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Multi-Source Encapsulation With Guaranteed Convergence Using Minimalist Robots

Himani Sinhmar, Hadas Kress-Gazit

TL;DR

This work addresses multisource encapsulation by a swarm of minimalist robots that lack memory, self-localization, and explicit communication. It introduces a derivative-free control policy based on simplex gradients to fuse dispersed sensor readings and locate multiple targets in an obstacle-cluttered environment, while enforcing safety distances and avoiding livelocks. The authors provide convergence guarantees by deriving bounds on sensor placement, target separation, and step sizes, ensuring all targets are encapsulated with a specified number of robots in each encapsulation ring. Simulations demonstrate robustness to occlusions, sensor noise, and asynchronous execution, and show that increasing sensor count accelerates task completion. The approach advances scalable, decentralized coordination for diffusive target encapsulation in challenging settings and suggests future extensions to non-isotropic sensing and relaxed emission assumptions.

Abstract

We present a decentralized control algorithm for a minimalist robotic swarm lacking memory, explicit communication, or relative position information, to encapsulate multiple diffusive target sources in a bounded environment. The state-of-the-art approaches generally require either local communication or relative localization to provide guarantees of convergence and safety. We quantify trade-offs between task, control, and robot parameters for guaranteed safe convergence to all the sources. Furthermore, our algorithm is robust to occlusions and noise in the sensor measurements as we demonstrate in simulation.

Multi-Source Encapsulation With Guaranteed Convergence Using Minimalist Robots

TL;DR

This work addresses multisource encapsulation by a swarm of minimalist robots that lack memory, self-localization, and explicit communication. It introduces a derivative-free control policy based on simplex gradients to fuse dispersed sensor readings and locate multiple targets in an obstacle-cluttered environment, while enforcing safety distances and avoiding livelocks. The authors provide convergence guarantees by deriving bounds on sensor placement, target separation, and step sizes, ensuring all targets are encapsulated with a specified number of robots in each encapsulation ring. Simulations demonstrate robustness to occlusions, sensor noise, and asynchronous execution, and show that increasing sensor count accelerates task completion. The approach advances scalable, decentralized coordination for diffusive target encapsulation in challenging settings and suggests future extensions to non-isotropic sensing and relaxed emission assumptions.

Abstract

We present a decentralized control algorithm for a minimalist robotic swarm lacking memory, explicit communication, or relative position information, to encapsulate multiple diffusive target sources in a bounded environment. The state-of-the-art approaches generally require either local communication or relative localization to provide guarantees of convergence and safety. We quantify trade-offs between task, control, and robot parameters for guaranteed safe convergence to all the sources. Furthermore, our algorithm is robust to occlusions and noise in the sensor measurements as we demonstrate in simulation.
Paper Structure (16 sections, 2 theorems, 12 equations, 7 figures)

This paper contains 16 sections, 2 theorems, 12 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Environment and Robot Model
  3. Problem Formulation
  4. Mathematical Preliminaries
  5. Approach
  6. Maintaining safety distances
  7. Target attraction
  8. Local Control Law
  9. Behavior Close to an Obstacle in the Secondary Zone
  10. Behavior in the Encapsulation Ring
  11. Convergence Guarantees
  12. Target Attraction
  13. Guaranteed Encirclement Behavior
  14. Absence of Livelocks: Minimum Separation Between Obstacles
  15. Simulations
  16. ...and 1 more sections

Key Result

lemma thmcounterlemma

Simplex Gradient:regis2015calculus Let $F:\mathbb{R}^n \rightarrow \mathbb{R}$ and $\mathcal{X} = \{\textbf{x}_0,\textbf{x}_1 \cdots \textbf{x}_k\}$ be an ordered set of $k+1$ affine independent points in $\mathbb{R}^n$ such that $k \geq n$. Define, $H(\mathcal{X}) = [\textbf{x}_1-\textbf{x}_0 \cdot

Figures (7)

  • Figure 1: Computing $d_r$ that ensures a safe distance from nearby obstacles
  • Figure 2: Environment zones.
  • Figure 3: (a) A robot circumnavigates an obstacle in the tangential direction closest to the LOS vector, shown with a thicker teal arrow. (b) When targets are closer to each other than their minimum separation threshold $D_g$ (Section \ref{['section_minSep']}), robots encapsulating them create an open obstacle. Robots at locations A and B both assess the obstacle as being behind them relative to the target's LOS vector $\zeta$, prompting them to advance toward the target. While this action is appropriate for the robot at B, it results in a livelock for the robot at A.
  • Figure 4: Gradient estimation deteriorates in critical region of $F_g$
  • Figure 5: The total time taken for task completion as a function of $p$.
  • ...and 2 more figures

Theorems & Definitions (2)

  • lemma thmcounterlemma
  • lemma thmcounterlemma