## 1 Introduction
Based on the coal seam geological model, the authors of this paper proposed a coal seam floor gradient identification method using piecewise linear representation (PLR), as shown in Figure 2a [17]. This method synthesized the control resolution of the shearer range arm and the geometric characteristics of the coal seam, so that horizon control was achieved with the maximum exploitation rate within the shearer's capacity. But this method can only analyze one cross section (such as 2-2\({}^{\prime}\) in Figure 2a) in the face-advancing direction, so it is insufficient for coal seams with undulations in the face direction or different floor series in the face-advancing direction. As shown in Figure 2b,c, the floor series at different face positions have different morphologies, and the gradients in the face direction are different. The distribution of the whole coal seam gradient in the face-advancing direction is necessary for the horizon control of longwall mining. Figure 1: Representation of a small portion of a longwall mining operation [7]. According to the concept of the transparent longwall face, the objective of this work is to obtain a coal seam floor cutting path planning method based on the geological model. In this work, the distribution of the coal seam gradient in both the face-advancing direction and the face direction was obtained using a multiple hierarchical clustering algorithm, as shown in Figure 3. First, a morphology similarity and coplanarity measurement method was proposed to evaluate the similarity of clusters. The floor series (Fs) were clustered using a hierarchical clustering algorithm according to the morphology similarity. The cluster centers are the representative morphology of the zones covered by each cluster. By analyzing the morphology-based cluster centers using the PLR method in Ref. [17], the distribution of the coal seam gradient in the face-advancing direction can be obtained. The surfaces (M\({}_{k}\)) composed of two neighbor floor series are clustered according to the coplanarity. The gradient of the coplanarity-based cluster center is the representative gradient of the zones covered by each cluster, so the distribution of the coal seam gradient in the face direction can be obtained. Meanwhile, taking the morphology-based and coplanarity-based cluster centers as the generating lines and stretching angle, respectively, the coal seam floor is reconstructed. And the reconstructed floor is the planned cutting path. Figure 2: The coal seam geological model of the 18,201 longwall face (**a**), and difference distributions of the floor in face direction (**b**) and face-advancing direction (**c**). The rest of this paper is structured as follows. Section 2 introduces the hierarchical clustering algorithm. Section 3 describes the morphology and gradient similarity measurement method. Section 4 introduces the validity measure method of clustering in order to determine the optimal number of clusters. The cutting path planning method and its limitations are described in Section 5. Section 6 presents the results and discussion. Finally, Section 7 concludes the paper and discusses future avenues for research.