Circumnavigation Using Distance Measurements (Extended Version)

TL;DR

This paper presents a nonlinear control law enabling a mobile agent to circumnavigate a stationary or drifting target at a fixed distance using only distance measurements, with proven exponential convergence and robustness to drift.

Contribution

It introduces a novel nonlinear periodic control law that combines target estimation and circumnavigation, ensuring global exponential convergence using only distance data.

Findings

Achieves circumnavigation with only distance measurements

Proven global exponential convergence of the control law

Robust to slow, persistent drift of the target

Abstract

Consider a stationary agent A at an unknown location and a mobile agent B that must move to the vicinity of and then circumnavigate A at a prescribed distance from A. In doing so, B can only measure its distance from A, and knows its own position in some reference frame. This paper considers this problem, which has applications to surveillance or maintaining an orbit. In many of these applications it is difficult for B to directly sense the location of A, e.g. when all that B can sense is the intensity of a signal emitted by A. This intensity does, however provide a measure of the distance. We propose a nonlinear periodic continuous time control law that achieves the objective. Fundamentally, B must exploit its motion to estimate the location of A, and use its best instantaneous estimate of where A resides, to move itself to achieve the ultimate circumnavigation objective. The control law we propose marries these dual goals and is globally exponentially convergent. We show through simulations that it also permits B to approximately achieve this objective when A experiences slow, persistent and potentially nontrivial drift.