Euler-Spiral Kinematic Modeling Of A Cable-Driven Continuum Robot With Passive Variable Stiffness For Neurosurgical Applications

This paper presents a kinematic modeling framework for a cable-driven continuum robot exhibiting passive variable stiffness along its arc-length parameter s, arising from non-uniform spacing between its vertebrae. Accurate kinematic modeling is a critical prerequisite for developing model-based control strategies for continuum robots. Unlike conventional rigid-link manipulators, continuum robots lack standardized kinematic formulations, and constant-curvature models are often adopted to map robot configurations to cable displacements and vice versa. While computationally efficient and widely used, the constant-curvature assumption may result in reduced accuracy for robots with non-uniform structural properties. To address this limitation, we propose a variable-curvature kinematic model based on Euler spirals for improved representation of the robot’s backbone geometry under actuation.