Abstract: For a long time, the advance hydraulic support has relied on manual operation during the step-by-step movement process, resulting in problems such as poor positioning accuracy, low efficiency and prominent safety risks, which have seriously restricted the development of intelligent support technology. This study proposes a navigation method for advance hydraulic support movement based on the optimal support path curve, aiming to achieve accurate perception, autonomous planning and coordinated control during the step-by-step support movement process. The navigation method constructs a 2D grid map of the roadway by means of tight coupling between LiDAR and Inertial Measurement Unit (IMU). The Random Sample Consensus (RANSAC) algorithm is adopted for robust fitting of the left and right boundary curves of the roadway. Combined with the Dynamic Time Warping (DTW) algorithm, the spatial correspondence of boundary points is established to generate the optimal support path curves for the left and right supports. These curves characterize the ideal support positions of the supports along the roadway direction, providing a geometric reference for pose optimization. The planar kinematics model of the hydraulic support is established to solve its pose in real time. Aiming at minimizing the area of the closed region between the hydraulic support projection and the support path curve, the optimal terminal pose of the single-side hydraulic support movement is solved. A smooth movement path is planned based on the third-order Bezier curve, and the hydraulic cylinder stroke planning is completed through kinematic inverse solution and time-scaling strategy, so as to realize the coordinated control of multiple hydraulic cylinders. Simulation and experimental results show that the actual support path obtained after the hydraulic cylinders execute the planned displacement is in high agreement with the ideal path planned by the navigation system. The hydraulic support exhibits stable path tracking during movement, with an average maximum position error of 22.91 mm and a direction angle error less than 0.14°. Meanwhile, the hydraulic support maintains a safe distance from the roadway ribs without interference. High-precision path tracking during the support shifting process is realized, and the control accuracy of position and direction angle meets the safety requirements of underground support operation.