Distributed Framework Construction for Affine Formation Control

TL;DR

This paper develops distributed geometric algorithms for constructing affine formation frameworks that adapt to agent addition or removal, ensuring rigidity and localizability in multi-agent systems.

Contribution

It introduces novel distributed strategies for affine framework construction that handle dynamic agent changes while maintaining rigidity and localizability.

Findings

Algorithms effectively maintain framework properties during agent changes.

Distributed methods outperform centralized approaches in time efficiency.

Successful multi-UAV formation tracking demonstrates practical applicability.

Abstract

In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the formation or link/agent failures emerge. Motivated by this observation, we investigate the problem of constructing affine frameworks in three scenarios, including vertex addition, edge deletion and vertex deletion. Our approach starts from the original affine formation and uses geometric methods to locally adjust the structure of the weighted graph to describe the topology, so that the modified framework maintains the universal rigidity and affine localizability. Notably, the developed strategies only utilize local measurements and exhibit distributed characteristics, laying the foundation for applications in multi-agent systems. To demonstrate the compatibility with affine formation control proposals, we present a case study on affine formation tracking in a multi-UAV formation, demonstrating the effectiveness of our algorithms in constructing eligible frameworks in aforementioned scenarios. Moreover, a comparative simulation is also conducted to highlight the low time complexity of our distributed algorithm relative to the centralized optimization-based method.