Cucker-Smale Flocking With Inter-Particle Bonding Forces

The Cucker-Smale (CS) flocking model is an interacting particle system, in which each particle updates its velocity by adding to it a weighted average of the differences of its velocity with those of other particles. It has been shown that by using the C-S model, the velocities of particles converge to a common value despite the absence of a central command. In this note, we make an extension of the C-S model by introducing additional interaction terms between agents which we refer to as the inter-particle bonding force, in order to incorporate collision avoidance between agents, and at the same time achieve tighter spatial configurations. The proposed inter-particle bonding force makes use of position and velocity information of other agents in order to achieve such separation and cohesion. With the inter-particle bonding forces and the velocity-alignment term of the original C-S model, we show the emergent behavior of asymptotic flocking to spatial equilibrium configurations.