# Controlling Parent Systems Through Swarms Using Abstraction

## TL;DR

This paper presents a general method for controlling parent-child systems using swarms by employing a low-dimensional abstract state space, enabling decoupled control and robust trajectory tracking in simulations.

## Contribution

It introduces a novel approach to decouple swarm and parent system control via abstraction, with stability analysis and controller design for constrained trajectory tracking.

## Key findings

- Controllers achieve local asymptotic stability.
- Method works for both homogeneous and heterogeneous swarms.
- Effective in simulation for various swarm configurations.

## Abstract

This study considers the control of parent-child systems where a parent system is acted on by a set of controllable child systems (i.e. a swarm). Examples of such systems include a swarm of robots pushing an object over a surface, a swarm of aerial vehicles carrying a large load, or a set of end effectors manipulating an object. In this paper, a general approach for decoupling the swarm from the parent system through a low-dimensional abstract state space is presented. The requirements of this approach are given along with how constraints on both systems propagate through the abstract state and impact the requirements of the controllers for both systems. To demonstrate, several controllers with hard state constraints are designed to track a given desired angle trajectory of a tilting plane with a swarm of robots driving on top. Both homogeneous and heterogeneous swarms of varying sizes and properties are considered to test the robustness of this architecture. The controllers are shown to be locally asymptotically stable and are demonstrated in simulation.