Deterministic Chaos Constraints for Control of Massive Swarms

Abstract

Problems such as the control of massive swarms or MANET radios in a Battlespace on the order of tens of thousands of entities is challenging with conventional approaches. Entities that enter or leave this space need to have either some means of coordination or known constraints. Moreover, each entity should have some limited awareness of the relative positioning of all the others, without the massive computational expense incurred by a combinatorial explosion. This may rule out the quantum state space type of approach where each entity is a computationally-unique unit vector. To control such behaviors, and allow self-organizing MANET relay nodes as well as collective swarm control, the author uses a topological structure based upon deterministic chaos—the fractal. Constraining the entities to “believe” that they exist only within the boundaries of an adaptive fractal forces their topological layout to map to topological clusters. The invariant features of a fractal topology allow each node to compute the IFS (Iterative Function System) to effectively “know” the relative positions of all the other entities, and form adaptive, self-healing MANET or swarm clusters. One of many possible equations for the adaptive fractal is given, which computationally is of O(n). Since it uses one floating point number, the computations for each entity/node to determine the relative positions of all Battlespace entities is trivial, therefore each entity can achieve situational awareness in near-realtime. A simulation of the dynamics for different adaptive fractal topologies written in Mathematica, can be demonstrated during the paper presentation.