  Multi-agent partially observable Markov decision processes (MPOMDPs) provide
a framework to represent heterogeneous autonomous agents subject to uncertainty
and partial observation. In this paper, given a nominal policy provided by a
human operator or a conventional planning method, we propose a technique based
on barrier functions to design a minimally interfering safety-shield ensuring
satisfaction of high-level specifications in terms of linear distribution
temporal logic (LDTL). To this end, we use sufficient and necessary conditions
for the invariance of a given set based on discrete-time barrier functions
(DTBFs) and formulate sufficient conditions for finite time DTBF to study
finite time convergence to a set. We then show that different LDTL
mission/safety specifications can be cast as a set of invariance or finite time
reachability problems. We demonstrate that the proposed method for
safety-shield synthesis can be implemented online by a sequence of one-step
greedy algorithms. We demonstrate the efficacy of the proposed method using
experiments involving a team of robots.
