# Connectivity-Preserving Swarm Teleoperation Over A Tree Network With Time-Varying Delays

## TL;DR

This paper introduces a control strategy for swarm teleoperation that maintains connectivity despite communication delays and distance limitations, ensuring stable and synchronized operation through Lyapunov-based analysis and experimental validation.

## Contribution

It proposes a novel gain updating law and control scheme that preserve swarm connectivity and stability under time-varying delays, extending prior work to more realistic communication scenarios.

## Key findings

- Connectivity is preserved under time-varying delays.
- The control scheme ensures input-to-state stability.
- Experimental results confirm effective synchronization and connectivity.

## Abstract

A teleoperated swarm must follow the unpredictable commands of its human operator while remaining connected. When the swarm communications are limited by distance and affected by delays, both the user input and the transmission delays endanger the connectivity of the swarm. This paper presents a constructive control strategy that overcomes both threats. The strategy modulates the intra-swarm couplings and the damping injected to each slave in the swarm based on a customized potential. Lyapunov-based set invariance analysis proves that the proposed explicit gain updating law limits the impact of the operator input and preserves the initial tree connectivity of a delay-free swarm. Further augmentation with stricter selection of control gains robustifies the design to time-varying delays in intra-swarm communications. The paper also establishes the input-to-state stability of a teleoperated time-delay swarm under the proposed dynamic control. Experiments validate connectivity maintenance and synchronization during time-delay swarm teleoperation with the proposed control.