Backstepping sliding mode control based on dual-path extreme learning machine and disturbance observer for robotic manipulator trajectory tracking

To achieve high-precision trajectory tracking for robotic manipulators subject to unknown nonlinearities and external disturbances, a backstepping sliding mode control strategy incorporating a dual-path extreme learning machine (DP-ELM) and a disturbance observer is proposed. The DP-ELM approximates the system’s unknown nonlinearities via two parallel paths: a main path driven by joint angle errors to capture dominant nonlinearities, and an auxiliary path utilizing angular velocity errors to compensate for unmodeled high-frequency residuals. To enhance approximation capability and computational efficiency, a multi-scale feature extraction mechanism and a Top-K dynamic sparse activation strategy are integrated into the network. Furthermore, an exponentially convergent disturbance observer is designed to estimate external disturbances online. Both numerical simulations in Simulink and experiments on a physical platform of a 3-degree-of-freedom (3-DOF) robotic manipulator demonstrate that the proposed scheme yields superior tracking accuracy, rapid convergence, and strong robustness against disturbances compared to existing methods.