Design and Modeling of Multi-vertebrae Continuum Robot for Minimally Invasive Surgery

The constant curvature assumption is normally utilized in kinematic modeling of continuum manipulators due to its simplicity. Nevertheless, in practical applications, factors such as frictional disturbances may cause the curvature of a continuum manipulator to deviate from being constant. In this article, we design a novel multi-vertebrae continuum manipulator that utilizes the uniform joint deformation curvature of a superelastic NITI alloy rod. We propose kinematic modeling approach for a multi-vertebrae continuum manipulator. To improve the unevenness of joint angles and increase motion accuracy, we inserted elastic beams into the multi-vertebrae continuum manipulator. The design takes into account frictional forces, and we established geometric constraint equations and force equilibrium equations for the hinged continuum manipulator. We employed an identification method to establish the physical equations of the deformation section. By solving these equations and analyzing the geometric relationships, we obtained the mapping relationship between the driving screw force and the end displacement of the continuum manipulator. To prove the effectiveness of the proposed method, we performed MATLAB simulations. This paper serves as a reference for the design and modeling of future minimally invasive surgical manipulators.