# Shearer-Positioning Method Based on Non-Holonomic Constraints
###### Abstract  
In the traditional shearer-positioning method, an odometer is used to assist the forward velocity correction of the inertial navigation system, but it cannot restrain the system's error divergence. For this reason, this paper proposes a shearer positioning method based on non-holonomic constraints. In this method, an inertial measurement unit and odometer are installed in the middle of the shearer body and on the traction gear, respectively, the shearer attitude, speed, and position information are calculated through the inertial measurement-unit mechanization, and the shearer's instantaneous velocity is calculated through the output of the odometer. The mechanization and error transfer process of the inertial navigation system are used to establish a Kalman filtering-state equation. The Kalman filtering observation equation is established through the difference between the projected velocity of the inertial navigation system at the joint and the output velocity of the odometer as the observation vector, and the non-holonomic constraint is introduced. Finally, the error feedback is derived from the results processed by the Kalman filtering algorithm, and the output of the inertial navigation system is corrected to obtain the optimal estimation of the shearer's attitude, speed and position. The experiment shows that compared with the traditional inertial navigation and odometer combined positioning method, the degree of divergence in the positioning results over time is significantly reduced after adding the non-holonomic constraint. The positioning method has good tracking ability for the trajectory of the shearer. The error of the positioning results in the forward direction is reduced by 66%, the lateral direction is reduced by 62%, and the vertical direction is reduced by 67%. s 2022 12 10050 10.3390/app121910050 10.3390/app121910050 10.  
process. However, since it is too difficult to establish the accurate geographical model of the fully mechanized long-wall face [5], the feasibility of this method remains to be determined. A different study [6] used the method of combining the odometer (ODO) and the inertial navigation system (INS) to correct the positioning results of the INS by collecting the speed or displacement information of the odometer. However, the odometer can adjust only the forward speed of the INS in the positioning process, and cannot correct its lateral and vertical speed. On the basis of establishing the ultrasonic positioning system, the authors of [7] used a Kalman filter (KF) algorithm to filter the combined positioning results of the inertial navigation system and the ultrasonic sensor. However, the underground non-line-of-sight (NLOS) environment reduces the measurement accuracy of the ultrasonic sensor and affects the accuracy of the ultrasonic positioning system [8]. The authors of [9; 10] constructed the INS/UWB combined-positioning scheme, which can efficiently suppress the divergence of the inertial navigation system, but it is necessary to add a large number of additional UWB anchor nodes, which increases the system's cost and complexity. In [11], a federated filter is used to form a sub filter with the inertial navigation system, the visual camera, and the odometer, respectively, in order to address the fact that single sensors with poor precision increase the positioning error of the whole positioning system in the traditional Kalman filter [12]. However, the large amount of dust, weak light, and strong vibration in the working face affect the positioning accuracy of the visual camera [13]. The authors of [14; 15; 16] established a Kalman-filter model with the distance between two INS kits as the constraint condition, which can effectively restrain the error divergence of a single kit of INS. However, the installation conditions of the two kits of the INS are strict, which affects the positioning accuracy of the model.