Abstract: When continuum robots are driven at high speeds, their inherent flexibility leads to significant residual vibrations during motion, which severely impacts motion precision. To address this issue, this paper proposes a driving optimization design method for suppressing residual vibrations in any configuration, based on the dynamic model of cable-driven continuum robots. A differential-algebraic equation model is developed, taking cable length as the driving variable for the continuum robot. This model is then used to analyze the factors influencing residual vibrations in various typical cable-driven continuum robots. Furthermore, a NURBS(non-uniform rational B-spline) curve-based dynamic driving laws is devised, and an optimization mathematical formulation is derived to minimize residual vibrations. Experimental results show that, prior to driving optimization, the maximum residual vibration amplitudes during high-speed(1 s) and medium-speed(5 s) motions are 108.4 and 11.1 mm, respectively. After optimization, these amplitudes are reduced to 20.1 and 0.9 mm, achieving up to 84.5% reduction in residual vibration indicator. These results strongly validate the effectiveness of the proposed dynamic driving optimization design method. Additionally, the proposed method is applied to scenarios such as rapid targeting and fast object transfer, significantly enhancing the dynamic motion performance of the continuum robot.