[Paper Review] Helical Tendon-Driven Continuum Robot with Programmable Follow-the-Leader Operation

Behnam Moradkhani, Raghav Sankaranarayanan+5 more|arXiv (Cornell University)|Jan 19, 2026

Pain Management and Treatment0 citations

TL;DR

The paper presents ExoNav, a helically notch-tube tendon-driven continuum robot designed to steer spinal cord stimulation leads using a Cosserat rod model, enabling programmable follow-the-leader motion with gravity-aware planning and experimental validation in phantoms.

ABSTRACT

Spinal cord stimulation (SCS) is primarily utilized for pain management and has recently demonstrated efficacy in promoting functional recovery in patients with spinal cord injury. Effective stimulation of motor neurons ideally requires the placement of SCS leads in the ventral or lateral epidural space where the corticospinal and rubrospinal motor fibers are located. This poses significant challenges with the current standard of manual steering. In this study, we present a static modeling approach for the ExoNav, a steerable robotic tool designed to facilitate precise navigation to the ventral and lateral epidural space. Cosserat rod framework is employed to establish the relationship between tendon actuation forces and the robot's overall shape. The effects of gravity, as an example of an external load, are investigated and implemented in the model and simulation. The experimental results indicate RMSE values of 1.76mm, 2.33mm, 2.18mm, and 1.33mm across four tested prototypes. Based on the helical shape of the ExoNav upon actuation, it is capable of performing follow-the-leader (FTL) motion by adding insertion and rotation DoFs to this robotic system, which is shown in simulation and experimentally. The proposed simulation has the capability to calculate optimum tendon tensions to follow the desired FTL paths while gravity-induced robot deformations are present. Three FTL experimental trials are conducted and the end-effector position showed repeatable alignments with the desired path with maximum RMSE value of 3.75mm. Ultimately, a phantom model demonstration is conducted where the teleoperated robot successfully navigated to the lateral and ventral spinal cord targets. Additionally, the user was able to navigate to the dorsal root ganglia, illustrating ExoNav's potential in both motor function recovery and pain management.

Motivation & Objective

• Design a nitinol, helically notched tube (ExoNav) optimized for lateral and ventral spinal navigation.
• Customize Cosserat rod theory to model tendon-driven deformation of notched continuum robots.
• Develop a tendon-tension input optimization framework to achieve close-to-follow-the-leader motion under external loads like gravity.
• Validate the model through experiments across four prototypes and a phantom spinal cord model.
• Demonstrate potential for precise spinal targets and dorsal root ganglia navigation for SCS applications.

Proposed method

• Adopt a Cosserat rod-based static equilibrium model for tendon-driven robots with spatially varying properties.
• Define the ExoNav effective cross-sectional area and neutral axis to compute A, r_na, and inertia I_x, I_y, I_z.
• Model tendon actuation via a tendon tension input tau and derive K matrices and boundary conditions for v and u (Eqs. 1–5).
• Specialize the model to ExoNav geometry (notched nitinol tube) with explicit expressions for p*, R*, v*, u* (Eqs. 6–13).
• Implement a shooting method in MATLAB to solve state equations and perform progressive and FTL motion simulations (Eqs. 14–15).
• Incorporate gravity as a distributed external force f_e and compare gravity-free vs gravity-aware predictions (Eq. 18).
• Optimize tendon tensions to follow FTL trajectories under progression factor eta, including rotation-translation coupling (Sec. II-C).
• Use a PI-control loop to manage tendon tension commands in the experimental tendon tension system (Fig. 7).
• Validate predictions with EM-tracked experimental positions and quantify errors (Table I, Fig. 6).

Experimental results

Research questions

• RQ1 Can ExoNav achieve accurate follow-the-leader navigation to ventral and lateral spinal cord targets under gravity?
• RQ2 How do gravity and notch-driven geometry affect deformation, and how can tendon tensions be optimized to maintain an FTL trajectory?
• RQ3 How well does the Cosserat-based model predict experimental deformations across multiple prototype geometries?
• RQ4 Is phantom-spinal-cord navigation feasible with ExoNav for potential SCS electrode delivery?

Key findings

• Tip-position RMSE in four prototypes under gravity-aware modeling: 1.76, 2.33, 2.18, and 1.33 mm (2.1–4.2% of robot length).
• FTL motion achieved with end-effector trajectories closely matching reference paths; maximum RMSE for FTL trials: 3.75 mm (<5% of robot length).
• Gravity modeling improves prediction accuracy over gravity-free models, reducing MED and RMSE especially near the end-effector (Table I).
• Progressive motion and FTL references were validated in simulation and experimentally with consistent repeatability across prototypes.
• Phantom spinal cord demonstrations showed successful navigation to lateral, ventral targets and dorsal root ganglia, illustrating ExoNav’s potential for motor recovery and pain management.
• The tendon-tension optimization framework can compute tendon tensions to follow desired FTL paths under external loads.