A Smooth Distributed Feedback for Global Rendezvous of Unicycles

TL;DR

This paper introduces a smooth, onboard measurement-based control law enabling a network of unicycles to achieve global rendezvous without GPS or orientation data, relying only on relative displacement measurements.

Contribution

It proposes a novel, simple, time-independent control law for unicycles that guarantees global rendezvous using only onboard relative displacement sensing.

Findings

Achieves global rendezvous from arbitrary initial conditions.

Does not require GPS or orientation information.

Uses only onboard relative displacement measurements.

Abstract

This paper presents a solution to the rendezvous control problem for a network of kinematic unicycles in the plane, each equipped with an onboard camera measuring its relative displacement with respect to its neighbors in body frame coordinates. A smooth, time-independent control law is presented that drives the unicycles to a common position from arbitrary initial conditions, under the assumption that the sensing digraph contains a reverse-directed spanning tree. The proposed feedback is very simple, and relies only on the onboard measurements. No global positioning system is required, nor any information about the unicycles' orientations.