Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Flexible and Resilient Formation Approach based on Hierarchical Reorganization

Yuzhu Li, Wei Dong

TL;DR

The paper tackles the fragility of fixed-hierarchy aerial formations in complex environments by introducing a reconfigurable hierarchical formation (RHF) that leverages affine formation theory and hierarchical reorganization. A power-centric topology switching mechanism is proposed to maintain coordination during intra-formation topological changes, supported by dynamic affine localizability and stress-matrix analyses to ensure follower positions remain computable from leaders. Key contributions include formal definitions and necessary/sufficient conditions for hierarchical reorganization, a topology-switching algorithm to mitigate disturbance during transitions, and extensive simulations and indoor experiments that demonstrate rapid reorganizations (as fast as $0.047$ s) and flight speeds up to $1.9$ m/s in both 2D and 3D spaces. The approach enables robust, flexible, and scalable multi-robot coordination, with practical implications for navigation through cluttered environments and mission-critical tasks requiring dynamic leadership reconfiguration.

Abstract

Conventional formation methods typically rely on fixed hierarchical structures, such as predetermined leaders or predefined formation shapes. These rigid hierarchies can render formations cumbersome and inflexible in complex environments, leading to potential failure if any leader loses connectivity. To address these limitations, this paper introduces a reconfigurable affine formation that enhances both flexibility and resilience through hierarchical reorganization. The paper first elucidates the critical role of hierarchical reorganization, conceptualizing this process as involving role reallocation and dynamic changes in topological structures. To further investigate the conditions necessary for hierarchical reorganization, a reconfigurable hierarchical formation is developed based on graph theory, with its feasibility rigorously demonstrated. In conjunction with role transitions, a power-centric topology switching mechanism grounded in formation consensus convergence is proposed, ensuring coordinated resilience within the formation. Finally, simulations and experiments validate the performance of the proposed method. The aerial formations successfully performed multiple hierarchical reorganizations in both three-dimensional and two-dimensional spaces. Even in the event of a single leader's failure, the formation maintained stable flight through hierarchical reorganization. This rapid adaptability enables the robotic formations to execute complex tasks, including sharp turns and navigating through forests at speeds up to 1.9 m/s.

A Flexible and Resilient Formation Approach based on Hierarchical Reorganization

TL;DR

The paper tackles the fragility of fixed-hierarchy aerial formations in complex environments by introducing a reconfigurable hierarchical formation (RHF) that leverages affine formation theory and hierarchical reorganization. A power-centric topology switching mechanism is proposed to maintain coordination during intra-formation topological changes, supported by dynamic affine localizability and stress-matrix analyses to ensure follower positions remain computable from leaders. Key contributions include formal definitions and necessary/sufficient conditions for hierarchical reorganization, a topology-switching algorithm to mitigate disturbance during transitions, and extensive simulations and indoor experiments that demonstrate rapid reorganizations (as fast as s) and flight speeds up to m/s in both 2D and 3D spaces. The approach enables robust, flexible, and scalable multi-robot coordination, with practical implications for navigation through cluttered environments and mission-critical tasks requiring dynamic leadership reconfiguration.

Abstract

Conventional formation methods typically rely on fixed hierarchical structures, such as predetermined leaders or predefined formation shapes. These rigid hierarchies can render formations cumbersome and inflexible in complex environments, leading to potential failure if any leader loses connectivity. To address these limitations, this paper introduces a reconfigurable affine formation that enhances both flexibility and resilience through hierarchical reorganization. The paper first elucidates the critical role of hierarchical reorganization, conceptualizing this process as involving role reallocation and dynamic changes in topological structures. To further investigate the conditions necessary for hierarchical reorganization, a reconfigurable hierarchical formation is developed based on graph theory, with its feasibility rigorously demonstrated. In conjunction with role transitions, a power-centric topology switching mechanism grounded in formation consensus convergence is proposed, ensuring coordinated resilience within the formation. Finally, simulations and experiments validate the performance of the proposed method. The aerial formations successfully performed multiple hierarchical reorganizations in both three-dimensional and two-dimensional spaces. Even in the event of a single leader's failure, the formation maintained stable flight through hierarchical reorganization. This rapid adaptability enables the robotic formations to execute complex tasks, including sharp turns and navigating through forests at speeds up to 1.9 m/s.
Paper Structure (17 sections, 7 theorems, 24 equations, 7 figures, 3 tables)

This paper contains 17 sections, 7 theorems, 24 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Hierarchical Affine Formation
  4. Topology Switching for Hierarchical Formation
  5. Preliminaries and Problem Statement
  6. Basic Graph and Formation Theory
  7. Affine Image and Affine Localizability
  8. Stress Matrices and Affine Maneuver
  9. Problem Statement
  10. Feasible Conditions For Reconfigurable Hierarchical Formation
  11. Reconfigurable Hierarchical Formation
  12. Power-Centric Topology Switching
  13. Experimental Verification
  14. Simulation
  15. Experimental Setup
  16. ...and 2 more sections

Key Result

Lemma 3.1

The formation $(\mathcal{G}, \boldsymbol r)$ if affinely localizability if and only if $\boldsymbol r$affinely span$\mathbb{R}^d$.

Figures (7)

  • Figure 1: A.The system architecture of reconfigurable hierarchical formation. B.Comparison of with leader-follower affine formation(LFA)Zhao2018, virtual structure formation(VSF)Zhou2018, dynamic leader selection(DLS)Li2017, particle swarm optimization(PSO)Zhou2022 and our proposed method RHF. The radar chart shows that moving outward from the center represents increasing corresponding versatile. Specifically, stability represents the ability of the formation to maintain its standard shape during movement. Resilience represents the formation's ability to recover when individual agents lose connectivity. Flexibility represents the formation's adaptability to complex environments. Optimality, as defined in Zhou2022, represents the ability to seek optimal formation in spatial, temporal, or other user-defined scales. Moreover, extensibility represents the ability to analyze and model formations for specific tasks.
  • Figure 2: Illustration of Feasible Configurations for Reconfigurable Hierarchical Formation.
  • Figure 3: Examples for 2d and 3d dynamic graph configurations.
  • Figure 4: The system architecture of reconfigurable hierarchical formation.
  • Figure 5: Simulation Process in 3D space.(a) Simulation in Gazebo. (b) Visulization in RViz.
  • ...and 2 more figures

Theorems & Definitions (13)

  • Lemma 3.1
  • Lemma 3.2
  • Definition 1
  • Theorem 4.1
  • proof
  • Definition 2
  • Theorem 4.2
  • proof
  • Lemma 4.1
  • Theorem 4.3
  • ...and 3 more