# Underwater Vehicle Path Planning Based on Bidirectional Path and Cached Random Tree Star Algorithm
## 1 Introduction  
Basic monitoring of the marine environment is essential for early warning and assessment of marine hydro-meteorological conditions, urban climate change, and ecosystem disasters [1, 2]. In the present age, we are facing a range of ocean changes that threaten the sustainable development of the human race, such as rising seawater temperatures [3, 4], increased acidity in the oceans [5], oxygen reduction [6], coral bleaching [7], declining numbers of sea creatures [8], and various forms of pollution [9], including plastic waste. Over recent decades, growths in ocean farming, mineral extraction, and shipping and tourism, as well as increases in anthropogenic pollution sources (including plastic and chemical pollutants), have led to escalating levels of pollution. By 2030, the global population is expected to reach 8.5 billion, with 40% of this figure residing within 100 km of the coastline, thereby precipitating an increase in demand for marine resources and capacity [10]. Concurrently, as terrestrial resources continue to diminish, it is becoming increasingly urgent to ensure that oceans are protected by formulating measures for the utilization and conservation of marine resources [1]. The core mission of marine conservation consists of observing, monitoring, and understanding the marine environment, which has recently garnered significant global attention in the field of marine science [11, 12]. In order to achieve large-scale monitoring and data collection in marine environments at a reduced cost, there are currently two primary approaches: utilizing remotesensing technology and autonomous underwater vehicles. The collection of data through remote sensing technology is associated with certain drawbacks, including limited temporal coverage, uncertainties in inversion models, and susceptibility to weather conditions. Additionally, satellites have a notable limitation in their inability to acquire information from the seafloor. The other platform is autonomous underwater vehicles (AUVs), which exhibit higher maneuverability in the marine environment [1, 13]. As such, they have seen widespread use in marine monitoring and conservation tasks. The adaptability of underwater robots for environmental monitoring allows them to quickly acquire high spatial resolution data, enabling their real-time monitoring of fluctuations in specific oceanic parameters and risks. This has helped to supplement the shortcomings of other platforms [14]. Automatic path planning is a crucial functionality of underwater robots. However, the complex and dynamic nature of marine environments poses challenges distinct from those encountered in terrestrial settings [15, 16]. Therefore, this paper places particular emphasis on investigating path-planning algorithms specifically tailored for application in underwater domains. Generally, the path planning for autonomous underwater vehicle navigation differs from that of land and presents typical challenges in 3D space [17]. Numerous techniques have been proposed for optimizing 3D paths, including statistical optimization-based strategies, for example, the A-star algorithm [18], potential-based methods [19], ant colony algorithms, and genetic algorithms. Despite their demonstrated capability, the majority of these approaches suffer from intrinsic intractability due to their NP-hardness, posing significant computational challenges for optimization [20]. To expedite the search process, an algorithm based on random sampling has been developed, including probabilistic roadmaps (PRMs) [21] and rapidly exploring random trees (RRTs). Sample-based methods efficiently optimize path solutions by eliminating the explicit delineation of impediments [22]. PRMs represent a sparse configuration space of vehicles using a graph model where waypoints serve as nodes, and graph edge reduction is utilized to optimize the path by minimizing the length of the connections between nodes [23].