A generalized model of flocking with steering

TL;DR

This paper presents a comprehensive model for flocking and steering that generalizes existing models, incorporating real-world features and providing rigorous conditions for coordinated movement, supported by theoretical analysis and simulations.

Contribution

It introduces a unified, generalized model of flocking and steering with conditions for coordinated behavior, including a singular perturbation analysis and numerical validation.

Findings

Agents flock and steer together under specified conditions.

The model accommodates acceleration bounds, masking effects, and orientation bias.

Numerical simulations confirm theoretical predictions.

Abstract

We introduce and analyze a model for the dynamics of flocking and steering of a finite number of agents. In this model, each agent's acceleration consists of flocking and steering components. The flocking component is a generalization of many of the existing models and allows for the incorporation of many real world features such as acceleration bounds, partial masking effects and orientation bias. The steering component is also integral to capture real world phenomena. We provide rigorous sufficient conditions under which the agents flock and steer together. We also provide a formal singular perturbation study of the situation where flocking happens much faster than steering. We end our work by providing some numerical simulations to illustrate our theoretical results.