Distal-Stable Beam for Continuum Robots

Ryouichi Saito; Takahiro Koide; Yuya Tanaka; Yasutaka Nakashima; Motoji Yamamoto; Ayato Kanada

cs.ROApr 1, 2026

Distal-Stable Beam for Continuum Robots

Authors: Ryouichi Saito, Takahiro Koide, Yuya Tanaka, Yasutaka Nakashima, Motoji Yamamoto, Ayato Kanada

Organizations: Ryouichi Saito, Takahiro Koide, Yasutaka Nakashima, Motoji Yamamoto are with the Department of Mechanical Engineering at Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan. · Takahiro Koide, Ayato Kanada are with the Department of Graduate School of Informatics and Engineering at The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585

Abstract

Continuum robots are well suited for constrained environments but suffer from low distal stiffness, resulting in large posture errors under external loads. In this paper, we propose a novel structural primitive, the Distal-Stable Beam, which achieves a strong stiffness gradient through purely geometric design, maintaining compliance in the intermediate section while ensuring high distal rigidity. The structure consists of two parallel rods and one convergent rod constrained by guide disks, introducing geometric coupling that suppresses deformation modes and preserves distal posture. Experiments show that the distal stiffness is 12 times higher than at the center, corresponding to an approximately 100-fold improvement over a conventional cantilever beam. The proposed mechanism enables simultaneous compliance and distal stability without active stiffness modulation, providing a new design approach for continuum robots requiring both safety and precision.

Figures & tables

Fig. 1: Concept of the distal-stable beam, illustrating simultaneous compliance and high distal stiffness.

Fig. 2: Geometric model of the distal-stable beam.

Fig. 3: Simulation results showing deformation while preserving distal orientation and tip trajectory.

$\alpha$	$L_{1}$	$L_{2}$	$L_{c}$	$\theta(L)$ [rad]	$y(L)/x(L)$
0	$1.00$	$0.92$	$1.01$	$0.52$	$0.053$
2.30	$1.00$	$0.92$	$1.01$	$0.52$	$0.053$
3.64	$1.00$	$0.92$	$1.01$	$0.52$	$0.056$

TABLE I: Numerical results validating invariance of rod lengths, tip angle, and tip position ratio.

Fig. 4: Design and fabrication of the prototype, including guide disks, joints, and rod configuration.

Fig. 5: Experimental results demonstrating that the tip follows a constrained linear trajectory under deformation.

Fig. 6: Design of the continuum robot incorporating the proposed distal-stable beam structure.

Fig. 7: Experimental demonstration of (a) extension, (b) bending, and (c) distal posture preservation in the robot.

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Discrete Geometric Modeling and Extended State Estimation of Continuum Robots

Maximilian Herrmann, Leander Pfeiffer, Paul Kotyczka

Technical University of Munich, TUM School of Engineering and Design, Munich Institute of Robotics and Machine Intelligence (MIRMI), Chair of Automatic Control.

Continuum Robot Control Robot State Estimation Extended Kalman Filtering

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In this paper, we present a fully discrete approach for the accurate and numerically efficient dynamical modeling and state estimation of continuum robots. The model is based on geometrically exact beams in a minimal, strain-based formulation and derived in the framework of Lie group variational integrators, allowing to preserve important geometric properties that we exploit to achieve high accuracy and numerical efficiency. We then propose a disturbance observer based on an extended Kalman filter formulation that reliably estimates system states as well as model uncertainties and external disturbances. Experiments on a real system validate the accuracy and efficiency of the proposed model and observer.

Abstract

Continuum Robot Design

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