I have finally checked off the career milestone of publishing in an IEEE Transactions journal. I was inspired to develop this solution after watching a flock of birds attack a squirrel on my neighbour’s roof. I noticed the birds produced a modified figure-eight pattern, which allowed them to dive down and attack the squirrel one-after-the-other in a coordinated manner.
Abstract
Inspired by the natural mobbing behavior of birds, this work presents a novel, quasi-distributed swarming strategy called the Dynamic Lemniscatic Arch. It resolves the problem of producing globally-stable, evenly-spaced lemniscate (or, figure-eight) trajectories while relying on local interactions only. Such trajectories are advantageous in applications where energy consumption and mechanical strain must be minimized. Previous work in lemniscate curves has typically relied on predetermined trajectories, rather than on the emergent structure of the swarm. Furthermore, we enrich the traditional 2-dimensional lemniscate plane curve structure by forming an arch in the third dimension. This arch provides more consistent coverage in surveillance type tasks and, with minor variations in parameters, can be used to produce mobbing behavior. The technique relies on time-varying quaternion rotations linked to the positions of dynamically induced virtual agents. We provide a mathematical proof of stability, which demonstrates the swarm converges to the desired geometry. Simulations show that the strategy performs well with multiple agents and in numerous different configurations.
The paper is published here.