# Target Encirclement with any Smooth Pattern Using Range-only Measurements

## TL;DR

This paper introduces a coordinate-free, backstepping-based controller enabling a mobile robot to encircle an unknown target using only range measurements, achieving zero steady-state error and exponential convergence.

## Contribution

It presents a novel controller that works for any smooth pattern, with convergence guarantees, using only range data, unlike prior methods requiring more information.

## Key findings

- Controller achieves zero steady-state error
- Ensures exponential convergence with fixed parameters
- Validated through simulations

## Abstract

This paper proposes a coordinate-free controller to drive a mobile robot to encircle a target at unknown position by only using range measurements. Different from the existing works, a backstepping based controller is proposed to encircle the target with zero steady-state error for any desired smooth pattern. Moreover, we show its asymptotic exponential convergence under a fixed set of control parameters, which are independent of the initial distance to the target. The effectiveness and advantages of the proposed controller are validated via simulations.