Path Planning for Aerial Relays via Probabilistic Roadmaps

Autonomous unmanned aerial vehicles (UAVs) can be utilized as aerial relays to serve users far from terrestrial infrastructure. Unfortunately, existing algorithms for aerial relay path planning cannot accommodate general flight constraints or channel models. This is required in practice due to connectivity constraints, the presence of obstacles (e.g. buildings), and regulations. This paper proposes a framework that overcomes these limitations by spatially discretizing the flight region. To cope with the resulting exponential growth in complexity, the framework adopts a probabilistic roadmap approach, where a shortest path is found through a graph of randomly generated states. To attain high optimality with affordable complexity, the probability distribution used to generate these states is designed based on heuristic path planners with theoretical guarantees. The algorithms derived in this framework not only overcome the main limitations of existing schemes but also entail smaller computational complexity. Extensive theoretical and numerical results corroborate the merits of the proposed approach.