  This paper describes a framework for multi-robot coordination and motion
planning with emphasis on inter-agent interactions. We focus on the
characterization of inter-agent interactions with sufficient level of
abstraction so as to allow for the enforcement of desired interaction patterns
in a provably safe (i.e., collision-free) manner, e.g., for achieving rich
movement patterns in a shared space, or to exchange sensor information. We
propose to specify interaction patterns through elements of the so-called braid
group. This allows us to not focus on a particular pattern per se, but rather
on the problem of being able to execute a whole class of patterns. The result
from such a construction is a hybrid system driven by symbolic inputs that must
be mapped onto actual paths that both realize the desired interaction levels
and remain safe in the sense that collisions are avoided.
