## 1 Introduction  
In recent years, the utilization of unmanned ground vehicles (UGVs) has become increasingly prevalent in a variety of applications, including transportation, investigation, and detection [1; 2; 3]. However, as the operational environment of UGVs becomes more complex, a number of challenging surface-path problems have emerged [4], such as field rescue and warfare path planning. Achieving accurate and efficient path planning is essential for UGVs to effectively execute their designated tasks. Despite advancements in autonomous UGV technology, path planning remains a challenging task due to the multifaceted and intricate factors influencing path selection in diverse environments, including information accuracy, cost considerations, and risk assessment. Traditional path-planning studies typically focus on obstacle avoidance while minimizing distance, using two-dimensional maps to identify feasible and impassable areas, while disregarding terrain height information and other costs. In practice, UGVs should consider terrain height information and other costs when deciding on a path. For example, [PERSON] et al. [5] used terrain complexity to calculate the optimal strategy for autonomous underwater vehicles. [PERSON] et al. [6] considered localization uncertainty, collision risk, and travel costs to the target area in their path-selection algorithm. [PERSON] et al. [7] integrated road roughness and path length to select the optimal path. Nevertheless, most current algorithms combine the multidimensional cost with varying weights, necessitating adjustments to the algorithm and weights when the environment changes, which can be difficult to handle. To address the above problems, we propose a new decoupled model for path planning with path cost, which divides the path-planning model into two parts: the cost map and the main path-planning algorithm. Specifically, the multidimensional path-cost fusion is represented as height information in the 3D map. The path-planning master algorithm can find the best path using input from the previous part. It only adjusts the 3D map without changing the algorithm parameters when the environment changes. The main advantage is that the factors and weights of the path cost can be easily changed even if the UGV is in motion. This approach can be applied to the autonomous navigation of UGVs, where cost factors often fluctuate, such as when the environment cost factors change during robot detection or when the driving path requires a more aggressive or conservative strategy. It has the potential to enhance the efficiency and accuracy of path planning. However, this requires the main algorithm to be adaptable and efficient in processing. Reinforcement learning (RL) maximizes the cumulative rewards through trial-and-error interactions with the environment, enabling agents to learn the best policy autonomously. Q-learning, as a popular model-free reinforcement learning algorithm, has been widely used in various fields [8]. For example, [PERSON] et al. [9] designed a path-planning model based on Q-learning that ensures obstacle avoidance and energy savings of underwater robots. [PERSON] et al. [10] used Q-learning to propose an automatic path-planning method that uses a camera to detect the location of obstacles and avoid them. However, the limitation of the Q-learning algorithm is that it is difficult to deal with the high-dimensional state required in this study. The deep Q-learning (DQL) method overcomes this limitation by combining deep learning and Q-learning. Deep learning enhances the feature extraction of the environment and realizes the fitting of an action value and environmental state, while Q-learning completes the mapping from state to action through the reward function and decides according to the output of deep neural network and exploration strategies [11]. As a result, high-dimensional states can be dealt with. Pictures are the input of states of DQL, and the output is the Q value of each action.