We propose a new algorithm to simplify the controller development for distributed robotic systems subject to external observations, disturbances, and communication delays. Unlike prior approaches that propose specialized solutions to handling communication latency for specific robotic applications, our algorithm uses an arbitrary centralized controller as the specification and automatically generates distributed controllers with communication management and delay compensation. We formulate our goal as nonlinear optimal control -- using a regret minimizing objective that measures how much the distributed agents behave differently from the delay-free centralized response -- and solve for optimal actions w.r.t. local estimations of this objective using gradient-based optimization. We analyze our proposed algorithms behavior under a linear time-invariant special case and prove that the closed-loop dynamics satisfy a form of input-to-state stability w.r.t. unexpected disturbances and observations. Our experimental results on both simulated and real-world robotic tasks demonstrate the practical usefulness of our approach and show significant improvement over several baseline approaches.
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