Distributed Velocity Controllers of the Individuals of Emerging Swarm Clusters

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.