  The goal of this report is to define abstractions for multi-agent systems
with feedback interconnection in their dynamics. In the proposed decentralized
framework, we specify a finite or countable transition system for each agent
which only takes into account the discrete positions of its neighbors. The
dynamics of the considered systems consist of two components. An appropriate
feedback law which guarantees that certain system and network requirements are
fulfilled and induces coupled constraints, and additional free inputs which we
exploit in order to accomplish high level tasks. In this work, we provide
sufficient conditions on the space and time discretization for the abstraction
of the system's behaviour which ensure that we can extract a well posed and
hence meaningful transition system. Furthermore, these conditions include
design parameters whose tuning provides the possibility for multiple
transitions, and hence, enable the construction of transition systems with
motion planning capabilities.
