Capstan-driven Continuum Surgical Robot: Design, Modeling, and Perception

The evolution of continuum robots in minimally invasive surgery has been driven by their ability to navigate complex, tortuous anatomical pathways. Early designs relied on rigid robotic arms, which lacked flexibility, limiting access to deep or convoluted regions. The advent of flexible, cable-driven continuum robots introduced high degrees of freedom and dexterity, enabling navigation through intricate pathways such as the gastrointestinal tract or vascular systems. Representative works by Laschi et al. and Webster et al. demonstrated the potential of soft and flexible structures, but these systems often lacked integrated sensing capabilities for shape and force, which are critical for safe and autonomous operation.

Traditional sensing approaches include external imaging, embedded fiber Bragg gratings, and strain gauges. While effective, these methods often involve bulky hardware, limited update rates, or complex calibration procedures. The challenge has been to develop compact, high-frequency sensing mechanisms compatible with the limited space within clinical tools. Cable-driven actuation remains dominant due to its compactness and efficiency, but integrating sensors within the tight confines of a capstan-driven system has proven difficult. Existing static models based on Euler–Bernoulli theory are inadequate for short, thick segments, especially under complex cable routing and non-planar interactions. Consequently, achieving accurate, real-time shape and force sensing in such systems remains an open problem, impeding progress toward fully autonomous or semi-autonomous surgical robots.

The core problem addressed in this work is how to realize high-precision, high-frequency shape and force sensing within a space-constrained, capstan-driven continuum robot. The limited internal volume of the robot's actuation module prevents the integration of traditional tension sensors, leaving cable tension unmeasured. This impairs the robot's ability to accurately estimate its shape and contact forces, which are essential for safe navigation and interaction with tissues. Additionally, the unconventional joint configurations resulting from spatial cable routing introduce complex nonlinear effects, such as shear deformation and multi-cable interactions, which are poorly modeled by classical slender-beam theories. These modeling inaccuracies lead to unreliable perception, especially under dynamic or complex bending conditions. The challenge is to develop a sensing and modeling framework that maintains high accuracy and real-time performance without enlarging the robot's footprint, enabling its deployment in minimally invasive surgical scenarios.

This work introduces several key innovations: 1) A micro-deformation based tension sensing mechanism embedded within the motor bracket, utilizing strain gauges to measure tiny elastic deformations caused by cable tension, achieving high-frequency (up to 1000Hz) measurements without space overhead. 2) A short-thick-beam static model that explicitly accounts for shear effects and multi-cable interactions, overcoming the limitations of classical slender-beam assumptions. 3) A parallelized matrix-based computation framework that organizes the mechanical variables of multiple beam segments into batch operations, enabling model updates at over 200Hz. 4) A spatial cable routing strategy that distributes cables along staggered paths within the limited diameter, reducing channel count from eight to four per rigid ring, thus optimizing space utilization. 5) Integration of a proximal multi-axis force/torque sensor, providing additional contact force data, and a multi-modal sensor fusion algorithm for stable shape and force estimation. These innovations collectively enable high-fidelity perception in space-constrained, multi-cable continuum robots, facilitating autonomous and semi-autonomous surgical functions.

• �� Mechanical Design: Incorporate a compliant element into the motor bracket, bonded with strain gauges, to measure micro-deformation induced by cable tension. The deformation signals are calibrated via neural networks to obtain tension values.
• �� Modeling: Develop a multibody static model based on short-thick-beam theory, explicitly capturing shear deformation and multi-cable effects. The model employs transfer matrices for each beam segment, considering non-planar cable routing and complex joint configurations.
• �� Parallel Computation: Organize the mechanical variables of all beam segments into matrix form, enabling batch processing of deformation and force calculations, significantly accelerating computation speed.
• �� Cable Routing: Design a staggered, multi-layer cable layout within the limited space, reducing the number of channels per rigid ring and supporting dense cable configurations.
• �� Sensing Fusion: Integrate strain gauge signals, encoder displacements, and proximal force/torque data, and apply an iterative estimation algorithm (Algorithm 1) to solve for shape, contact point, and force simultaneously.
• �� Experimental Validation: Conduct tension calibration, shape reconstruction, and contact force sensing tests on prototypes, analyzing errors and real-time performance metrics.

The experimental setup involves fabricating single- and dual-segment continuum robot prototypes with 3.5mm diameter and wall thickness below 0.4mm, driven by 8 cables. Calibration experiments used known weights to establish the strain gauge-tension relationship, achieving an average error of 0.12N. Shape estimation tests involved applying known bending loads and comparing the reconstructed tip position against ground truth, with errors below 2mm. Contact force sensing was validated by pressing the robot tip against calibrated force sensors at various locations, demonstrating force measurement errors within 0.4N. The system's update rate was measured under dynamic conditions, consistently exceeding 200Hz. Additional tests assessed the spatial cable routing scheme's effectiveness in dense packing, confirming the feasibility of 8 cables within minimal space. Cross-scenario robustness was evaluated by varying load and bending conditions, confirming the model's adaptability and stability. The experiments collectively demonstrate the system's high accuracy, real-time capability, and suitability for clinical applications.

The tension sensing mechanism achieved an average error of 0.12N across a range of 0-9.5N, with maximum errors not exceeding 0.4N, validating its high precision. The shape estimation maintained tip position errors below 2mm under various bending scenarios, demonstrating robustness against nonlinear shear effects. The parallel computation framework enabled model updates at over 200Hz, ensuring real-time feedback essential for surgical control. The spatial cable routing scheme successfully supported 8 cables within a diameter of 3.5mm, with a 50% reduction in channel count per rigid ring, optimizing space without sacrificing performance. Contact force sensing accuracy was confirmed through experiments, aligning closely with external force measurements. Overall, the integrated sensing and modeling approach significantly advances the capability of miniaturized continuum robots, enabling reliable perception in complex, space-limited environments.

This technology can be directly applied to micro-invasive surgical procedures, providing high-frequency shape and force feedback for navigation and tissue manipulation. It supports autonomous or semi-autonomous control strategies, reducing surgeon workload and improving safety. The compact design makes it suitable for endoscopic and catheter-based interventions, especially in tortuous or confined anatomical regions. Beyond medical applications, the sensing framework can be adapted for industrial micro-assembly, precision manipulation, and inspection tasks requiring high spatial resolution and real-time feedback. The prerequisites include stable hardware calibration, robust signal processing, and integration with control algorithms. Its deployment promises to enhance surgical precision, reduce complications, and facilitate the development of intelligent robotic systems in constrained environments.

The current model's accuracy may decline under extreme bending or high load conditions where shear effects become nonlinear or unmodeled, potentially affecting force estimation reliability. The spatial cable routing, while optimized, may still face interference or cross-talk in highly convoluted paths, necessitating further routing strategies. Hardware dependencies, such as high-frequency sensors and computational resources, limit portability and ease of clinical integration. Additionally, the calibration process is complex and sensitive to environmental factors, which could impact long-term stability. Future work should focus on adaptive modeling, sensor miniaturization, and robust calibration methods to address these limitations and expand clinical applicability.