Longwall Mining Automation—The Shearer Positioning Methods between the Longwall Automation Steering Committee and China University of Mining and Technology

: The shearer positioning method is of great signiﬁcance to the automation of longwall mining. The research teams in the Longwall Automation Steering Committee (LASC) of Australia and China University of Mining and Technology (CUMT) have focused on shearer positioning and identiﬁed the shearer inertial navigation system, the measurement of longwall retreat and creep displacement, and the backward calibration of the shearer trajectory as three key technologies to obtain accurate shearer positioning information. In underground environments without GPS, due to the characteristics of inertial navigation system (INS) autonomous full-parameter navigation, shearer positioning based on INS is adopted by the LASC and CUMT, and error reduction algorithms are proposed to inhibit the rapid error accumulation of INS. In order to obtain the periodic calibration information when the shearer reaches the end of the longwall face, it is necessary to measure the retreat and creep displacements in order to back-correct the shearer trajectory. Finding a suitable measurement method for this task is challenging, especially in the presence of dust and moisture. The LASC used a scanning laser and FMR 250 microwave radar to measure these two displacements, while CUMT adopted an ultra-wideband (UWB) radar. In terms of the backward calibration method, minimum-variance ﬁxed-interval smoothing (MFS) proposed by LASC and the global optimization model (GOM) for the shearer trajectory from CUMT are described in detail. The experiment demonstrates that the GOM outperforms MFS in terms of accuracy but requires more computational resources. Therefore, our next research objective is to develop an efﬁcient and accurate algorithm for performing backward calibration on the shearer trajectory.


Introduction
Longwall mining is a primary method for extracting coal from underground mines.As shown in Figure 1, three kinds of mining equipment used in the longwall face are a shearer, an armored face conveyor (AFC), and a roof support system.The shearer moves back and forth along a rail connected to the AFC, while the roof support system maintains the stability of the coal seam roof.Traditionally, the shearer and roof support system are controlled manually, which inevitably causes the rock to contaminate the coal and reduces the mining productivity.In addition, worker safety is greatly threatened because they are directly exposed to the mining worksite.Improving mining productivity, protecting worker safety, and achieving environmental sustainability are the goals that the coal mining industry has been pursuing [1,2].Longwall mining automation is a mining process that is carried out using mining equipment without the need for manual intervention.It involves the intelligent perception of the mining environment, intelligent control of the mining equipment, and autonomous operation of the mining process [3,4].Longwall oped by CUMT for this purpose.The digital model of a coal seam is constructed using drill geological data and the seismic CT detection technique.Combining the digital model of the coal seam, shearer positioning technology is employed to obtain the shearer 3D positioning within the coal seam [10].Based on this, it is possible to achieve AFC trajectory straightening and shearer cutting path planning.The industrial test was carried out and demonstrated satisfactory performance.
Whether it is for LASC or CUMT, the shearer positioning method plays an important role in longwall mining automation.The shearer inertial navigation system, the measurement of longwall retreat and creep displacement, and the backward calibration of shearer trajectory are three crucial technologies to acquire the shearer's accurate positioning.Therefore, this paper aims to present an overview of three technologies utilized by the LASC and CUMT, and compares the backward calibration methods proposed by the LASC and CUMT through a conducted experiment.As early as 2001, the Commonwealth Scientific and Industrial Research Organization (CSIRO) of Australia began developing the longwall automation technology known as the Longwall Automation Steering Committee (LASC).LASC is the abbreviation for the research team responsible for this technology.The LASC can fix the 3D position of the shearer, maintain the straightness of the conveyor and supports, raise the shearer drum automatically, and provide 3D remote monitoring video feeds [7][8][9].The technical framework is shown in Figure 2b.The latest version, LASC 2.0, has been adopted in 70% of Australia's coal mines.DBT, JOY, and Eickhoff are all licensed manufacturers of LASC.The social benefits of LASC application have contributed to reducing the number of accidents and deaths, and the costs that are avoided as a result are likely to save mining industries millions of dollars each year.In addition, improving the accuracy of longwall mining operations and reducing the amount of waste rock leads to less environmental disruption.LASC technology has great influence on the development of longwall mining automation around the world.In China, research on the automation of longwall mining commenced at a relatively later stage.Under the support of the National High-tech Research and Development Program (863 Program) and the National Natural Science Foundation of China, our research group at China University of Mining and Technology (CUMT) has devoted significant efforts to the longwall mining automation.Figure 3 shows the technical framework developed by CUMT for this purpose.The digital model of a coal seam is constructed using drill geological data and the seismic CT detection technique.Combining the digital model of the coal seam, shearer positioning technology is employed to obtain the shearer 3D positioning within the coal seam [10].Based on this, it is possible to achieve AFC trajectory straightening and shearer cutting path planning.The industrial test was carried out and demonstrated satisfactory performance.

Longwall Mining Method
Longwall mining is widely recognized as a highly efficient method for extracting coal from underground mines.In a coal seam, many elongated and narrow roadways are excavated to form the boundaries of several longwall panels, as shown in Figure 4a.The roadways serve as a passageway of transportation for coal, equipment, and workers.The sectional area of roadway is approximately 5 × 4 m in general.The coal is extracted from the longwall panel, which is generally 300 min wide and 5000 min long, with a thickness ranging from 1.2 to 8.0 m.At the end of the longwall panel, the shearer, AFC, and roof support system are installed across the longwall face.
As shown in Figures 4b and 5, the shearer moves along a rail associated with the AFC, cutting a 0.8 m-wide slice of coal from the coal seam.The extracted coal is deposited onto the AFC and subsequently transported far away the longwall face.When the shearer is in motion, the hydraulic push arms, which are connected to the roof support system, gradually push a section of the AFC behind the shearer along the advancing direction for the next cutting cycle.In Figure 6, the shearer is in operation during n-th cycle, while the Whether it is for LASC or CUMT, the shearer positioning method plays an important role in longwall mining automation.The shearer inertial navigation system, the measurement of longwall retreat and creep displacement, and the backward calibration of shearer trajectory are three crucial technologies to acquire the shearer's accurate positioning.Therefore, this paper aims to present an overview of three technologies utilized by the LASC and CUMT, and compares the backward calibration methods proposed by the LASC and CUMT through a conducted experiment.

Longwall Mining Method
Longwall mining is widely recognized as a highly efficient method for extracting coal from underground mines.In a coal seam, many elongated and narrow roadways are excavated to form the boundaries of several longwall panels, as shown in Figure 4a.The roadways serve as a passageway of transportation for coal, equipment, and workers.The sectional area of roadway is approximately 5 × 4 m in general.The coal is extracted from the longwall panel, which is generally 300 min wide and 5000 min long, with a thickness ranging from 1.2 to 8.0 m.At the end of the longwall panel, the shearer, AFC, and roof support system are installed across the longwall face.
As shown in Figures 4b and 5, the shearer moves along a rail associated with the AFC, cutting a 0.8 m-wide slice of coal from the coal seam.The extracted coal is deposited onto the AFC and subsequently transported far away the longwall face.When the shearer is in motion, the hydraulic push arms, which are connected to the roof support system, gradually push a section of the AFC behind the shearer along the advancing direction for the next cutting cycle.In Figure 6, the shearer is in operation during n-th cycle, while the AFC behind the shearer has been moved into the n + 1 cycle.When the coal is cut, the roof support systems support the roof of the coal seam.There are approximately 200 roof support systems in a typical longwall face.After the AFC is pushed towards the coal seam, the roof support systems are relocated along the advancing direction.Behind the roof support systems, the collapse of the roof results in the formation of a goaf.

Shearer Positioning Technology
The shearer positioning method includes three components, the shearer inertial navigation system, the measurement of longwall retreat and creep displacements, and the backward calibration of the shearer trajectory.Researchers in the LASC and CUMT have been focusing on those three aspects and have acquired good results.

The Shearer Inertial Navigation System
Due to the unavailability of Global Position System (GPS) and BeiDou Navigation Satellite System (BDS) signals in underground environments, the positioning method based on the inertial navigation system (INS) is considered to be a feasible shearer positioning method.The INS exhibits a high level of autonomy, making it widely applied in aircraft [12], ships [13], submarines [14], and so on.The accelerometer and gyroscope serve as the core measurement units to obtain the state of an object.The tri-axis accelerometer measures the linear accelerations of an object with respect to its body reference frame in three orthogonal axes.The gyroscopes are utilized to quantify the angular velocities of rotation of the object with respect to the inertial reference frame.In summary, the navigation algorithm of the INS is founded upon the principles of Newton's laws of motion.The attitude angles are derived through the integration of rotational angular velocities.Subsequently, the rotation matrix, also known as the direction cosine matrix (DCM), is obtained.Through integrating the measured accelerations from the accelerometers and applying the rotation matrix transformation, the velocity and position in the navigation coordinate frame can be determined [15,16].
In order to acquire the shearer position in three dimensions (3D), the LASC has developed a measurement system known as the Shearer Position Measurement System (SPMS).This system utilizes a Northrop Grumman LN270 INS, as shown in Figure 7a.The LN270 was installed within an explosion-proof enclosure in the shearer body.In addition to the INS, an odometer, connected to the shearer haulage unit, was required to accurately measure the distance traveled across the longwall face.Afterwards, the second-generation SPMS (SPMS-II) using IXSEA PHINS INS was finished, as shown in Figure 7b.Due to the noise and vibration in underground environments, the INS calculation error increases exponentially over time.That is to say, the INS exhibits a very low relative error over short time periods, but over long time periods, the error increases dramatically.Based on this, Reid et al. [17] employed zero-velocity updating technology (ZUPT) to periodically correct the velocity error during stationary motion for an INS.Furthermore, the development of integrated navigation with an INS and odometer aims to continually enhance performance.After replacing the odometer with a Doppler radar, Dunn et al. [18,19] introduced a practical and accurate aiding source.Through analyzing the longwall mining method, Reid et al. [20] determined that the horizontal closing distance between two adjacent cutting cycles remained constant.This constant value was found to be instrumental in enhancing the longtime stability of the INS.The 3D path of a shearer in an underground mine, measured using the SPMS, is shown in Figure 8.

Shearer Positioning Technology
The shearer positioning method includes three components, the shearer inertial igation system, the measurement of longwall retreat and creep displacements, and backward calibration of the shearer trajectory.Researchers in the LASC and CUMT h been focusing on those three aspects and have acquired good results.

The Shearer Inertial Navigation System
Due to the unavailability of Global Position System (GPS) and BeiDou Naviga Satellite System (BDS) signals in underground environments, the positioning me based on the inertial navigation system (INS) is considered to be a feasible shearer p tioning method.The INS exhibits a high level of autonomy, making it widely applie aircraft [12], ships [13], submarines [14], and so on.The accelerometer and gyroscope s as the core measurement units to obtain the state of an object.The tri-axis accelerom measures the linear accelerations of an object with respect to its body reference fram three orthogonal axes.The gyroscopes are utilized to quantify the angular velocitie rotation of the object with respect to the inertial reference frame.In summary, the nav tion algorithm of the INS is founded upon the principles of Newton's laws of motion.attitude angles are derived through the integration of rotational angular velocities.Su quently, the rotation matrix, also known as the direction cosine matrix (DCM), is obtai Through integrating the measured accelerations from the accelerometers and appl the rotation matrix transformation, the velocity and position in the navigation coordi frame can be determined [15,16].
In order to acquire the shearer position in three dimensions (3D), the LASC has veloped a measurement system known as the Shearer Position Measurement Sys (SPMS).This system utilizes a Northrop Grumman LN270 INS, as shown in Figur The LN270 was installed within an explosion-proof enclosure in the shearer body.In dition to the INS, an odometer, connected to the shearer haulage unit, was require accurately measure the distance traveled across the longwall face.Afterwards, the sec generation SPMS (SPMS-II) using IXSEA PHINS INS was finished, as shown in Figur Due to the noise and vibration in underground environments, the INS calculation e increases exponentially over time.That is to say, the INS exhibits a very low relative e over short time periods, but over long time periods, the error increases dramatic Based on this, Reid et al. [17] employed zero-velocity updating technology (ZUPT) to riodically correct the velocity error during stationary motion for an INS.Furthermore development of integrated navigation with an INS and odometer aims to continually hance performance.After replacing the odometer with a Doppler radar, Dunn et al. [18 introduced a practical and accurate aiding source.Through analyzing the longwall mi method, Reid et al. [20] determined that the horizontal closing distance between two jacent cutting cycles remained constant.This constant value was found to be instrume in enhancing the longtime stability of the INS.The 3D path of a shearer in an undergro mine, measured using the SPMS, is shown in Figure 8.In CUMT, the authors of this paper built the Shearer Positioning and Attitude Systems (SPAS), including SPAS-I and SPAS-II, as shown in Figure 9.The Spatial FOG INS from ADVANCED NAVIGATION provided the attitude angles of heading, pitch, and roll.The axial encoder connected to the travelling unit provided the velocity value of the shearer.The shearer position was then obtained using the dead-reckoning algorithm.The effect of the installation and initial alignment noncoincidence of the INS on the shearer positioning error was analyzed, and a calibration method for the two deviation angles with the two-point method was proposed [22,23].The current axial encoder is a 12-bit system with a resolution of 1/4096.This implies that the accuracy of INS attitude greatly affects the position error, especially the heading angle accuracy.Based on previous research, the heading angle error was found to increase at a faster rate than the pitch error and roll error over time.Furthermore, it was observed that the heading angle error directly affected the plane positioning accuracy [24,25].According to the longwall mining method, two constraints on the shearer velocity and position were obtained.Therefore, the dynamic zero velocity update (DZUPT) model [26] and the closing path optimal estimation model [27] were built using a Kalman filter.In order to improve shearer positioning accuracy, an information filter was proposed to integrate these two models [11].An underground field test was performed at 18,201 longwall faces in Shanxi Province, China, and Figure 10b shows the shearer trajectory acquired via the SPAS.In CUMT, the authors of this paper built the Shearer Positioning and Attitud tems (SPAS), including SPAS-I and SPAS-II, as shown in Figure 9.The Spatial FO from ADVANCED NAVIGATION provided the attitude angles of heading, pitch, an The axial encoder connected to the travelling unit provided the velocity value shearer.The shearer position was then obtained using the dead-reckoning algorith effect of the installation and initial alignment noncoincidence of the INS on the s positioning error was analyzed, and a calibration method for the two deviation with the two-point method was proposed [22,23].The current axial encoder is a system with a resolution of 1/4096.This implies that the accuracy of INS attitude affects the position error, especially the heading angle accuracy.Based on previ search, the heading angle error was found to increase at a faster rate than the pitc and roll error over time.Furthermore, it was observed that the heading angle error d affected the plane positioning accuracy [24,25].According to the longwall mining m two constraints on the shearer velocity and position were obtained.Therefore, t namic zero velocity update (DZUPT) model [26] and the closing path optimal esti model [27] were built using a Kalman filter.In order to improve shearer positionin racy, an information filter was proposed to integrate these two models [11].An ground field test was performed at 18,201 longwall faces in Shanxi Province, Chin Figure 10b shows the shearer trajectory acquired via the SPAS.

The Measurement Method of Longwall Retreat and Creep Displacements
In Section 3.1, the utilization of auxiliary sensors, ZUPT, DZUPT, and kine model reduced INS drift error and improved the positioning accuracy.However, the lack of periodic GPS calibration, the INS longtime error is still relatively large several cutting cycles, the shearer positioning accuracy cannot meet the requirem the longwall mining automation.According to the longwall mining method, the s reciprocates between two roadways along the longwall face.When the shearer reach end of the longwall face, the longwall retreat and creep displacements become sign parameters to measure, which can be utilized to back-correct the shearer trajectory the completion of each cutting cycle.As shown in Figure 11, according to the lon mining method, the retreat displacement is actually the advancing distance of the m equipment along the advancing direction every time.Due to the different levels o nation of the longwall face, there will be a height difference between the two ends longwall face.When the mining equipment is installed on the inclined longwall fa force acting on the equipment is not balanced, which makes the equipment slide alo longwall-face direction and produces the displacement of sliding up and down.In the LASC, Reid et al. [20] installed the scanning laser on the roadway con structure linked to the AFC to scan the roadway profile.Accordingly, the first gene of a scanning device with SICK LMS200 as the core sensor and the second generat an explosion-proof 3D laser scanning device called ExScan have been developed.Th rent scan was matched to the global map with the scan-matching algorithm to acqu retreat and creep displacements, as shown in Figure 12.However, the dust and mo in an underground mine would greatly increase the attenuation and distortion of th

The Measurement Method of Longwall Retreat and Creep Displacements
In Section 3.1, the utilization of auxiliary sensors, ZUPT, DZUPT, and kinematics model reduced INS drift error and improved the positioning accuracy.However, due to the lack of periodic GPS calibration, the INS longtime error is still relatively large.After several cutting cycles, the shearer positioning accuracy cannot meet the requirement of the longwall mining automation.According to the longwall mining method, the shearer reciprocates between two roadways along the longwall face.When the shearer reaches the end of the longwall face, the longwall retreat and creep displacements become significant parameters to measure, which can be utilized to back-correct the shearer trajectory after the completion of each cutting cycle.As shown in Figure 11, according to the longwall mining method, the retreat displacement is actually the advancing distance of the mining equipment along the advancing direction every time.Due to the different levels of inclination of the longwall face, there will be a height difference between the two ends of the longwall face.When the mining equipment is installed on the inclined longwall face, the force acting on the equipment is not balanced, which makes the equipment slide along the longwall-face direction and produces the displacement of sliding up and down.

The Measurement Method of Longwall Retreat and Creep Displacements
In Section 3.1, the utilization of auxiliary sensors, ZUPT, DZUPT, and kinematics model reduced INS drift error and improved the positioning accuracy.However, due to the lack of periodic GPS calibration, the INS longtime error is still relatively large.After several cutting cycles, the shearer positioning accuracy cannot meet the requirement of the longwall mining automation.According to the longwall mining method, the shearer reciprocates between two roadways along the longwall face.When the shearer reaches the end of the longwall face, the longwall retreat and creep displacements become significant parameters to measure, which can be utilized to back-correct the shearer trajectory after the completion of each cutting cycle.As shown in Figure 11, according to the longwall mining method, the retreat displacement is actually the advancing distance of the mining equipment along the advancing direction every time.Due to the different levels of inclination of the longwall face, there will be a height difference between the two ends of the longwall face.When the mining equipment is installed on the inclined longwall face, the force acting on the equipment is not balanced, which makes the equipment slide along the longwall-face direction and produces the displacement of sliding up and down.In the LASC, Reid et al. [20] installed the scanning laser on the roadway conveyor structure linked to the AFC to scan the roadway profile.Accordingly, the first generation of a scanning device with SICK LMS200 as the core sensor and the second generation of an explosion-proof 3D laser scanning device called ExScan have been developed.The current scan was matched to the global map with the scan-matching algorithm to acquire the retreat and creep displacements, as shown in Figure 12.However, the dust and moisture in an underground mine would greatly increase the attenuation and distortion of the laser In the LASC, Reid et al. [20] installed the scanning laser on the roadway conveyor structure linked to the AFC to scan the roadway profile.Accordingly, the first generation of a scanning device with SICK LMS200 as the core sensor and the second generation of an explosion-proof 3D laser scanning device called ExScan have been developed.The current scan was matched to the global map with the scan-matching algorithm to acquire the retreat and creep displacements, as shown in Figure 12.However, the dust and moisture in an underground mine would greatly increase the attenuation and distortion of the laser beam, which affect the laser measurement accuracy.Then, Hargrave et al. [29][30][31] used the FMR 250 radar from Endress-Hauser company in Germany to measure the retreat and creep displacements, and a field test in Australia's Beltana mine was carried out to verify the effectiveness of the proposed method, as shown in Figure 13.The radar is sensitive to distance information, and the creep displacement was obtained through measuring the distance between the radar and roadway wall.The number of bolt-plates on the roadway surface represented the position information, thus enabling the measurement of retreat displacement through the recognition of these bolt-plates.However, in the majority of mines, the bolt-plates lack position information, thereby limiting the applicability of this method.

AFC
Appl.Sci.2023, 13, x FOR PEER REVIEW 8 of 17 beam, which affect the laser measurement accuracy.Then, Hargrave et al. [29][30][31] used the FMR 250 radar from Endress-Hauser company in Germany to measure the retreat and creep displacements, and a field test in Australia's Beltana mine was carried out to verify the effectiveness of the proposed method, as shown in Figure 13.The radar is sensitive to distance information, and the creep displacement was obtained through measuring the distance between the radar and roadway wall.The number of bolt-plates on the roadway surface represented the position information, thus enabling the measurement of retreat displacement through the recognition of these bolt-plates.However, in the majority of mines, the bolt-plates lack position information, thereby limiting the applicability of this method.
(a) (b) In CUMT, the authors of this paper provided a novel measurement solution with the ultra-wideband (UWB) radar imaging method [32].UWB radar is characterized by a radar with a fractional bandwidth exceeding 25%.Through transmitting electromagnetic wave signals with a strong ability to penetrate a coal-dust environment, UWB radar can obtain target or scene images all day and in all weather, which has the technical advantage of application in the complex environment at the end of a longwall face.As shown in Figure 14a, the radar was mounted on a slide-way, and the slide-way was placed on the roadway conveyor structure connected to the head of the AFC.The radar was moved along the slide-way to image the bolt-plates.Two imaging results were obtained before and after the movement of the longwall face.Then, the feature-based image registration algorithm was employed to identify the correct-match pairs, and subsequently, the similarity transformation model was calculated to determine the retreat and creep displacements.The measurement device was developed (Figure 14b), and the algorithm program including radar imaging and image registration were embedded.The field text was performed in Appl.Sci.2023, 13, x FOR PEER REVIEW 8 beam, which affect the laser measurement accuracy.Then, Hargrave et al. [29][30][31] the FMR 250 radar from Endress-Hauser company in Germany to measure the retrea creep displacements, and a field test in Australia's Beltana mine was carried out to v the effectiveness of the proposed method, as shown in Figure 13.The radar is sensiti distance information, and the creep displacement was obtained through measurin distance between the radar and roadway wall.The number of bolt-plates on the road surface represented the position information, thus enabling the measurement of re displacement through the recognition of these bolt-plates.However, in the majori mines, the bolt-plates lack position information, thereby limiting the applicability o method.
(a) (b) In CUMT, the authors of this paper provided a novel measurement solution wit ultra-wideband (UWB) radar imaging method [32].UWB radar is characterized by a with a fractional bandwidth exceeding 25%.Through transmitting electromagnetic signals with a strong ability to penetrate a coal-dust environment, UWB radar can o target or scene images all day and in all weather, which has the technical advanta application in the complex environment at the end of a longwall face.As shown in F 14a, the radar was mounted on a slide-way, and the slide-way was placed on the road conveyor structure connected to the head of the AFC.The radar was moved alon slide-way to image the bolt-plates.Two imaging results were obtained before and the movement of the longwall face.Then, the feature-based image registration algor was employed to identify the correct-match pairs, and subsequently, the similarity t formation model was calculated to determine the retreat and creep displacements measurement device was developed (Figure 14b), and the algorithm program inclu radar imaging and image registration were embedded.The field text was perform In CUMT, the authors of this paper provided a novel measurement solution with the ultra-wideband (UWB) radar imaging method [32].UWB radar is characterized by a radar with a fractional bandwidth exceeding 25%.Through transmitting electromagnetic wave signals with a strong ability to penetrate a coal-dust environment, UWB radar can obtain target or scene images all day and in all weather, which has the technical advantage of application in the complex environment at the end of a longwall face.As shown in Figure 14a, the radar was mounted on a slide-way, and the slide-way was placed on the roadway conveyor structure connected to the head of the AFC.The radar was moved along the slide-way to image the bolt-plates.Two imaging results were obtained before and after the movement of the longwall face.Then, the feature-based image registration algorithm was employed to identify the correct-match pairs, and subsequently, the similarity transformation model was calculated to determine the retreat and creep displacements.The measurement device was developed (Figure 14b

The Backward Calibration of Shearer Trajectory
According to the measured retreat and creep displacements outlined in Section 3 the start and end points of each cutting cycle can be determined.In the LASC, the min mum-variance fixed-interval smoothing (MFS) algorithm was applied to correct t shearer trajectory backwardly when the shearer remains stationary at the end of t longwall face [33].In fixed-interval smoothing, the estimation of the current state is bas on the utilization of the measurement data from both before and after the current tim within the interval.Smoothing is an off-line processing algorithm.Compared with filte ing, smoothing can provide better estimation accuracy with the double computation loa The minimum-variance fixed-interval smoothing algorithm is briefly expressed as f lows.
Suppose that the system satisfies the state equation and observation equation Equations ( 1) and ( 2).
where Xk is the state vector, Fk is the state transition matrix, Bk is the noise transition m trix, and Wk is the state noise whose covariance is Qk.
where Zk is the observation vector, Hk is the observation transition matrix, and Vk is t observation noise whose covariance is Rk.

The Backward Calibration of Shearer Trajectory
According to the measured retreat and creep displacements outlined in Section 3.2, the start and end points of each cutting cycle can be determined.In the LASC, the minimumvariance fixed-interval smoothing (MFS) algorithm was applied to correct the shearer trajectory backwardly when the shearer remains stationary at the end of the longwall face [33].In fixed-interval smoothing, the estimation of the current state is based on the utilization of the measurement data from both before and after the current time within the interval.Smoothing is an off-line processing algorithm.Compared with filtering, smoothing can provide better estimation accuracy with the double computation load.The minimum-variance fixed-interval smoothing algorithm is briefly expressed as follows.
Suppose that the system satisfies the state equation and observation equation as Equations ( 1) and (2).
where X k is the state vector, F k is the state transition matrix, B k is the noise transition matrix, and W k is the state noise whose covariance is where Z k is the observation vector, H k is the observation transition matrix, and V k is the observation noise whose covariance is R k .
There are N sample data in the system.The smoothing algorithm has two steps.
where K k is the gain, which can be given as ( 5), and P k is the mean square of the system, which is updated as (6).
Therefore, the estimated output is expressed as In CUMT, the authors of this paper proposed the global optimization model (GOM) for shearer trajectory through borrowing the simultaneous localization and mapping (SLAM) technology.The SLAM frame is divided into front-end and back-end procedures [34,35].The front-end process acquires the environment information using a camera or lidar to realize the map construction.The back-end step is to realize the map optimization and obtain the estimated pose according to the constraint information from the loop closure.This step is generally implemented using g2o [36] and Ceres-solver [37].The GOM is described in detail as follows.
The dead-reckoning algorithm is used to calculate the shearer position based on the INS and axial encoder as (8).
where N k , E k , and U k are the shearer measurement position in the north, east, and up; v k is the shearer velocity provided by the axial encoder; T is the sampling period; and ϕ k and θ k are the heading and pitch angles measured by the INS.As introduced in Section 3.1, the heading drift error is much larger than the drift error of the pitch.Therefore, this paper only considers the heading drift error.According to the dead-reckoning algorithm, the position error caused by the heading drift in the north (∆N k ) from k − 1 to k can be expressed as where ∆ϕ k is the absolute drift error of heading angle at k time, which is the sum of relative drift error (e k ) in each sampling period as (10).
Similarly, the position error caused by the heading drift in the east (∆E k ) from k − 1 to k is given as (13).
∆E k is expanded into a power series of ∆ϕ k as where Based on the above analysis, the objective function F(e k ) is defined as where m is the number of sampling periods in a cutting cycle, and ∆P N and ∆P E are specifically described as (17).
where N 1 and E 1 are the measured position coordinates of the start point in the north and east, N m and E m are the measured position coordinates of the end point, N start and E start are the accuracy position coordinates of the start point, and N end and E end are the accuracy position coordinates of the end point.Therefore, the global optimization problem of shearer positioning trajectory is reformulated as solving the minimum value of the objective function F(e k ) as expressed in (18).In this study, the genetic algorithm (GA) is employed to compute this equation.
The corrected heading angle is obtained via (19), which is used to obtain the shearer optimization trajectory with the dead-reckoning algorithm.
In order to compare the performance of MFS and the GOM, an experiment was carried out as shown in Figure 15.The INS was installed at the center location of the mobile platform, and the axial encoder was connected to the wheel of mobile platform.At the same time, a Global Positioning System-Real-Time Kinematic (GPS-RTK) mobile station was installed above the INS, while the GPS-RTK base station was securely fixed on a predetermined location with known coordinates.The measurement trajectory of the base station was used to evaluate the positioning accuracy of the mobile platform.Additionally, it provided the position coordinates of the start point and end point for each cutting cycle.GPS-RTK height measurement exhibited an accuracy of less than 15 mm, while plane measurement demonstrated an accuracy of less than 8 mm.The mobile platform simulated four cutting cycles at a velocity of 0.1~0.2m/s, and each cutting cycle covered a distance of about 100 m.The calculation period is set as 0.5 s.There were 2013, 2182, 2309, and 2047 sampling data during four cutting cycles, respectively.Figure 16 shows the comparison between GPS-RTK trajectory and shearer trajectories without processing, with MFS, and with GOM.It was evident that the trajectories with MFS and the GOM exhibited a higher degree of proximity to the RTK trajectory in comparison to the unprocessed trajectory.The position error in the north and east during each cutting cycle were calculated as described in Figures 17-20.For both the north and the east, the absolute values of position error with MFS first increased and then decreased.However, there was no such trend in position error with the GOM, which indicated that the GOM could restrain the heading drift well.The maximum position error during four cutting cycles with MFS and the GOM are listed in Table 1.The mean errors with MFS in the north and east were 0.1551 m and 0.1920 m, while the mean errors with the GOM were 0.0634 m and 0.0786 m, respectively.Table 2 shows the recorded duration with MFS and the GOM for four cutting cycles.In the GOM, the population size was 20 individuals, and the number of generations was set to 100.It was easily observed that the GOM took much more time than MFS.In brief, MFS had an advantage in terms of computation load, while the GOM achieved excellent accuracy.
determined location with known coordinates.The measurement trajectory of th tion was used to evaluate the positioning accuracy of the mobile platform.Add it provided the position coordinates of the start point and end point for each cutt GPS-RTK height measurement exhibited an accuracy of less than 15 mm, w measurement demonstrated an accuracy of less than 8 mm.The mobile platfo lated four cutting cycles at a velocity of 0.1~0.2m/s, and each cutting cycle cove tance of about 100 m.The calculation period is set as 0.5 s.There were 2013, 2 and 2047 sampling data during four cutting cycles, respectively.Figure 16 show parison between GPS-RTK trajectory and shearer trajectories without proces MFS, and with GOM.It was evident that the trajectories with MFS and the GOM a higher degree of proximity to the RTK trajectory in comparison to the unproc jectory.The position error in the north and east during each cutting cycle were as described in Figures 17-20.For both the north and the east, the absolute val sition error with MFS first increased and then decreased.However, there wa trend in position error with the GOM, which indicated that the GOM could re heading drift well.The maximum position error during four cutting cycles with the GOM are listed in Table 1.The mean errors with MFS in the north and east w m and 0.1920 m, while the mean errors with the GOM were 0.0634 m and 0.0 spectively.Table 2 shows the recorded duration with MFS and the GOM for fo cycles.In the GOM, the population size was 20 individuals, and the number of ge was set to 100.It was easily observed that the GOM took much more time tha brief, MFS had an advantage in terms of computation load, while the GOM ach cellent accuracy.

Discussion
The industrial experiments in acquiring the 3D shearer position conducted b LASC and CUMT have all demonstrated satisfactory performance, which indicates integrated navigation using the INS and axial encoder is an effective approach fo dressing the shearer automation positioning.One difference is that the LASC uses th SEA PHINS INS, while the Spatial FOG INS is adopted in CUMT.The cost of the Sp FOG INS is only one fifth that of the IXSEA PHINS INS.The same performance as a tary INS is achieved because the authors of this paper develop a series of error redu

Discussion
The industrial experiments in acquiring the 3D shearer position conducted b LASC and CUMT have all demonstrated satisfactory performance, which indicates integrated navigation using the INS and axial encoder is an effective approach fo dressing the shearer automation positioning.One difference is that the LASC uses th SEA PHINS INS, while the Spatial FOG INS is adopted in CUMT.The cost of the Sp FOG INS is only one fifth that of the IXSEA PHINS INS.The same performance as a tary INS is achieved because the authors of this paper develop a series of error redu

Discussion
The industrial experiments in acquiring the 3D shearer position conducted by the LASC and CUMT have all demonstrated satisfactory performance, which indicates that integrated navigation using the INS and axial encoder is an effective approach for addressing the shearer automation positioning.One difference is that the LASC uses the IXSEA PHINS INS, while the Spatial FOG INS is adopted in CUMT.The cost of the Spatial FOG INS is only one fifth that of the IXSEA PHINS INS.The same performance as a military INS is achieved because the authors of this paper develop a series of error reduction algorithms through fully analyzing the longwall mining method as introduced in Section 3.1.
For the measurement of longwall retreat and creep displacements, the proposed SAR imaging method has two advantages.First, the propagation of radar signals in underground mines is hardly affected by the presence of dust and moisture.Second, this method is an autonomous measurement technology which does not depend on external information.This method images the bolt-plates fixed in the roadway wall as the targets due to their higher reflective intensity.Although the surrounding objects may affect the imaging result, this method still has strong robustness from the final result of image registration.
Compared with MFS, the GOM has better performance in backward-correcting the shearer trajectory.Because it needs to iterate to find the optimal value with GA, the GOM has more working time.In the experiment, there are about 2000 data in each cutting cycle, which takes 4 min for the GOM to complete.If a typical longwall face is 300 m long, the running time of the GOM (more than 12 min) will be greater than the time when the shearer is stationary at the end of the longwall face, which limits its practical application.Therefore, it is an urgent problem to find a backward calibration method with high precision and small calculation load.

Conclusions
In order to realize the automatic and accurate positioning of shearers in underground mines, the LASC and CUMT adopt the same technical route, which includes three key technologies, the shearer inertial navigation system, the measurement of longwall retreat and creep displacements, and the backward calibration of the shearer trajectory.With INS as the core unit, the LASC and CUMT develop SPMS and SPAS, respectively.At the end of a longwall face, a scanning laser and a FMR 250 microwave radar are used to measure the retreat and creep displacements, and a UWB radar is adopted in CUMT to measure those two displacements with consideration of the complex environment with dust and water vapor.In order to perform backward calibration of the shearer trajectory, MFS and the GOM are proposed by the LASC and CUMT, respectively.Comparisons are made through the experiment, which shows that MFS has better performance in computation load, while the GOM achieves satisfactory accuracy.Next, a high efficiency and accurate algorithm to back-correct the shearer trajectory is our research goal.

Figure 1 .
Figure 1.The diagram of the shearer, AFC, and roof support system.Figure 1.The diagram of the shearer, AFC, and roof support system.

Figure 1 .
Figure 1.The diagram of the shearer, AFC, and roof support system.Figure 1.The diagram of the shearer, AFC, and roof support system.

Figure 2 .
Figure 2. The diagram of (a) the development stage of LASC [6] and (b) the technical framewor LASC.

Figure 2 .
Figure 2. The diagram of (a) the development stage of LASC [6] and (b) the technical framework of LASC.

Figure 2 .Figure 3 .
Figure 2. The diagram of (a) the development stage of LASC [6] and (b) the technical framework of LASC.
Appl.Sci.2023,13,  x FOR PEER REVIEW 4 of 17 AFC behind the shearer has been moved into the n + 1 cycle.When the coal is cut, the roof support systems support the roof of the coal seam.There are approximately 200 roof support systems in a typical longwall face.After the AFC is pushed towards the coal seam, the roof support systems are relocated along the advancing direction.Behind the roof support systems, the collapse of the roof results in the formation of a goaf.

Figure 4 .
Figure 4. Typical plan view of (a) a coal mine and (b) a longwall face [11].

Figure 5 .Figure 6 .
Figure 5.The shearer, AFC, and roof support system across the longwall face in an underground mine.

Figure 4 .
Figure 4. Typical plan view of (a) a coal mine and (b) a longwall face [11].

Figure 4 .
Figure 4. Typical plan view of (a) a coal mine and (b) a longwall face [11].

Figure 5 .Figure 6 .
Figure 5.The shearer, AFC, and roof support system across the longwall face in an underground mine.

Figure 5 .
Figure 5.The shearer, AFC, and roof support system across the longwall face in an underground mine.

Figure 4 .
Figure 4. Typical plan view of (a) a coal mine and (b) a longwall face [11].

Figure 5 .Figure 6 .
Figure 5.The shearer, AFC, and roof support system across the longwall face in an underground mine.

Figure 6 .
Figure 6.The diagram of the AFC profile as the shearer moves.Figure 6.The diagram of the AFC profile as the shearer moves.

Figure 11 .
Figure 11.The diagram of the longwall retreat and creep displacements.

Figure 10 .
Figure 10.The diagram of (a) the underground field test in Shanxi and (b) the shearer trajectory acquired using the SPAS [28].

Figure 10 .
Figure 10.The diagram of (a) the underground field test in Shanxi and (b) the shearer trajectory acquired using the SPAS [28].

Figure 11 .
Figure 11.The diagram of the longwall retreat and creep displacements.

Figure 11 .
Figure 11.The diagram of the longwall retreat and creep displacements.

Figure 12 .
Figure 12.The diagram of (a) the SICK LMS200 scanning laser and (b) ExScan.

Figure 13 .
Figure 13.The diagram of (a) the Endress-Hauser FMR 250 radar and the (b) field test in an underground mine [29-31].

Figure 14 .
Figure 14.The diagram of (a) the measurement principle, (b) the measurement device, and (c) a fie test in an underground coal mine [32].

Figure 14 .
Figure 14.The diagram of (a) the measurement principle, (b) the measurement device, and (c) a field test in an underground coal mine [32].

Figure 15 .
Figure 15.The diagram of the experiment site and device.

Figure 15 .
Figure 15.The diagram of the experiment site and device.

Figure 17 .
Figure 17.The position error of first cutting cycle in the (a) north and (b) east.

Figure 18 .
Figure 18.The position error of the second cutting cycle in the (a) north and (b) east.Figure 18.The position error of the second cutting cycle in the (a) north and (b) east.

Figure 19 .Figure 20 .
Figure 19.The position error of the third cutting cycle in the (a) north and (b) east.

Figure 19 .Figure 19 .Figure 20 .
Figure 19.The position error of the third cutting cycle in the (a) north and (b) east.

Figure 20 .
Figure 20.The position error of the fourth cutting cycle in the (a) north and (b) east.

Table 1 .
The maximum position error (m) with MFS and the GOM during four cutting cycles.

Table 2 .
The elapsed time (s) with MFS and the GOM during four cutting cycles.

Table 1 .
The maximum position error (m) with MFS and the GOM during four cutting cycles.

Table 2 .
The elapsed time (s) with MFS and the GOM during four cutting cycles.

Table 1 .
The maximum position error (m) with MFS and the GOM during four cutting cycles.

Table 2 .
The elapsed time (s) with MFS and the GOM during four cutting cycles.