General kinematics model and algorithm for three continuum surgical robots

Continuum surgical robots, with their flexible structure and continuous bending characteristics, have shown excellent adaptability and precise control capabilities in minimally invasive surgery, but their complex kinematic characteristics pose great challenges to modeling and control. This paper proposes a general kinematic model and inverse kinematics solution algorithm for the cable-driven continuum robot, the concentric tube continuum robot and the hybrid continuum robot. Based on the constant curvature assumption, the structures of the three continuum robots are simplified into a general model. The Archimedean spiral models the continuum robot’s terminal trajectory, simplifying inverse kinematics. The proposed inverse kinematics algorithm has high solution efficiency and accuracy. Simulation results confirm the algorithm’s effectiveness, with an average solution time of 2.88 × 10^–3s. These findings offer theoretical and technical support for continuum surgical robot path planning and control in complex surgical environments.