A Variable Curvature Model for Multi-Backbone Continuum Robots to Account for Inter-Segment Coupling and External Disturbance

Multi-backbone continuum robots demonstrated potentials for dexterous manipulation with proper payload capability in minimally invasive surgeries. Most prior works assume constant curvature shapes of the continuum segments in the modeling and control of the multi-backbone continuum robots. The actuation coupling effects between adjacent continuum segments and the segments' variable curvature shapes under environmental interactions have not been fully addressed by a static-kinematic model specifically for multi-backbone continuum robots. This letter hence proposes a variable curvature model for multi-backbone continuum robots with relatively low bending curvature based on the Cosserat rod theory. The model focuses on the major factors that affect the robot's shape: the length-prescribed push-pull actuation, the elastic elongation of the backbone rods, and the external loads. With five assumptions made to simplify the constraints in the multi-backbone continuum robot, a compact statics-kinematics formulation is derived with computational performance acceptable for real-time control. Experiments were conducted on a continuum robotic system to quantify the modeling accuracy and computational efficiency. The proposed model was shown to have substantially improved accuracy over the constant curvature model. The average computational time for solving the inverse kinematics was 0.7ms on a 2.6 GHz Intel i7-5600U platform, which is promising for real-time control.