Efficient Dynamics Modeling and Adaptive Tracking Control for a Rigid‐Flexible Manipulator

Vibration suppression and trajectory tracking are pivotal areas of current robotics research, significantly influencing the operational performance of flexible manipulators. This article proposes a novel dynamics modeling strategy for flexible manipulators based on the multi‐body system transfer matrix method, which achieves comparable accuracy to the traditional Lagrange method while improving computational efficiency by approximately 35.5% and 35.9% in two representative cases, respectively. On this basis, an adaptive hybrid control strategy is developed by integrating the dynamics model with an improved particle swarm optimization (PSO) algorithm and a fuzzy approximation‐based backstepping controller. The improved PSO accelerates convergence and reduces residual elastic vibrations to 5.28E5 and 7.16E5 m under two typical cases, representing a reduction of over 80% compared to baseline trajectory planning methods. The proposed controller further decreases residual vibration to 5.94E5 m while ensuring trajectory tracking errors remain below , even under external disturbances. These simulation results validate the effectiveness of the proposed approach, demonstrating clear improvements in both vibration suppression and tracking accuracy compared to conventional PD and Legendre polynomial‐based controllers.