# Research on Division of Labor Decision and System Stability of Swarm Robots Based on Mutual Information

## TL;DR

This paper studies how swarm robots make decisions and maintain stability using information interaction models.

## Contribution

A novel game-theoretic model based on mutual information is introduced to analyze division of labor and system stability in swarm robots.

## Key findings

- As ν1 varies, the system transitions from stable Nash equilibrium to chaos.
- Higher mutual information leads to a shift from Cournot to Stackelberg decision-making.
- Increased mutual information reduces system sensitivity to parameter changes.

## Abstract

In rational decision-making processes, the information interaction among individual robots is a critical factor influencing system stability. We establish a game-theoretic model based on mutual information to address division of labor decision-making and stability issues arising from differential information interaction among swarm robots. Firstly, a mutual information model is employed to measure the information interaction among robots and analyze its influence on the behavior of individual robots. Secondly, employing the Cournot model and the Stackelberg model, we model the diverse decision-making behaviors of swarm robots influenced by discrepancies in mutual information. The intricate decision dynamics exhibited by the system under the disparity mutual information values during the game process, along with the stability of Nash equilibrium points, are analyzed. Finally, dynamic complexity simulations of the game models are simulated under the disparity mutual information values: (1) When ν1 of the game model varies within a certain range, the Nash equilibrium point loses stability and enters a chaotic state. (2) As I(X;Y) increases, the decision-making pattern of robots transitions gradually from the Cournot game to the Stackelberg game. Concurrently, the sensitivity of swarm robotics systems to changes in decision parameter decreases, reducing the likelihood of the system entering a chaotic state.