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
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.
α
L1
L2
Lc
θ(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.
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.
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.
The utility of flexible continuum mechanisms for dexterous navigation is often impaired by their low stiffness, making them ineffective at manipulation in high-force scenarios. To address this challenge, we propose a novel continuum mechanism that achieves both flexible and rigid behavior by antagonistic extension and contraction of a rod-driven continuum helical structure. The helical design combines variable-length capacity with force locking for workspace and stiffness enhancement. In this article, we present the detailed design of the proposed mechanism and characterize its performance through experiments that quantify bending and stiffness. The results demonstrate 180 degree bending range of motion with an average distal positioning error of <10%. Further tests demonstrate that force locking directly improves axial stiffness and thus indirectly increases bending stiffness anisotropically, with maximum bending stiffness along load paths with a large axial component. Tensioning the driving rods provides additional stiffness tunability in the force-locked state, where increasing rod tension proportionally increases bending stiffness with a dimensionless gain of 0.56.
Katelyn King, Veronica Fish, Allison M. Okamura
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Supportive continuum robots (SCRs) enhance the load-bearing capability of an operative continuum robot by mechanically coupling it with a supportive arm. However, their passive stiffness is determined by the mechanical configuration and cannot be adjusted online for varying payloads or interaction forces. Active stiffness control is therefore needed to regulate the load response and maintain positioning accuracy. Meanwhile, the closed-chain structure introduces kinematic constraints that complicate task-space regulation and stiffness control. This paper presents an active task-space stiffness control framework for a tendon-driven SCR. An existing geometric variable strain model describes the closed-chain dynamics, which are projected onto the constraint-consistent motion subspace. A projected sliding mode controller regulates the operative arm tip while preserving the constraints, and closed-loop stability is established through Lyapunov analysis. After position regulation, active apparent stiffness is introduced through a virtual Cartesian spring based on position-error feedback to shape the force--displacement response. The framework is evaluated in simulation and experimentally validated under prescribed external loads and different desired configurations. Results show that increasing the commanded stiffness gain reduces load-induced tip deflection and increases apparent directional stiffness, thereby improving load resistance and positioning robustness under external loading.
Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University, Toronto, ON, Canada · Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QC, Canada