Distributed Velocity Controllers of the Individuals of Emerging Swarm Clusters

Abstract

This paper presents the distributed velocity-based control laws of n ∈ N individuals considered rigid bodies, which gives rise to swarm clusters in a partially known environment. The motion of the individuals is based on Reynold's rules of separation, alignment, and cohesion. If two individuals are in the detection range of each other, there is an attraction between the two for alignment. There is a short-range repulsion to avoid the inter-individual collision. A total potential function is developed using attractive and repulsive potential functions, representing general anisotropic swarms. The decentralized velocity-based controllers of the individuals, which gives rise to a gradient system, are derived from the total potential function. The effectiveness of the decentralized velocity-based controllers is validated through computer simulations carried out using the Mathematica software.

Herding Predators Using Swarm Intelligence

“…The spatial approach includes space (environment) in the model and analysis, either explicitly or implicitly. This approach can be divided into two distinct frameworks; Lagrangian framework (individual-based) and Eulerian framework (continuum) [1], [6], [7], [9], [11], [24], [27]. In the Lagrangian framework, the state of an individual and its relationship with other individuals in the swarm are investigated [1], [6].…”

“…In the Eulerian framework, the swarm is regarded as a continuum, defined by its density in one, two, or three dimensions. Partial differential equations describe the evolution of swarm density over time [1], [6], [7], [9], [11], [24], [27]. The advectiondiffusion-reaction equation is the fundamental equation of Eulerian models, in which advection and diffusion are the combined outcomes of individual behavior and environmental factors, while the response term is related to population dynamics [24].…”

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