  We address multi-robot safe mission planning in uncertain dynamic
environments. This problem arises in several applications including
safety-critical exploration, surveillance, and emergency rescue missions.
Computation of a multi-robot optimal control policy is challenging not only
because of the complexity of incorporating dynamic uncertainties while
planning, but also because of the exponential growth in problem size as a
function of number of robots. Leveraging recent works obtaining a tractable
safety maximizing plan for a single robot, we propose a scalable two-stage
framework to solve the problem at hand. Specifically, the problem is split into
a low-level single-agent control problem and a high-level task allocation
problem. The low-level problem uses an efficient approximation of stochastic
reachability for a Markov decision process to derive the optimal control policy
under dynamic uncertainty. The task allocation is solved using polynomial-time
forward and reverse greedy heuristics and in a distributed auction-based
manner. By leveraging the properties of our safety objective function, we
provide provable performance bounds on the safety of the approximate solutions
proposed by these two heuristics. We evaluate the theory with extensive
numerical case studies.
