In this paper, we propose a fully distributed, scalable method of controlling agents with nonholonomic constraints using a Morse potential function. This method successfully controls a swarm of differential-drive (unicycle-type) agents to stable and predictable formations whose structures are not defined a priori. The system achieves a stable, minimal energy state.
We consider the effect of numerosity constraints, as observed in birds and fish in their shoaling and flocking behavior as a mechanism of reducing complexity, in the interest of achieving fully distributed control over a swarm of any size. The application of numerosity constraints to a swarm system allows the swarm to grow without bound and with no increase in required processing capability of the individual agents. We explore this parameter as a method of minimizing processing and storage requirements while still achieving the qualitative swarm performance. Results from simulations are given for swarms ranging in size over N = {6,…,100} acting under our proposed controller as applied to differential-drive (unicycle-type) robots.
