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A Differentiable Framework for Hollow Tendon-Driven Continuum Robots With Implicit Internal Routing
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DOI：10.1109/tro.2026.3714660.png)
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Abstract
En 中文
In this article, we present a study of a novel continuum manipulator comprising a hollow deformable tube actuated by internal cables that are constrained to remain within the structure. The hollow design simplifies fabrication, requiring only an off-the-shelf flexible tube with simple end caps, while eliminating complex backbones or predefined routing structures. This minimal hardware enables fully contained cable routing and compact operation in cluttered environments. Unlike prior works that assume fixed cable paths or external routing, the internal routing in our system is not predefined; instead, it emerges as an implicit function of manipulator deformation. We introduce a nested differentiable modeling framework based on the geometric variable strain formulation, where cable routing is computed as an inner optimization problem that minimizes the cable length within the deforming body. By applying the implicit function theorem, we obtain analytical derivatives of the optimal routing parameters with respect to the manipulator state, which enables computation of the analytical Jacobian of the static residual. The resulting model enables differentiable simulation, gradient-based parameter identification, and inverse kinetostatic control. We experimentally validate our framework on single- and multisection manipulators with one and two cables, showing an average error below 5% of the manipulator body length and a maximum error of 7.54%. Finally, we demonstrate an application of the approach for a three-cable manipulator prototype in an inspection task.
Keywords:
Continuum robot
differentiable simulation
optimization
tendon-driven continuum robots
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