  In this paper, we consider the multi-robot path execution problem where a
group of robots move on predefined paths from their initial to target positions
while avoiding collisions and deadlocks in the face of asynchrony. We first
show that this problem can be reformulated as a distributed resource allocation
problem and, in particular, as an instance of the well-known Drinking
Philosophers Problem (DrPP). By careful construction of the drinking sessions
capturing shared resources, we show that any existing solutions to DrPP can be
used to design robot control policies that are collectively collision and
deadlock-free. We then propose modifications to an existing DrPP algorithm to
allow more concurrent behavior, and provide conditions under which our method
is deadlock-free. Our method does not require robots to know or to estimate the
speed profiles of other robots and results in distributed control policies. We
demonstrate the efficacy of our method on simulation examples, which show
competitive performance against the state-of-the-art.
