A Modular Kinetostatic External Force and Shape Prediction System Towards Tendon-Driven Continuum Robots

The ability to accurately and rapidly predict the shape of a continuum robot during physical interaction is a prerequisite for its safe and effective deployment. Kinetostatic models, which compute the robot’s shape under external loads, are critically dependent on knowing the precise location and nature of those loads. This paper presents a comprehensive framework that solves this challenge by synergistically integrating a modular, single-axis proximity sensor with a high-fidelity Chained Spatial Beam Constraint Model (CSBCM). The sensor module is pre-calibrated to provide reliable contact detection, instantly identifying the specific node on the robot’s body where an external force is applied. This critical location data allows our system to directly map a known external force to the robot’s complete 3D configuration. The computationally efficient CSBCM then rapidly solves for the robot’s final equilibrium shape. The entire framework is rigorously validated through physical experiments, demonstrating that the sensor-integrated model accurately predicts the robot’s full-body deformation with a mean tip error of 3.85 mm (5.5% relative error) and achieves processing rates of 60 Hz, well-suited for real-time control loops. This work demonstrates a practical, modular system that bridges the gap between localized sensing and state estimation, paving the way for more robust and force-aware continuum robots in medical applications. © 2025 IEEE.