Control of one-dimensional guided formations using coarse information

TL;DR

This paper demonstrates that mobile agents in a one-dimensional formation can be guided to desired positions using only minimal, coarse information, with control laws ensuring convergence despite severe communication limitations.

Contribution

It introduces control laws that achieve formation guidance with at most four bits of information per agent, expanding the understanding of minimal communication control in formation systems.

Findings

Guidance is possible with only four bits of information per agent.

The control laws guarantee convergence for most initial conditions.

Non-smooth analysis tools are effective for convergence proof.

Abstract

Motivated by applications in intelligent highway systems, the paper studies the problem of guiding mobile agents in a one-dimensional formation to their desired relative positions. Only coarse information is used which is communicated from a guidance system that monitors in real time the agents' motions. The desired relative positions are defined by the given distance constraints between the agents under which the overall formation is rigid in shape and thus admits locally a unique realization. It is shown that even when the guidance system can only transmit at most four bits of information to each agent, it is still possible to design control laws to guide the agents to their desired positions. We further delineate the thin set of initial conditions for which the proposed control law may fail using the example of a three-agent formation. Tools from non-smooth analysis are utilized for the convergence analysis.