Collision Avoidance Mechanism for Symmetric Circular Formations of Unitary Mass Autonomous Vehicles at Constant Speed

Collective motion is a promising field that studies how local interactions lead groups of individuals to global behaviors. Biologists try to understand how those subjects interplay in nature, and engineers are concerned with the application of interaction strategies to mobile vehicles, satellites, robots, etc. There are several models in literature that employ strategies observed in groups of beings in nature. The aim is not to literally mimic them but to extract suitable strategies for the chosen application. These models, constituted of multiple mobile agents, can be used in tasks such as data collection, surveillance and monitoring. One approach is to use phase-coupled oscillators to design the mobile agents, in which each member is an oscillator and they are coupled according to an interconnection network. This design usually does not keep track and handle the possible collisions within the group, and real applications obviously must manage these situations to prevent the equipment from crashing. This paper introduces a collision avoidance mechanism to a model of particles with phase-coupled oscillators dynamics for symmetric circular formations.