Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Source-Seeking Problem with Robot Swarms

Antonio Acuaviva, Hector Garcia de Marina, Juan Jimenez

TL;DR

This work tackles source localization in a scalar field by leveraging a robot swarm with flexible, non-degenerate geometry and two dynamical models. It replaces gradient estimation with an ascending-direction control $\hat{L}_{\sigma}$ that is computable from field measurements and remains effective across diverse swarm configurations, including non-holonomic unicycle dynamics. The authors prove convergence to the source using Lyapunov/LaSalle analyses and extend the framework to guiding-field-based control for unicycles, supported by numerical simulations that validate robustness and performance. The approach enhances resilience to obstacles and dynamic swarm changes, offering practical impact for real-world sensing, search, and environmental monitoring tasks.

Abstract

We present an algorithm to solve the problem of locating the source, or maxima, of a scalar field using a robot swarm. We demonstrate how the robot swarm determines its direction of movement to approach the source using only field intensity measurements taken by each robot. In contrast with the current literature, our algorithm accommodates a generic (non-degenerate) geometry for the swarm's formation. Additionally, we rigorously show the effectiveness of the algorithm even when the dynamics of the robots are complex, such as a unicycle with constant speed. Not requiring a strict geometry for the swarm significantly enhances its resilience. For example, this allows the swarm to change its size and formation in the presence of obstacles or other real-world factors, including the loss or addition of individuals to the swarm on the fly. For clarity, the article begins by presenting the algorithm for robots with free dynamics. In the second part, we demonstrate the algorithm's effectiveness even considering non-holonomic dynamics for the robots, using the vector field guidance paradigm. Finally, we verify and validate our algorithm with various numerical simulations.

Source-Seeking Problem with Robot Swarms

TL;DR

This work tackles source localization in a scalar field by leveraging a robot swarm with flexible, non-degenerate geometry and two dynamical models. It replaces gradient estimation with an ascending-direction control that is computable from field measurements and remains effective across diverse swarm configurations, including non-holonomic unicycle dynamics. The authors prove convergence to the source using Lyapunov/LaSalle analyses and extend the framework to guiding-field-based control for unicycles, supported by numerical simulations that validate robustness and performance. The approach enhances resilience to obstacles and dynamic swarm changes, offering practical impact for real-world sensing, search, and environmental monitoring tasks.

Abstract

We present an algorithm to solve the problem of locating the source, or maxima, of a scalar field using a robot swarm. We demonstrate how the robot swarm determines its direction of movement to approach the source using only field intensity measurements taken by each robot. In contrast with the current literature, our algorithm accommodates a generic (non-degenerate) geometry for the swarm's formation. Additionally, we rigorously show the effectiveness of the algorithm even when the dynamics of the robots are complex, such as a unicycle with constant speed. Not requiring a strict geometry for the swarm significantly enhances its resilience. For example, this allows the swarm to change its size and formation in the presence of obstacles or other real-world factors, including the loss or addition of individuals to the swarm on the fly. For clarity, the article begins by presenting the algorithm for robots with free dynamics. In the second part, we demonstrate the algorithm's effectiveness even considering non-holonomic dynamics for the robots, using the vector field guidance paradigm. Finally, we verify and validate our algorithm with various numerical simulations.
Paper Structure (12 sections, 11 theorems, 61 equations, 6 figures)

This paper contains 12 sections, 11 theorems, 61 equations, 6 figures.

Table of Contents

  1. Introduction
  2. The location problem
  3. Preliminaries and Problem Formulation
  4. The ascending direction
  5. Convergence results
  6. Free Dynamics case
  7. Non-Holonomic Swarm
  8. Numerical simulations
  9. Numerical simulation of free-dynamics systems
  10. Numerical simulation of constant-speed unicycle dynamics
  11. Conclusions
  12. Appendix

Key Result

Proposition II.4

Let $\sigma$ be a signal distribution and $\vec{R} = (\vec{r}_1^T, \dots, \vec{r}_N^T)^T$ be a swarm of robots. Then we have where is an ascending direction at the centroid provided $\nabla \sigma (\vec{r}_c) \neq 0$ and the geometry $\vec{X}$ is non-degenerate.

Figures (6)

  • Figure 1: Deployment of a swarm of $N=4$ robots in the plane.
  • Figure 2: Orientation of a robot and directed angles.
  • Figure 3: Convergence under a Gaussian signal for swarms with free dynamics randomly distributed in the plane. The top figure details the trajectories of centroids of various swarms with arbitrary non-degenerate geometries. The bottom figure shows the evolution of the distances between the maximum of the field and the centroids of the swarms. Time and distance units are arbitrary.
  • Figure 4: Convergence of robot swarms with nearly degenerate geometries. The top figure shows a trajectory with nearly degenerate geometry in the horizontal axis. The bottom figure illustrates a trajectory with nearly degenerate geometry in the vertical axis.
  • Figure 5: Convergence of robot swarms with constant-speed unicycle dynamics for a Gaussian signal, using the guiding field algorithm (\ref{['eq:campoaprox']}).
  • ...and 1 more figures

Theorems & Definitions (24)

  • Definition II.1
  • Definition II.2
  • Proposition II.4
  • proof
  • Remark II.5
  • Lemma II.6
  • proof
  • Theorem III.1
  • proof
  • Corollary III.2
  • ...and 14 more