# Formation control on Jordan curves based on noisy proximity measurements

## TL;DR

This paper develops a robust formation control strategy for multi-agent systems on Jordan curves, accommodating noisy measurements and limited information flow, bridging the gap between theoretical models and real-world applications.

## Contribution

It introduces a novel estimation and control approach using interval analysis for formation control on arbitrary closed curves with noisy, limited data.

## Key findings

- Effective formation control on Jordan curves demonstrated
- Robustness achieved despite noisy proximity measurements
- Applicable to real-world scenarios with restricted information flow

## Abstract

The paradigmatic formation control problem of steering a multi-agent system towards a balanced circular formation has been the subject of extensive studies in the control engineering community. Indeed, this is due to the fact that it shares several features with relevant applications such as distributed environmental monitoring or fence-patrolling. However, these applications may also present some relevant differences from the ideal setting such as the curve on which the formation must be achieved not being a circle, or the measurements being neither ideal nor as a continuous information flow. In this work, we attempt to fill this gap between theory and applications by considering the problem of steering a multi-agent system towards a balanced formation on a generic closed curve and under very restrictive assumptions on the information flow amongst the agents. We tackle this problem through an estimation and control strategy that borrows tools from interval analysis to guarantee the robustness that is required in the considered scenario.