Kinematic models for Cable-driven Continuum Robots with multiple segments and varying cable offsets

Cable-driven Continuum Robots (CCRs) represent a subset of flexible robotic systems with diverse applications encompassing medical, quality control, and search and rescue. Multi-segmented CCRs can independently actuate different CCR segments and deform into a series of connected circular arcs. While this method generates constant-curvature profiles, CCRs with varying radial cable offsets can generate shapes with varying curvatures. However, there are no kinematic models for such robots in the literature. This paper introduces optimization-based formulations to accurately estimate the deformed profile of CCRs, considering both variable cable offset and multi-segment configurations. The presented kinematic approach can predict the deformed profiles with an RMS error less than 5% of the total length of the robot. The application of the proposed method to determine the inverse kinematics of multi-segmented CCRs is demonstrated—even considering obstacles in the robot’s workspace. Practical implementation of the formulation is illustrated using a 3-segmented CCR with a cable-driven soft gripper that imitates biological grippers such as an elephant’s trunk or creeper vine to grasp objects.