  Verifying the correct behavior of robots in contact tasks is challenging due
to model uncertainties associated with contacts. Standard methods for testing
often fall short since all (uncountable many) solutions cannot be obtained.
Instead, we propose to formally and efficiently verify robot behaviors in
contact tasks using reachability analysis, which enables checking all the
reachable states against user-provided specifications. To this end, we extend
the state of the art in reachability analysis for hybrid (mixed discrete and
continuous) dynamics subject to discrete-time input trajectories. In
particular, we present a novel and scalable guard intersection approach to
reliably compute the complex behavior caused by contacts. We model robots
subject to contacts as hybrid automata in which crucial time delays are
included. The usefulness of our approach is demonstrated by verifying safe
human-robot interaction in the presence of constrained collisions, which was
out of reach for existing methods.
