Modeling and stability analysis of social foraging swarms in multi-obstacle environment

In this article we specify an individual-based foraging swarm (i.e., group of agents) model with individuals that move in an n-dimensional multi-obstacle environment. The motion of each individual (i) is determined by three factors: i) attraction to the local object position (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar x_{io + } $$ \end{document}) which is decided by the local information about the individuals’ position that individual i can find; ii) repulsion from the other individuals on short distances; and iii) attraction to the global object position (xgoal) or repulsion from the obstacles in the environment. The emergent behavior of the swarm motion is the result of a balance between inter-individual interaction and the simultaneous interactions of the swarm members with their environment. We study the stability properties of the collective behavior of the swarm based on Lyapunov stability theory. The simulations show that the swarm can converge to goal regions and diverge from obstacle regions of the environment while maintaining cohesive.