The improvements to catheter manipulation by the use of robot-assisted catheter navigation for endovascular procedures include increased precision, stability of motion and operator comfort. However, navigation through the vasculature under fluoroscopic guidance is still challenging, mostly due to physiological motion and when tortuous vessels are involved. In this paper, we propose a motion-adaptive catheter navigation scheme based on shape modelling to compensate for these dynamic effects, permitting predictive and dynamic navigations. This allows for timed manipulations synchronised with the vascular motion. The technical contribution of the paper includes the following two aspects. Firstly, a dynamic shape modelling and real-time instantiation scheme based on sparse data obtained intra-operatively is proposed for improved visualisation of the 3D vasculature during endovascular intervention. Secondly, a reconstructed frontal view from the catheter tip using the derived dynamic model is used as an interventional aid to user guidance. To demonstrate the practical value of the proposed framework, a simulated aortic branch cannulation procedure is used with detailed user validation to demonstrate the improvement in navigation quality and efficiency.