## 1 Introduction  
Longwall mining, as the most efficient extracting method for underground coal mines, will remain the principal extraction method in the world in the foreseeable future [1; 2]. Usually, the equipment used for working in a longwall mining face include a longwall shearer, an armored face conveyor (AFC), and more than 100 hydraulic supports, as shown in Figure 1. The shearer cuts the coal seam while traveling across the longwall face along rails attached to the AFC. The cut coal is transported by the AFC. The hydraulic supports provide temporary support of the roof material above the extracted coal seam. As the shearer moves across the coal seam, large hydraulic push rams attached to the supports advance the AFC progressively in the face-advancing direction, and thereby the longwall mining moves in a programmed sequence. Longwall mining is a coupling process between the mining equipment and coal-rock mass. In addition to the mechanical adaptability between the mining equipment and coal-rock mass (such as coal fracture mechanics induced by the shearer drum and pick cutter [3; 4; 5; 6]), the space adaptability between them, which means that the mining equipment cuts in the coal seam, is a key issue that must be addressed in longwall mining automation. Longwall mining automation, which can improve productivity and safety for mining personnel, is the focus of the world coal industry. Two key problems facing longwall mining automation are that of machine and face guidance to ensure the machines cut in the seam, and the face is kept straight [7,8]. Face alignment [9, 10, 11], produced from the shearer positioning with an inertial navigation system (INS), has been researched and applied widely in many coal mines [12,13]. It can keep the face straight for consistent production and minimal wear of the conveyor system. Ensuring the machines cut in the seam needs two technologies: horizon control and extraction control. Horizon control guides the machine to follow the seam undulations in the direction of the longwall face's advance. Extraction control allows the machine to follow defined floor and roof profiles along the face, better following any given coal seam undulations for optimal extraction and production [14]. Enhanced horizon control (EHC), an outcome of the ARCAP landmark project, which is based on a cut model and some other information (manual input, coal interface input, and other seam information), can make a prediction of what the next floor and roof horizon should be [15]. The EHC is a memory-cut-based method [16], and will absolutely degenerate into a memory cut if the other information (manual input, coal interface input, and other seam information) becomes unavailable. Memory cutting is incapable of working for uneven coal seams [17]. Shield-data-based horizon control (SDHC) [18], based on the fact that the coal seam trend is given by the inclination of the support's canopy, automatically adjusts the cutting drum height according to data from the roof support so that the longwall face follows the seam trend in the face-advancing direction. In fact, EHC and SDHC are not completely the same as horizon control, described in reference [14]. They include some functions of extraction control, described in reference [14]. The intrinsic and principal problem is to maintain the alignment of the shearer's exploitation gradient with the coal seam gradient in the face-advancing direction, regardless of EHC, SDHC, and horizon control, described in reference [14]. The coal seam gradient in the face-advancing direction is the control target of horizon control. The concept of the transparent longwall face [19,20] was proposed, which aims at autonomous cutting by the longwall shearer in the coal seam with the use of a high-precision transparent geological model [21, 22, 23]. But research about how to decide the cutting path of the longwall shearer according to the geological model is rarely reported.