Novel Optimal Trajectory Design in UAV-Assisted Networks: A Mechanical Equivalence-Based Strategy

Unmanned aerial vehicles (UAVs), also known as drones, have already been widely implemented in wireless networks for promoting network performance and enabling new services. To efficiently explore the diversity introduced by the mobility of UAV, many efforts have been made in the design of the UAV trajectory under various wireless scenarios. However, the continuity of a UAV trajectory in both time and topology forces researchers to approximate the UAV trajectory by a discrete model, which always results in a sub-optimal solution. To tackle the difficulty and obtain the optimal trajectory, in this work we introduce an artificial potential field (APF) to reformulate the objective in trajectory design, with which the UAV trajectory problem can be completely equivalent to a mechanical problem. In such mechanical problem, the UAV trajectory is represented by an extremely soft and thin rope with variable density carrying UAV speed information, and the original objective of optimizing the system performance is transformed to minimizing the overall artificial potential energy on the rope. As a result, the rope in the optimal solution stays in a state of equilibrium and the UAV trajectory can be equivalently optimized by designing the shape of a rope under the APF via mechanical principles. We provide a case study to describe in detail the problem equivalence, i.e., taking a single-user network as an example in which the throughput between UAV and the user is considered as the objective performance. In particular, the optimal trajectory of a UAV is constructed based on mechanical principles, while the global optimality is also rigorously proved and further confirmed via simulations. Moreover, we also highlight that the novel strategy of constructing equivalent mechanical problem has the possibilities to be extended to various UAV trajectory problems under different scenarios with different performance optimization objectives.