## 2 Related Work  
These days a huge amount of research works are being carried out in the domain of UAVs and drones in connection with wireless sensor networks, vehicular networks as well as IoT devices because of the possibilities of huge applications expected to enhance the performance of those systems [2; 3; 4; 25]. When the number of such networks, nodes, or IoT devices increases up to a great extent, these nodes or devices are generally clustered and UAVs have to hover on these CHs. Cluster members submit their tasks to their own CHs which are received by the UAVs that execute those tasks by hovering over the CHs. This hovering costs a huge amount of energy, especially if the CHs are traversed in a zigzag manner [10; 26]. Therefore, for energy-efficient operation of the system, the trajectories of the UAVs should be planned properly [4; 16]. Additionally, in multi-UAV systems, there may be the intersection of trajectories of different UAVs, leaving a nonzero probability of collision. This collision must be avoided at any cost for which proper trajectory planning is extremely necessary [27; 28; 29]. A deep reinforcement learning best trajectory design is presented in [16] where energy efficiency is ensured through minimizing residual energy, safe distance between multiple UAVs, and minimizing the application of age information in the current context. This technique is especially applicable for a multi-UAV system where the authors have given special attention to reducing dependencies of testing data on the training data. The comprehensive energy consumption (CEC) model is studied in [18; 19] where energy consumed by a UAV consists of two components: propulsion energy and communication energy. Communication energy is due to the transmission of tasks from network nodes to UAV and returning back the results from UAV to nodes. Propulsion energy is because of the hovering of UAVs on nodes. However, a lot of propulsion energy is wasted if the task queue is not full (or approximately full) when the UAV arrives over one particular network node for task execution of a collection of nodes under it. The minimization of propulsion energy(PEM) of fixed-wing UAVs is considered by authors in [19] where the communication energy part of UAV's energy consumption is ignored. These days, gradually, applications of UAV-assisted systems have started to become processing intensive; additionally, the number of real-time tasks has increased for which delay has become an important performance metric along with energy, as proposed in [30]. In order to finish all the tasks within a specific time duration, hovering decisions of UAVs have to be based on recent information; therefore, age-of-information needed to be considered these days as an important criterion [31]. The recency of information is considered by authors of [4] where trajectory planning(AoI-IP) is based on dynamic programming. However, the communication energy part is ignored in this paper as well. Various learning algorithms have been presented in the literature some of which are limited to only trajectory optimization of single or multiple UAVs [32; 33; 34] whereas some others consider trajectory optimization along with scheduling [10; 35]. In this article, IoT devices are not clustered, but rather all these devices apply Time Division Multiple Access