A Discrete-Time Model for Swarm Formation With Coordinates Coupling Matrix

In this letter a discrete-time kinematic model for a swarm of agents moving in a multi-dimensional space is proposed. The model contains two terms accounting for the attraction to a common goal position and the interactions among agents. The latter can be tuned by using a coordinates coupling matrix that weighs the inter-agents displacements and permits to define the region of attraction. The main model properties are studied proving that agents aggregate in finite-time in some regions, ensuring the swarm centroid convergence to a target position. The analysis is performed by assuming that each agent has a limited detection range. The agents connections evolution is also discussed together with conditions to reach, in finite-time, a swarm configuration where each agent can always detect all the other ones. Finally, numerical simulations and a laboratory experiment are developed to illustrate the obtained results.