We study the large time behavior of a system of interacting agents modeling the relaxation of a large swarm of robots, whose task is to uniformly cover a portion of the domain by communicating with each other in terms of their distance. To this end, we generalize a related result for a Fokker- Planck-type model with a nonlocal discontinuous drift and constant diffusion, recently introduced by three of the authors, of which the steady distribution is explicitly computable. For this new nonlocal Fokker-Planck equation, exis- tence, uniqueness and positivity of a global solution are proven, together with precise equilibration rates of the solution towards its quasi-stationary distri- bution. Numerical experiments are designed to verify the theoretical findings and explore possible extensions to more complex scenarios.
IMPACT OF INTERACTION FORCES IN FIRST ORDER MANY-AGENT SYSTEMS FOR SWARM MANUFACTURING
Ferdinando Auricchio;Massimo Carraturo;Giuseppe Toscani;Mattia Zanella
2024-01-01
Abstract
We study the large time behavior of a system of interacting agents modeling the relaxation of a large swarm of robots, whose task is to uniformly cover a portion of the domain by communicating with each other in terms of their distance. To this end, we generalize a related result for a Fokker- Planck-type model with a nonlocal discontinuous drift and constant diffusion, recently introduced by three of the authors, of which the steady distribution is explicitly computable. For this new nonlocal Fokker-Planck equation, exis- tence, uniqueness and positivity of a global solution are proven, together with precise equilibration rates of the solution towards its quasi-stationary distri- bution. Numerical experiments are designed to verify the theoretical findings and explore possible extensions to more complex scenarios.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
