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This paper studies the adaptive trajectory design of a rotary-wing UAVserving as a relay between ground nodes dispersed in a circular cell andgenerating uplink data transmissions randomly according to a Poisson process,and a central base station. We seek to minimize the expected averagecommunication delay to service the data transmission requests, subject to anaverage power constraint on the mobility of the UAV. The problem is cast as asemi-Markov decision process, and it is shown that the policy exhibits atwo-scale structure, which can be efficiently optimized: in the outer decision,upon starting a communication phase, and given its current radius, the UAVselects a target end radius position so as to optimally balance a trade-offbetween average long-term communication delay and power consumption; in theinner decision, the UAV selects its trajectory between the start radius and theselected end radius, so as to greedily minimize the delay and energyconsumption to serve the current request. Numerical evaluations show that,during waiting phases, the UAV circles at some optimal radius at the mostenergy efficient speed, until a new request is received. Lastly, the expectedaverage communication delay and power consumption of the optimal policy iscompared to that of several heuristics, demonstrating a reduction in latency byover 50% and 20%, respectively, compared to static and mobile heuristicschemes.

Power-Constrained Trajectory Optimization for Wireless UAV Relays with Random Requests