ESO-SMC-based control method for underground coal mine robotic arms

To address insufficient control accuracy and weak robustness of underground coal mine robotic arms subject to strong nonlinearities, parameter uncertainties, and complex external disturbances, a control method based on an Extended State Observer (ESO) and Sliding Mode Control (SMC) was proposed. Robotic arm dynamic equations incorporating model parameter uncertainties, unmodeled dynamics, and external disturbances were established using the Lagrangian method, and an extended state-space model was constructed by augmenting the state variables. A third-order ESO was designed to treat parameter perturbations, time-varying friction, and underground impact loads collectively as the total system disturbance for real-time online estimation and feedforward compensation, thereby reducing the dependence of SMC on high switching gains. A sliding mode control law was designed using the disturbance estimates, with a saturation function replacing the sign function to suppress chattering. The stability of the closed-loop system was established through an analysis based on Lyapunov stability theory. Simulations were conducted on joints 4–6 of a PUMA560 robotic arm. The results showed that the ESO rapidly and effectively estimated the total system disturbance, with an estimation error of no more than 5%. Under ESO-SMC, the steady-state tracking Root Mean Square Error (RMSE) values for joints 4–6 were 0.026 1, 0.029 1, and 0.016 9°, respectively, representing reductions of 45.2%, 45.4%, and 26.2% compared with conventional SMC. The maximum tracking errors were 0.046 3, 0.055 0, and 0.032 5°, respectively, representing reductions of 38.4%, 33.7%, and 17.3%. The average RMSE and average maximum tracking error decreased by 41.7% and 32.3%, respectively. The sliding surface also converged faster and exhibited smaller steady-state fluctuations. These results confirm that the proposed method provides good trajectory tracking accuracy and disturbance rejection performance.