Optimization of trajectory tracking accuracy and vibration suppression for continuum flexible robotic arm

Drawbacks of continuous flexible manipulators, such as insufficient trajectory tracking accuracy and obvious flexible vibration, were targeted, and an integrated hierarchical strategy of trajectory replanning and disturbance rejection control was proposed for cable-driven flexible manipulators. A STO-MPC (Stochastic Trajectory Optimization Model Predictive Control) framework was constructed. Probabilistic obstacle avoidance constraints and gradient-independent solving mechanisms were introduced to tackle the high computational delay and poor dynamic adaptability of traditional planning approaches, while stiffness constraints and residual vibration suppression requirements of flexible structures were fully satisfied. A cooperative control framework of ADO-RITSMC (Adaptive Disturbance Observer-Rapid Integral Terminal Sliding Mode Control) was established. Model-free real-time compensation for multi-source disturbances was realized, finite-time convergence of tracking errors was achieved by the improved terminal sliding mode, and residual vibration of flexible links was effectively suppressed accordingly. Comprehensive comparative tests were conducted on standard O-shaped trajectories and high-curvature V-shaped trajectories, with GO-MPC (Gaussian Observer-based Model Predictive Control), APF-MPC (Artificial Potential Field-based Model Predictive Control) sliding mode algorithms. Experimental results demonstrated that STO-MPC can achieve the lowest peak computation time, completes the convergence of obstacle state estimation within 0.5 s, and yields a steady-state velocity estimation error of 0.0015 m/s. Its trajectory tracking RMSE (Root Mean Square Error) is 18.7 % and 36.8 % lower than that of GO-MPC and APF-MPC respectively, delivering superior real-time performance, estimation stability and tracking accuracy. The proposed ADO-RITSMC reduces vibration amplitude by 16.7 % with a peak vibration acceleration of –1.0 g, and exhibits faster vibration attenuation and slighter trajectory oscillation during dynamic obstacle avoidance, which fully verifies the hierarchical collaborative advantages of STO-MPC trajectory replanning and ADO-RITSMC vibration suppression.