Lyapunov-based nonlinear model predictive control for the path following of bevel-tip flexible needles in 3D environment

This paper develops a Lyapunov-based nonlinear model predictive control (NMPC) method for the path-following task of bevel-tip flexible needle in 3D environments. First, a nonholonomic and nonlinear kinematic model of the bevel-tip flexible needle system is established to describe the needle inserting and steering motion. Then, an efficient NMPC strategy is designed to deal with the system nonlinearity based on the kinematic model and further guide the flexible needle to accurately track the desired 3-dimensional path. Specifically, the control Lyapunov function is also integrated into the NMPC framework to ensure the operational safety of the bevel-tip flexible needle system in human tissue. Finally, simulation experiments are carried out to demonstrate the effectiveness of the proposed approach.