Mechanistic modeling of swarms

In this work, we provide an introduction to an emerging field which has recently received considerable attention, namely the analysis and modeling of swarms. In a very general sense, the term swarm is usually meant to signify a group of objects (agents) that interact with one another and have a collective goal. Point-mass, particulate-like models are frequently used to simulate the behavior of groups comprised of individual units whose interaction are represented by inter-particle forces. The interaction “forces” can represent, for example in the case of Unmanned Airborne Vehicles (UAVs), motorized propulsion arising from inter-vehicle communication and then actuation resulting in thrust. For a swarm member, these forces have two main components, attraction and repulsion, with the fellow swarm members and the surrounding environment. This work develops and investigates (1) basic models of such systems, (2) properties of swarm models and (3) numerical algorithms, in particular temporally adaptive methods, for swarm-like systems.