# Adaptive Path Planning for UAV-Based Pollution Sampling
## 1 Introduction  
Unmanned Aerial Vehicles (UAVs) have witnessed a steady rise in popularity across diverse applications, including military operations, environmental monitoring, and delivery systems [1, 2, 3]. As noted by [PERSON] et al. [4], the development of Remotely Piloted Aircraft Systems (RPASs) began in the mid-1800s, marking the start of their evolution. [PERSON] et al. observed an increasing trend in the number of publications related to UAV path planning. From 2008, the growth rate was moderate during the initial seven years. Between 2014 and 2016, the trend experienced minor fluctuations. However, a notable rise in the number of publications was reported for 2017 and 2018 [5]. [PERSON] et al. suggested that UAVs could achieve greater cost-efficiency and effectiveness by acquiring the capability to intelligently adapt their internal plans in response to environmental changes. Adaptive path planning is among the key areas that could significantly benefit from enhanced autonomy [3]. Consequently, path planning and trajectory generation [6] are essential for advancing Unmanned Aerial Systems (UASs). These processes enable UAVs to determine efficient and safe routes through an environment while adhering to specific constraints [6]. It is crucial to recognize that obstacles in aviation are not limited to solid objects; weather conditions also significantly influence flight safety. [PERSON] et al. highlighted that adverse weather has been a major factor in many fatal aircraft accidents. UAVs, being generally smaller than manned aircraft, are even more vulnerable to unfavorable weather conditions. Therefore, avoiding hazardous weather is a critical considerationfor unmanned flights [7]. In their 2020 study, [PERSON] et al. emphasized the significant attention UAVs have garnered over the past decade, spanning both military and civilian applications [1]. UAVs are commonly deployed for tasks deemed repetitive, non-essential, or hazardous for human operations [6]. The deployment of UAVs on the battlefield represents a clear trend in the evolution of modern aerial weaponry [8; 9]. [PERSON] and [PERSON] observed growing utilization of UAVs in military missions, which include activities such as target detection and destruction, close-range reconnaissance, electronic warfare, precision strikes, high-resolution video recording, and damage assessment [3; 9]. Additionally, drones are frequently used for tracking, protecting, and providing surveillance for ground-based vehicles [10]. Multi-UAV convoys have proven to be particularly effective for these operations [11]. Research on UAV technologies is considered to be a cornerstone for enhancing air force battle capabilities, closely tied to national security [8]. Civilian UAV applications are particularly prevalent in Europe. Research by [PERSON] et al. indicated that, as of April 2016, Europe accounted for 2500 UAV operators, surpassing the 2342 operators registered in the rest of the world. Furthermore, they suggested that the UAV industry could represent 10 percent of the aviation market, with the annual demand expected to rise to EUR 10 billion by 2035 and surpass EUR 15 billion by 2050 [4]. Tasks such as reconnaissance, search and rescue missions, weather monitoring, aerial mapping, and cinematography are encompassed within civil UAV applications [3; 6]. In construction, UAVs are employed for continuous site monitoring, accessing hazardous or hard-to-reach areas, and facilitating reconstruction after a disaster [12]. The limited capacity of fuel tanks or batteries imposes constraints on many UAV missions. To overcome this, solar-powered UAVs are frequently employed, with High-Altitude Long-Endurance (HALE) UAVs forming a significant subcategory. These highly efficient unmanned aircraft operate at altitudes between 20 and 100 km, above conventional atmospheric flight and below spacecraft trajectories [13]. Depending on platform efficiency and solar availability, HALE UAVs have the potential for indefinite flight durations.