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A Unified Stochastic Mechanism Underlying Collective Behavior in Ants, Physical Systems, and Robotic Swarms

Lianhao Yin, Haiping Yu, Pascal Spino, Daniela Rus

TL;DR

The study introduces a unified stochastic framework in which agent-level randomness arises from entropy maximization under energy constraints, applicable to ant swarms, physical particles, and robotic swarms. Empirical ants exhibit a two-energy-component, exponential distribution for speed and a velocity-dependent steering-angle temperature, while robots emulate the same distributions via energy-based policies that enable decenteralized, scalable coordination. The results demonstrate phase-like swarming behaviors (gas-like and liquid-like) and object-transport capabilities without inter-robot communication, with performance improving as system size grows. This cross-domain framework provides a scalable design principle for robust swarm robotics and links statistical physics with collective biological and engineered systems. It suggests practical pathways for decentralized control in large-scale autonomous systems and microrobotics, grounded in a common entropy-based mechanism.

Abstract

Biological swarms, such as ant colonies, achieve collective goals through decentralized and stochastic individual behaviors. Similarly, physical systems composed of gases, liquids, and solids exhibit random particle motion governed by entropy maximization, yet do not achieve collective objectives. Despite this analogy, no unified framework exists to explain the stochastic behavior in both biological and physical systems. Here, we present empirical evidence from \textit{Formica polyctena} ants that reveals a shared statistical mechanism underlying both systems: maximization under different energy function constraints. We further demonstrate that robotic swarms governed by this principle can exhibit scalable, decentralized cooperation, mimicking physical phase-like behaviors with minimal individual computation. These findings established a unified stochastic model linking biological, physical, and robotic swarms, offering a scalable principle for designing robust and intelligent swarm robotics.

A Unified Stochastic Mechanism Underlying Collective Behavior in Ants, Physical Systems, and Robotic Swarms

TL;DR

The study introduces a unified stochastic framework in which agent-level randomness arises from entropy maximization under energy constraints, applicable to ant swarms, physical particles, and robotic swarms. Empirical ants exhibit a two-energy-component, exponential distribution for speed and a velocity-dependent steering-angle temperature, while robots emulate the same distributions via energy-based policies that enable decenteralized, scalable coordination. The results demonstrate phase-like swarming behaviors (gas-like and liquid-like) and object-transport capabilities without inter-robot communication, with performance improving as system size grows. This cross-domain framework provides a scalable design principle for robust swarm robotics and links statistical physics with collective biological and engineered systems. It suggests practical pathways for decentralized control in large-scale autonomous systems and microrobotics, grounded in a common entropy-based mechanism.

Abstract

Biological swarms, such as ant colonies, achieve collective goals through decentralized and stochastic individual behaviors. Similarly, physical systems composed of gases, liquids, and solids exhibit random particle motion governed by entropy maximization, yet do not achieve collective objectives. Despite this analogy, no unified framework exists to explain the stochastic behavior in both biological and physical systems. Here, we present empirical evidence from \textit{Formica polyctena} ants that reveals a shared statistical mechanism underlying both systems: maximization under different energy function constraints. We further demonstrate that robotic swarms governed by this principle can exhibit scalable, decentralized cooperation, mimicking physical phase-like behaviors with minimal individual computation. These findings established a unified stochastic model linking biological, physical, and robotic swarms, offering a scalable principle for designing robust and intelligent swarm robotics.

Paper Structure

This paper contains 28 sections, 8 equations, 17 figures, 3 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Ant swarm experiments
  3. The stochastic behaviour in ant swarm
  4. Robotic experiments: apply stochastic mechanism to robotic swarm decisions
  5. Disucssion
  6. Conclusion
  7. Methods
  8. Biological experimental settings
  9. Biological experimental setup
  10. Annotation
  11. Video analysis and tracking
  12. Detection method
  13. Tracking method
  14. Swarm tracking analysis
  15. Formulation of energy for the ant
  16. ...and 13 more sections

Figures (17)

  • Figure 1: (a) We track the ants on the up and low side of the wood road, which is marked by red squares. (b) We put the wood road on the ant path between the ant nest and the forage areas. (c) The probability density of the angle rate of the ant. The red is fitted with an exponential distribution. (d) Illustrate how the speed and angle are defined. (e) The probability density function of energy of an ant, which is defined as ($E=\frac{1}{2}mv^2$), where $m$,$v$ are the mass and speed of the ant, respectively. (f) The setting of robotic experiments for narrow road crossing. (g) Illustration of the robot hardware. (h) The setting of robotic experiments for moving object.
  • Figure 2: The speed distribution ($p(v^2_i) = \phi \frac{1}{kT_1}e^{-\frac{1}{kT_1}v^{2}_{i}} + (1-\phi) \frac{1}{kT_2} e^{-\frac{1}{kT_2}v^{2}_{i}}$ in red). (a-h) Energy level at 25, 26, 27, 28, 31, 34, 36, 39 respectively, (g) Probability density curve at different energy level. Unit:$1/10^10$ J, (j) KS of 1 phase versus 2 phases fitting, (i) Ratio of ant at upper and lower side in phase 2
  • Figure 3: Steering angle rate distribution at different energy level. (a) 4.5 (ks-statistic: 0.060, p-value: 0.3) (b) 10, (ks-statistic: 0.060, p-value: 0.3) (c) 18, (ks-statistic: 0.076, p-value: 0.4) (d) 28, (ks-statistic: 0.076, p-value: 1) (e) 40, (ks-statistic: 0.076, p-value: 1) (f) 54, (ks-statistic: 0.073, p-value: 1) (g) 71, (ks-statistic: 0.10, p-value: 1) (h) 90, (ks-statistic: 0.088, p-value: 1), (i) Temperature of the steering angle rate distribution $p(\theta) = \frac{1}{kT_\theta(v)}e^{-\frac{1}{kT_\theta(v)}\theta}$ at different energy level, where $T$ is a function energy. Intuitively, the steering angle rate range are wider at low energy and low speed.
  • Figure 4: Long time robotic crossing experiments
  • Figure 5: Robots move the green object toward the light sources. Robots in illuminated regions (red LEDs visible) behave in a gas-like phase; those in darkness remain in a liquid-like phase.
  • ...and 12 more figures