Geometric static coupling model and motion control study of an under-constrained temporary support robot

The shield type intelligent tunneling robot system effectively solves the problem of "mining excavation imbalance, fast mining, and slow tunneling" in coal mining, as an important component of the system, temporary support robots play a crucial role in improving operational efficiency. However, due to structural limitations, the temporary support robots can only achieve vertical lifting movements, making it difficult to effectively cope with the temporary support operations of complex roadways. To solve the problem of limited motion of the temporary support robot, an under-constrained temporary support robot was designed, and a terminal sliding mode control method based on RBF neural network block approximation was proposed to achieve high-precision motion control of the under-constrained temporary support robot. Firstly, the modified G–K formula was used to analyze the degrees of freedom of the robot. In response to the difficulty in solving the forward kinematics of the under-constrained temporary support robot, a geometric static coupling model was established, and an improved dung beetle optimization algorithm was proposed to solve the forward and inverse geometric static problems, and simulations of the geometric static problems were carried out. Secondly, a terminal sliding mode controller based on RBF neural network block approximation was designed. Given the uncertainty of the parameter matrix of the end support platform, multiple sets of RBF neural networks were used to approximate it, and the weights were adjusted online according to the adaptive law to realize the reconstruction of the dynamic model, and a robust term was designed to eliminate the model reconstruction error and external disturbances. To alleviate the chattering problem of the controller, a fuzzy system was designed to adaptively approximate the switching gain to replace the robust term, and the stability of the control system was proved by using the Lyapunov criterion. Finally, a simulation was carried out with a planar circular trajectory as an example. The results show that the single-point verification accuracy of the improved dung beetle optimization algorithm for forward and inverse kinematics is less than 10^–20, and the continuous kinematics solution results are good. The position tracking error of the terminal sliding mode control method using RBF neural network block approximation for the predetermined trajectory is 0−0.011 m, and the attitude tracking error is 0−0.003 1°. Compared with the overall approximation of the RBF neural network and PD control, the maximum tracking error is reduced by 99.0% and 95.5% respectively, and the root mean square error is reduced by 98.3% and 96.5% respectively. It is proved that the terminal sliding mode control method based on RBF neural network block approximation can further improve the motion control accuracy of the under-constrained temporary support robot and has stronger robustness under the condition of external interference.