Kinematic Analysis of Magnetic Continuum Robots Using Continuation Method and Bifurcation Analysis

Magnetic continuum robots (m-CR) have grown interest in several applicative contexts that take benefits from their high flexibility and remote control. When submitted to external magnetic fields, m-CR exhibit large elastic deformations, which may lead to a highly nonlinear and complex behavior that is yet difficult to analyze. This letter aims to provide a tool to improve the understanding of m-CR kinematics. To do so, a numerical approach composed of continuation methods and bifurcation analysis is proposed. The numerical tool is first described. Qualitative and quantitative results are further introduced by computing multiple equilibrium branches and bifurcations of m-CR configurations within homogeneous and inhomogeneous magnetic fields. Our simulations are ultimately compared to experimental data using a magnetic navigation system.