Joint Optimization of Charging Station Placement and UAV Trajectory for Fresh Data Collection

Unmanned aerial vehicles (UAVs) offer exceptional maneuverability and mobility, making them valuable for data collection in the Internet of Things (IoT). However, to ensure sustainable data services, UAVs with limited battery capacity require energy replenishment during their operational period. In this study, we investigate the joint design of charging station (CS) placement and UAV trajectory to enable continuous and timely data gathering in IoT networks. We formulate a mixed combinatorial optimization problem aimed at minimizing the network's peak Age of Information (AoI) by deploying a specific number of CSs from a set of potential sites and designing the UAV trajectory for data gathering and energy recharging. Convex optimization techniques are employed to find the optimal UAV trajectory, given any feasible CS placement solution. Furthermore, we demonstrate that, with the optimized UAV trajectory, the optimal CS placement problem becomes a maximization problem of a nonsubmodular nondecreasing set function under a cardinality constraint, known to be NP-hard. To tackle this challenge, we propose a greedy CS deployment algorithm that provides an approximate optimal solution within a constant factor of (1/alpha)[1-(1-[alpha gamma]/K)(K)], where alpha is an element of [0,1] represents the generalized curvature, gamma is an element of[0,1] denotes the submodularity ratio, and K represents the number of CSs. Additionally, we introduce a low-complexity CS placement algorithm based on path allocation, which is particularly useful in scenarios involving UAVs with very limited battery capacity. Through simulation results, we demonstrate that our proposed approaches, which jointly optimize CS placement and UAV trajectory, achieve significantly smaller AoI values compared to distance-based strategies, both with and without UAV trajectory optimization.