Continuum Robot Design

We develop an uncertainty-aware, operator-learning-based surrogate for tendon-driven continuum robots (TDCRs) that generalizes across robot design and actuation while predicting the complete equilibrium configuration. Our central idea is a nonstationary Gaussian-process (GP) kernel whose metric is learned by a shallow neural network from mechanics-aware design coordinates. The network learns how similarity changes across design space, while the resulting kernel defines the design-to-pose operator, its posterior uncertainty, and a criterion for sequential simulator acquisition. We represent backbone position and rotational strain with spatial kernels and reconstruct orientation directly on SO(3), preserving valid material frames and tendon geometry. We use ASkotch with Nystrom preconditioning for scalable kernel operator solves and a separate Nystrom approximation for posterior covariance. Experiments show that kernel-coverage acquisition reduces mean trajectory error by approximately 15% relative to IID sampling, while posterior variance increases for increasingly unsupported designs. Compared with prior neural-operator TDCR models, the method is 30-50% more accurate using approximately 5x fewer training designs while additionally providing posterior uncertainty estimates.

Octopuses exhibit a powerful form of embodied intelligence from a highly adaptable soft body. One key mechanism is the ability to instantiate bending points at any location along the arm, which enables performant and dexterous behaviours. Taking inspiration from the octopus for its dexterity, this study focuses on changing the curvature of a tendon-actuated arm by adaptively changing the anchoring end-point along the arm. An array of inflatable shells is integrated into the arm, where inflating a shell causes an increase in friction at the location, jamming the tendon and creating a temporary new anchoring point. The novel soft actuator does not break the continuity of the arm between the actuated segment and the loose segment. Experiments show that the actuated segment has a non-constant bell-shaped curvature which is comparable to that of a real octopus arm during a reaching motion. Compared to conventional single-tendon continuum manipulators, the proposed design offers an expanded workspace and enhanced dexterity through the ability to independently shape different regions of the arm through selective curvature tuning. At the same time, it avoids the mechanical complexity typically associated with multi-segment, multi-actuator systems.

Continuum robots enable dexterous access to confined spaces in applications such as minimally invasive surgery and industrial inspection. However, their actuation systems are often custom-designed for specific robot architectures and tasks, limiting reuse across publications, institutions, and applications. This paper presents a unified actuation platform that decouples actuation hardware and software from continuum robot design. The platform provides modular actuation across continuum robot classes, scales to a large number of degrees of freedom (DOFs), and integrates with conventional serial manipulators for hybrid architectures. We validate the platform on an open-sourced surgical robotic system and experimentally characterize the actuation modules, achieving sub-millimeter translational accuracy and less than $5^\circ$ rotational error over ranges of $30$~mm and $180^\circ$, respectively. We further demonstrate the platform in two surgical use cases: teleoperation of a continuum camera in a constrained environment and bimanual manipulation using $2.53$~mm concentric-tube-robot-based forceps alongside a conventional wristed instrument. All hardware designs and ROS-based software are open-sourced to facilitate reuse and further research in continuum and surgical robotics.

With the global population rapidly aging, maintaining independence in Activities of Daily Living (ADLs), particularly bathing or showering, has become a critical challenge. Older adults who sit while showering currently have limited options, often relying on rigid overhead showerheads or flexible hand-held hoses that require continuous gripping and precarious user maneuvers, increasing the risk of falls. To address this need, this paper introduces a highly articulated, pseudo-static balanced continuum mechanism designed specifically for accessible bathing assistance. The proposed mechanism features a modular continuum architecture composed of friction-locked ball-and-socket joints (loc-line), seamlessly integrated with a retractable spring-loaded reel for effective gravity compensation. This hybrid design achieves an intuitive "Push-and-Stay" interaction logic, maintaining an approximate static equilibrium with ergonomically low actuation force, without any external electronic power, while significantly minimizing the force needed for repositioning. Theoretically, we established a recursive forward kinematics framework to construct the geometric model of the structure, coupled with a comprehensive static equilibrium analysis to evaluate the system's holding capacity across its 51-DOF structure. Numerical simulations utilizing Monte Carlo methods validate the system's morphological adaptability and stability at various extreme positions within a standard bath space. Physical experiments further validate the prototype's real-world performance, confirming its intrinsic static stability against gravity and ensuring that the actuation force remains well within the ergonomic capabilities of older adults. Ultimately, this research provides a low-cost, intrinsically safe showerhead design that reduces physical strain, restoring dignity and autonomy in personal hygiene.

Performing complex medical procedures with continuum robots requires careful selection of their geometric design parameters. The robot should have high dexterity in the specific anatomical environment of its procedure. This work presents a design optimization method that considers both dexterity and anatomy. We introduce the Reachable Volumetric Dexterous Solid Angle (RVDSA) metric as our objective, which measures the ability of a robot's end effector to reach the points in a goal volume from different directions via collision-free paths from a start configuration. We present a computationally efficient motion planner to compute this objective function for a given robotic design, and we use an asymptotically optimal simulated annealing optimizer to compute an optimized design. We applied our new method to optimize the design of a bimanual dexterous sheaths robot for performing procedures on cancerous polyps in colon anatomies, achieving a 78% higher RVDSA on average than optimizing for 3D voxel coverage alone.

Continuum robots enable smooth shape morphing and safe interaction in confined environments. However, most existing systems are task-specific and depend on external sensing infrastructure, limiting their adaptability and real-world deployment. This paper presents a self-contained modular continuum robotic platform that combines mechanical reconfigurability with onboard pose estimation. The robot is constructed from interchangeable continuum joints with analytically precomputed stiffness, allowing rapid assembly and direct programming of the robot shape. Proprioceptive sensing is achieved using magnetic sensors and a modular learning-based framework, where a single model is trained per joint and reused across configurations. The system is experimentally validated in real world, demonstrating self-sensing capabilities and adaptation without external tracking.

Large language models (LLMs) have recently emerged as a promising tool for automating robot design from high-level specifications, yet they remain ineffective for robots operating under complex physical interactions. This limitation stems from the gap between language-based reasoning and the physical consequences of embodiment, often resulting in designs with low physical validity. In this work, we propose a multi-layered framework, AID-SR, that establishes a closed loop by translating simulator-observed physical states into structured feedback for the LLM designer. Combined with semantic critique, human feedback, and iterative refinement, the framework promotes the generation of physically feasible and functionally meaningful robot designs. We evaluate our approach on tendon-driven continuum robots across a benchmark of 14 tasks spanning reaching, grasping, locomotion, and manipulation. The proposed framework achieves 96.2% rate for passing the simulation feasibility check and by applying a common reinforcement learning training, 26.7% robots can successfully fulfill the corresponding task. We then fabricate three designed robots of AID-SR that successfully complete the task in real-world. These extensive experiments across simulation and real-world environments demonstrate and break the wall of utilizing the LLMs for automated design of continuum robots. The source code and experimental resources are publicly available at https://github.com/UNITES-Lab/AID-SR.

Rerouting the tendon path in tendon driven continuum manipulators (TDCMs) enables a broad range of deformation modes. This work presents a Reconfigurable TDCM design which allows independent rotation of intermediate spacer disks, thereby locally rerouting the tendon and achieving non-trivial backbone spatial deformations. Two such designs, (a) Manual Disk Locked (MDL) and (b) Continuous Disk Rotor (CDR) manipulators are presented to achieve disk rotations before and during operation, respectively. A predictive static model based on the piecewise constant strain (PCS) assumption is developed within a potential energy minimization framework, incorporating (a) disk rotations, (b) discrete tendon paths between disk segments, (c) rigid thickness of spacer disks, and (d) elasticity of the tendons. The model is validated against experimental results, demonstrating an average tip error of $1.2\%$ of the manipulator's total length for parallel tendon routing and around $3\%$ for the case when multiple disks are rotated. The computation time is an order of magnitude lower than the state of the art Cosserat rod solver.

Shape and force sensing have long been critical bottlenecks in the development of compact capstan-driven continuum surgical robots, primarily due to the difficulty of obtaining cable tension information within the confined capstan assembly. To overcome these challenges, this paper presents an integrated design-modeling-sensing approach based on the concept of actuation-perception co-design. A compliant element is introduced into the motor mounting bracket of the drive system, enabling micro-deformation under the cable reaction force and thereby allowing real-time cable tension measurement without occupying the compact capstan space. To address the modeling complexity arising from unconventional joint configurations introduced by the spatial cable routing strategy, a parallel computation framework based on a multibody short-thick-beam model is proposed, which captures shear effects in short beam segments and synergistic multi-cable interactions while achieving real-time performance. Building on this framework, stable shape and force sensing is achieved by incorporating a proximal multi-axis force/torque sensor as an additional measurement anchor. Following this design-modeling-sensing framework, capstan-driven continuum surgical robots with single- and dual-segment configurations are developed. Experimental results validate the proposed framework in both single- and dual-segment continuum robots, demonstrating real-time tip pose estimation together with contact force and location perception. By enabling cable tension feedback without compromising the compact capstan architecture, the proposed framework makes integrated perception feasible for capstan-driven continuum surgical robots.

Continuum robots often operate in uncertain environments, where accurate state estimation is essential for safe interactions. Estimate uncertainty is inherently spatially non-uniform: confidence varies depending on where measurements are available. Global estimation accuracy is not always the top priority, but rather achieving sufficient confidence at task-relevant locations along the robot. This extended abstract introduces mechanically reconfigurable sensing enabling uncertainty-shaping in state estimation for continuum robots. We present a concept hardware design demonstrating the feasibility of longitudinal translation of a sensor within a continuum robot. We demonstrate that state estimation confidence can be reconfigured by varying the sensor location, and show a reduction of full-body shape estimation errors when sliding the sensor back and forth over time, compared to a single fixed tip sensor.

The elephant trunk is a dexterous and versatile manipulator whose performance is still unmatched in robotics. In previous works, modularity was prioritized and relatively small-scale continuum robots were built. We take the natural proboscis of the Loxodonta africana species as a model and propose a different design approach which favors structural continuity and dynamic properties that plausibly emulate those of the natural trunk, while conferring high adaptability to the environment and humans. Instead of targeting prescribed behaviors, we show that a biomimetic design based on the macroscopic properties of the natural system enables elephant-like movements and grasping. We build by 3D printing an 85 cm long, compliant, tapered, volumetrically tessellated continuum arm, which is combined with tendon-driven actuation mimicking the longitudinal and oblique muscles of the natural model. We demonstrate whole-body grasping of objects having different shapes and dimensions and discuss a comparison to the biological trunk highlighting aspects of both biology and robotics.

Continuum manipulators mounted on multi-rotor UAVs enable compliant aerial manipulation, but payloads and propeller downwash amplify out-of-plane bending and twisting that degrade end-effector pose accuracy. To address this problem, we present a universal-joint-based continuum manipulator designed to improve resistance to out-of-plane deformation during aerial manipulation. The proposed design uses a tubular backbone with spring-reinforced universal joints and an integrated conduit for internal routing and fluid delivery. We evaluate the design in still air and under peak propeller downwash across varying payloads, and benchmark it against a prior Nitinol-backbone CM. Bench tests show improved resistance to out-of-plane deformation across all conditions. Under peak downwash, the proposed design reduces mean error by 2.5-4x in yaw, 2-45x in y-axis, and up to 5x in roll compared to the NiTi-backbone design. We further analyze hover stability through in-flight coupled-disturbance tests over varying payloads and actuation speeds, and demonstrate the system in water sampling, spot spraying, and object transport.

Continuum robots offer strong potential for manipulation tasks due to their high degrees of freedom, compliant structures, and operational safety. However, their adoption in both research and practical applications has been hindered by reproducibility issues arising from complex fabrication and assembly processes, challenging kinematic modeling, and a lack of intuitive control interfaces. To address these challenges, we present a novel open-source continuum robot design. The platform features a simplified fabrication pipeline enabled by multi-material 3D printing, allowing the arm to be fabricated as a monolithic compliant structure with minimal assembly. Control is achieved through an isomorphic teleoperation interface that establishes a direct actuator-level mapping, eliminating the need for explicit kinematic modeling and providing a singularity-free mapping. Building on this hardware design, the platform further supports imitation-learning-based autonomous control. The proposed system is evaluated through hardware characterization and a set of manipulation tasks. Experimental results demonstrate that the platform provides a reproducible, learning-ready continuum robot system, accelerating algorithmic development and systematic benchmarking for the continuum robotics community.

Continuum robots enable dexterous manipulation in constrained environments, but require accurate and efficient models for real-time manipulation and control. Traditional physics-based models can be computationally expensive and may suffer from inaccuracies due to unmodeled effects, while current learning-based methods often generalize poorly beyond the specific robot on which they are trained. We present a formulation of surrogate modeling for tendon-driven continuum robots as an operator learning problem that maps robot design parameters and tendon actuation inputs to resulting configurations. This formulation enables a single trained model to generalize across a large class of robot designs. We develop four novel neural operator architectures--two based on Deep Operator Networks (DeepONets) and two based on Fourier Neural Operators (FNOs)--and train them on simulation data to predict robot configurations. All architectures achieve good accuracy while allowing for fast and accurate generalization across designs. Our results demonstrate that operator learning provides an effective and generalizable surrogate for continuum robot mechanics in the design space, enabling fast modeling for control, planning, and design optimization in surgical and industrial applications.

In this paper, we discuss a novel continuum robot design that enables the online tuning of the magnetic response at its tip. The proposed method allows for the change of both effective magnetic direction and intensity, introducing steering DOF without the need to control the external fields. This is unattainable with classical designs, which rely on fixed internal magnetic content and steer solely under the effect of a controllable magnetic field. The proposed robot design can be used in both controllable and fixed magnetic fields, potentially widening the clinical applicability of these robots. We experimentally show a max tip deflection of 33.8 mm from the resting state (23 % of the length of the robot). We discuss a model based on modified beam theory that captures the mechanical behavior of the continuum robot, with a mean absolute tip tracking error of 1.86 mm (1.2 % of the length) and maximum errors of less than 4.8 mm (3.2 % of the length) for all experimental points.

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.

This paper presents the design, modeling, and fabrication of 3D-printed, tendon-actuated continuum robots featuring a flexible, tapered backbone constructed from thermoplastic polyurethane (TPU). Our scalable design incorporates an integrated electronics base housing that enables direct tendon tension control and sensing via actuators and compression load cells. Unlike many continuum robots that are single-purpose and costly, the proposed design prioritizes customizability, rapid assembly, and low cost while enabling high curvature and enhanced distal compliance through geometric tapering, thereby supporting a broad range of compliant robotic inspection and manipulation tasks. We develop a generalized forward kinetostatic model of the tapered backbone based on Cosserat rod theory using a Newtonian approach, extending existing tendon-actuated Cosserat rod formulations to explicitly account for spatially varying backbone cross-sectional geometry. The model captures the graded stiffness profile induced by the tapering and enables systematic exploration of the configuration space as a function of the geometric design parameters. Specifically, we analyze how the backbone taper angle influences the robot's configuration space and manipulability. The model is validated against motion capture data, achieving centimeter-level shape prediction accuracy after calibrating Young's modulus via a line search that minimizes modeling error. We further demonstrate teleoperated grasping using an endoscopic gripper routed along the continuum robot, mounted on a 6-DoF robotic arm. Parameterized iLogic/CAD scripts are provided for rapid geometry generation and scaling. The presented framework establishes a simple, rapid, and reproducible pathway from parametric design to controlled tendon actuation for tapered, tendon-driven continuum robots manufactured using fused deposition modeling 3D printers.