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Self-Healing Distributed Swarm Formation Control Using Image Moments

C. Lin Liu, Israel L. Donato Ridgley, Matthew L. Elwin, Michael Rubenstein, Randy A. Freeman, Kevin M. Lynch

TL;DR

This work introduces a scalable, self-healing approach to swarm formation control by encoding planar robot distributions with image moments. Robots locally estimate the current swarm moments using a distributed push-sum mechanism and steer toward the desired moments via a gradient-based controller, yielding distributed, centralized-free formation control. The key contributions are simultaneous distributed estimation and control with Legendre Moments and pseudo-Zernike Moments, memory-enabled robustness to packet loss, and validation on a 50-robot experimental swarm under substantial communication dropout. The results demonstrate accurate formation achievement and self-healing behavior (e.g., regrowth after robot removal) in both simulations and hardware experiments, underscoring the practical potential for large-scale, low-bandwidth human-swarm interfaces.

Abstract

Human-swarm interaction is facilitated by a low-dimensional encoding of the swarm formation, independent of the (possibly large) number of robots. We propose using image moments to encode two-dimensional formations of robots. Each robot knows its pose and the desired formation moments, and simultaneously estimates the current moments of the entire swarm while controlling its motion to better achieve the desired group moments. The estimator is a distributed optimization, requiring no centralized processing, and self-healing, meaning that the process is robust to initialization errors, packet drops, and robots being added to or removed from the swarm. Our experimental results with a swarm of 50 robots, suffering nearly 50% packet loss, show that distributed estimation and control of image moments effectively achieves desired swarm formations.

Self-Healing Distributed Swarm Formation Control Using Image Moments

TL;DR

This work introduces a scalable, self-healing approach to swarm formation control by encoding planar robot distributions with image moments. Robots locally estimate the current swarm moments using a distributed push-sum mechanism and steer toward the desired moments via a gradient-based controller, yielding distributed, centralized-free formation control. The key contributions are simultaneous distributed estimation and control with Legendre Moments and pseudo-Zernike Moments, memory-enabled robustness to packet loss, and validation on a 50-robot experimental swarm under substantial communication dropout. The results demonstrate accurate formation achievement and self-healing behavior (e.g., regrowth after robot removal) in both simulations and hardware experiments, underscoring the practical potential for large-scale, low-bandwidth human-swarm interfaces.

Abstract

Human-swarm interaction is facilitated by a low-dimensional encoding of the swarm formation, independent of the (possibly large) number of robots. We propose using image moments to encode two-dimensional formations of robots. Each robot knows its pose and the desired formation moments, and simultaneously estimates the current moments of the entire swarm while controlling its motion to better achieve the desired group moments. The estimator is a distributed optimization, requiring no centralized processing, and self-healing, meaning that the process is robust to initialization errors, packet drops, and robots being added to or removed from the swarm. Our experimental results with a swarm of 50 robots, suffering nearly 50% packet loss, show that distributed estimation and control of image moments effectively achieves desired swarm formations.
Paper Structure (18 sections, 2 theorems, 31 equations, 13 figures)

This paper contains 18 sections, 2 theorems, 31 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Human-Swarm Interaction
  4. Image Moments
  5. Low-Dimensional Representations of Formations and Distributed Formation Control
  6. Contributions
  7. Distributions Using Image Moments
  8. Legendre Moments (LMs)
  9. Pseudo-Zernike Moments (PZMs)
  10. Estimation and Control
  11. Distributed Moment Estimation
  12. Control of Swarm Moments
  13. Simultaneous Estimation and Control
  14. Experimental Implementation
  15. Coachbot V2.0 System
  16. ...and 3 more sections

Key Result

Theorem 1

For a strongly-connected constant digraph network, the estimator of eq:wholesysv-eq:wholesysw, and a constant input $u[t] = u$, each $v_i$ converges exponentially to where $z_i$ is the $i$th component of the vector $z \in \mathbb{R}^N$ that satisfies $\mathfrak{L}^\top z=0$ and $\mymathbb{1}^\top z=1$. Therefore $\hat{M}_i$ (Equation eq:moments) converges to the correct moments $M(s)$.

Figures (13)

  • Figure 1: The left image specifies a desired two-dimensional swarm distribution. White indicates zero robot density and purple indicates a constant positive density. Top row: Standard computer vision image reconstruction using representations of the desired distribution based on Legendre moments of up to fifth, tenth, 15th, and 20th order, respectively. Bottom row: The final configurations of 1000 simulated robots after moving so their collective Legendre moments, up to fifth, tenth, 15th, and 20th order, respectively, approximately match the desired Legendre moments.
  • Figure 2: Block diagram for robot $i$.
  • Figure 3: Time to convergence for eighth-order LM estimation.
  • Figure 4: Time to convergence for eighth-order PZM estimation.
  • Figure 5: The 2-norm of the moment vector error for varying maximum orders of LMs and PZMs using the controller with perfect moment estimates.
  • ...and 8 more figures

Theorems & Definitions (4)

  • Remark 1
  • Theorem 1
  • Remark 2
  • Theorem 2