# PDDL Task Planning for Tunnel Spraying Based on a Multivariate Coating Accumulation Model
## 1 Introduction  
Currently, the initial support for tunnels constructed by the blasting and excavation method mainly relies on manually operated wet-spray platforms for concrete spraying. However, long-term practice has shown that, due to the complex surrounding rock conditions and limitations of construction technology, the concrete spraying process often depends excessively on the operator's experience. This not only increases construction costs but also poses potential risks to both the quality of the project and the health of the workers. Therefore, research on tunnel spraying task planning methods is of greatsignificance for improving construction quality control and promoting the development of automated spraying technology. Research on tunnel spraying task planning has primarily focused on wet-spray path planning and the development of coating thickness models [1; 2; 3]. For example, some studies have established a kinematic model of the spray robotic arm based on the three-dimensional profile of the tunnel using robotics methods, and they have designed the corresponding path planning system [4]. Other work has analyzed wet-spray tasks and proposed an automated wet-spray method to generate the three-dimensional operational trajectories [5]. Existing coating thickness models can be roughly divided into unbounded-range models and bounded-range models: unbounded-range models (such as the Gaussian distribution [6] and the Cauchy distribution [7]) are suitable for planar surfaces with relatively low requirements in terms of spray quality, while bounded-range models (such as the \(\beta\) distribution model [8], the elliptical double \(\beta\) distribution model [9], and the parabolic model [10]) are more appropriate for describing spray areas of specific shapes. Research based on the elliptical double \(\beta\) distribution model has constructed a generalized coating thickness model using multiple variable spraying process parameters, achieving the prediction of the cumulative coating thickness under different process conditions [11]. In addition, studies aimed at improving the uniformity of paint film thickness by optimizing the spraying rate, spraying height, and trajectory spacing have also achieved notable results [12]. Similarly, in addressing the issue of uneven spray quality during robotic spray path planning, some researchers have optimized relevant parameters by using the variance between the theoretical and actual values of the paint film thickness as the objective function, thereby enhancing the spray quality [13]. Furthermore, work on the influence of the acceleration and deceleration zones on the paint film thickness uniformity has achieved optimal uniformity through adjustments to the spraying speed and spacing [14]. In recent years, with the rapid development of intelligent planning technology, new approaches have emerged for planning tunnel spraying tasks and autonomously generating action sequences [15]. Early modeling methods for intelligent planning include the STRIPS (Stanford Research Institute Problem Solver) method [16], the Hierarchical Task Network (HTN) planning method [17], and the Planning Domain Definition Language (PDDL) method [18]. Among these, the STRIPS method is only applicable to idealized task scenarios, while the HTN method requires separate handling of spatial constraints, temporal reasoning, and motion control dimensions. In contrast, the PDDL method has been widely adopted due to its comprehensive modeling capabilities. Previous studies have expanded the definitions of resources and activity instances based on the PDDL, covering the duration and effect attributes of activities, thereby improving the descriptive accuracy [19]. Other research has employed the PDDL for domain modeling and proposed a generic hierarchical task planning software architecture, further demonstrating its advantages in solving complex planning problems [20].