On the Emergent Hypocycloidal and Epicycloidal Formations in a Swarm of Double Integrator Agents

In this letter, a multi-agent system with emergent hypocycloidal and epicycloidal behaviors is analyzed. Agents are assumed to be modeled as double integrators with an acceleration law designed so that the swarm exhibits cycloidal like trajectories. The resulting control protocol benefits from speeds and positions coupling among neighbors agents to let each agent perform hypocycloidal or epicycloidal curves according to the choice of the controller parameters and the agents initial conditions. As a first step, the model properties are obtained assuming that the communication topology of the multi-agent system is defined by a complete graph. As a further step, the model main features are extended by relaxing the complete connection assumption and replacing it with a more realistic one in which a connected graph is considered. This latter step is achieved by means of a consensus-based estimation of the swarm centroid, so that to virtualize the complete graph starting from a connected one. Simulations have been performed to show the properties of the obtained agents evolution.