  In this report, we aim at the development of an online abstraction framework
for multi-agent systems under coupled constraints. The motion capabilities of
each agent are abstracted through a finite state transition system in order to
capture reachability properties of the coupled multi-agent system over a finite
time horizon in a decentralized manner. In the first part of this work, we
define online abstractions by discretizing an overapproximation of the agents'
reachable sets over the horizon. Then, sufficient conditions relating the
discretization and the agent's dynamics properties are provided, in order to
quantify the transition possibilities of each agent.
