Design, modeling, and validation of a self-balancing cable-driven continuum robot using internal force equilibrium

Ensuring effective operation is crucial for continuum robots, especially in tasks requiring precision under varying external loads. This study introduces a Self-Balancing Cable-Driven Continuum Robot (SB-CDCR) designed to minimize vibrations and enhance mechanical stability, defined here as the robot's ability to maintain shape, resist deformation, and suppress oscillations during motion. The initial robot design consists of three modules, each composed of adjacent disk pairs interconnected by four springs: one central compression spring for axial support and three lateral tension springs for passive balancing. The proposed design integrates several key features, including a lightweight structure, high flexibility, and reinforced internal support. This configuration, combined with a pre-stressed internal force distribution, ensures smooth motion, vibration suppression, and improved structural integrity, thereby enabling precise control of spatial movements. Kinematic models are developed using the Constant Curvature (CC) approach, allowing the analytical formulation of forward kinematics and workspace analysis. The inverse kinematics is addressed as a quadratic optimization task and is effectively solved using the Weighted Particle Swarm Optimization (W-PSO) algorithm. Numerical simulations demonstrate accurate trajectory tracking with a positional error of 2.616×10-3 mm and a computation time of 3.954 ms. Experimental validations further confirm the robot's accuracy under load-handling conditions.