Group-Control Motion Planning Framework for Microrobot Swarms in a Global Field

TL;DR

This paper introduces a group-control paradigm for microrobot swarm motion planning in a global field, proving small-time local controllability and analyzing trade-offs between control complexity and planning efficiency.

Contribution

It presents a novel group-control framework, proves controllability conditions, and explores trade-offs and instantiations through simulations.

Findings

Small-Time Local Controllability achieved with log2(n+2)+1 groups.

Motion planning complexity can be reduced with appropriate primitives.

Simulations demonstrate the effectiveness of the proposed group-control approach.

Abstract

This paper investigates how a novel paradigm called group-control can be effectively used for motion planning for microrobot swarms in a global field. We prove that Small-Time Local Controllability (STLC) in robot positions is achievable through group-control, with the minimum number of groups required for STLC being $\log_2(n + 2) + 1$ for $n$ robots. We then discuss the trade-offs between control complexity, motion planning complexity, and motion efficiency. We show how motion planning can be simplified if appropriate primitives can be achieved through more complex control actions. We identify motion planning problems that balance the number of motion primitives with planning complexity. Various instantiations of these motion planning problems are explored, with simulations used to demonstrate the effectiveness of group-control.