Stiffness Control of Cable-Driven Continuum Robots Based on Null Space Tension Optimization

Abstract

The inherent compliance of cable-driven continuum robots (CDCRs) enables safe interaction but often degrades manipulation accuracy and payload capacity. To address this trade-off, this article proposes a novel variable stiffness control (VSC) framework that exploits actuation redundancy for stiffness regulation. Unlike existing approaches, where internal tension redistribution perturbs the end-effector pose due to structural coupling, the proposed method regulates cable preloads within the actuation null space, achieving decoupling between stiffness modulation and task-space motion. A unified analytical model is formulated by incorporating the Hessian of potential energy to capture second-order geometric nonlinearities, thereby revealing the coupling between cable tensions and Cartesian stiffness. Based on this model, a null space optimization scheme is developed to solve the inverse tension distribution problem. Furthermore, a stiffness–tension mapping is established to convert equivalent directional stiffness specifications into feasible tension commands, while maintaining static equilibrium and actuator saturation constraints via quadratic programming (QP). Experimental results on a prototype validate the proposed framework, demonstrating an approximately 75% increase in equivalent stiffness while maintaining sub-millimeter positioning accuracy under large-scale internal tension redistribution. Note to Practitioners—This paper addresses a fundamental challenge in the practical deployment of CDCRs. Although these systems are well suited for operation in confined environments, their inherent compliance limits their ability to perform precision force-interaction tasks, including drilling, cutting, and pushing. A software-based control framework is developed to overcome this limitation without requiring hardware modifications. By leveraging cable redundancy, the proposed method computes optimal tensions to establish a stiff and stable configuration that can resist external disturbances while preserving the end-effector pose. In contrast to existing approaches that induce pose drift during stiffness enhancement, the proposed method achieves decoupling between stiffness modulation and end-effector motion. This enables system integrators to enhance the performance of existing platforms through control-level upgrades alone. The proposed framework is particularly beneficial for applications requiring lightweight and variable-compliance manipulation, such as minimally invasive surgery, on-orbit servicing, and hazardous remote maintenance. Moreover, the convex QP formulation ensures low computational overhead. With an average solve time of approximately 0.45 ms on standard hardware, the method supports high-frequency real-time control and ensures reliable performance in interaction scenarios.