Design and modeling of a multi-backbone continuum robot with a large extension ratio

Multi-backbone continuum robots (MBCRs), operated through parallel elastic rods, offer superior compliance compared to rigid robots and improved reliability over tendon-driven continuum robots. Despite their high performance in flexible manipulation, MBCRs have been underutilized on mobile robotic platforms due to packaging constraints. In this work, we present a novel MBCR design with a large extension ratio, comprising two extensible sections connected in series. Each section is equipped with intermediate constraints, providing significant length variability and omnidirectional bending capabilities. To analyze the robot’s kinematics, we develop a modeling approach based on Euler–Bernoulli beam theory and Lagrangian mechanics, enhanced with an optimization-based solution method. To validate our design and model, we construct an MBCR prototype with an extension ratio of 5.0. Both theoretical and experimental validations demonstrate that intermediate constraints significantly expand the workspace of the extensible sections and reduce the compressive force on the rods. Additionally, we evaluate the feasible space of the model and test the robot’s capability in path following, with an average deviation of only 1.3% when tracking a spatial helix path.