Rendezvous Without Coordinates¹

Jingjin Yu ${}^{\dagger}$		Steven M. LaValle ${}^{\dagger *}$		Daniel Liberzon${}^{*}$
jyu18@uiuc.edu		lavalle@uiuc.edu		liberzon@uiuc.edu

Department of Computer Science ${}^{\dagger}$	Coordinated Science Laboratory${}^{*}$
University of Illinois	University of Illinois
Urbana, IL 61801 USA	Urbana, IL 61801 USA

Abstract:

We study minimalism in sensing and control by considering a multi-agent system in which each agent moves like a Dubins car and has a limited sensor that reports only the presence of another agent within some sector of its windshield. Using a simple quantized control law with three values, each agent tracks another agent (its target) assigned to it by maintaining that agent within this windshield sector. We use Lyapunov analysis to show that by acting autonomously in this way, the agents will achieve rendezvous given a connected initial assignment graph and the assumption that an agent and its target will merge into a single agent when they are sufficiently close. We then proceed to show that, by making the quantized control law slightly stronger, a connected initial assignment graph is not required and the sensing model can be weakened further. A distinguishing feature of our approach is that it does not involve any estimation procedure aimed at reconstructing coordinate information. Our scenario thus provides an example in which an interesting task is performed with extremely coarse sensing and control, and without state estimation. The system was implemented in computer simulation, accessible through the Web, of which the results are presented in the paper.