On the completeness of ensembles of motion planners for decentralized planning

We provide a set of sufficient conditions to establish the completeness of an ensemble of motion planners-that is, a set of loosely-coupled motion planners that produce a unified result. The planners are assumed to divide the total planning problem across some parameter space(s), such as task space, state space, action space, or time. Robotic applications have employed ensembles of planners for decades, although the concept has not been formally unified or analyzed until now. We focus on applications in multi-robot navigation and collision avoidance. We show that individual resolutionor probabilistically-complete planners that meet certain communication criteria constitute a (respectively, resolution- or probabilistically-) complete ensemble of planners. This ensemble of planners, in turn, guarantees that the robots are free of deadlock, livelock, and starvation.