a control strategy for a vehicle to approach a target area using only distance measurements, without GPS or bearing information.

## Contribution

A novel local controller is proposed that uses only range-only measurements to ensure convergence to a target region.

## Key findings

- The control strategy guarantees convergence to the target region with at most three velocity adjustments.
- Theoretical analysis and outdoor experiments validate the effectiveness of the proposed method.

## Abstract

In this paper, we investigate the target-approaching control problem for a discrete-time first-order vehicle system where the target area is modeled as a static circular region. In the absence of absolute bearing or position information, we propose a simple local controller that relies solely on range measurements to the target obtained at two consecutive sampling instants. Specifically, if the measured distance decreases between two successive samples, the vehicle maintains a constant velocity; otherwise, it rotates its velocity vector by an angle of π/2 in the clockwise direction. This control strategy guarantees convergence to the target region, ensuring that the vehicle’s velocity direction remains unchanged in the best-case scenario and is adjusted at most three times in the worst case. The effectiveness of the proposed method is theoretically established and further validated through outdoor experiments with a mobile vehicle.