Continuum manipulators offer intrinsic dexterity and safe geometric compliance for navigation within confined and obstacle-rich environments. However, their infinite-dimensional backbone deformation, unmodeled internal friction, and configuration-dependent stiffness fundamentally limit the reliability of model-based kinematic formulations, resulting in inaccurate Jacobian predictions, artificial singularities, and unstable actuation behavior. Motivated by these limitations, this work presents a complete model-less control framework that bypasses kinematic modeling by using an empirically initialized Jacobian refined online through differential convex updates. Tip motion is generated via a real-time quadratic program that computes actuator increments while enforcing tendon slack avoidance and geometric limits. A backbone-tension optimization term is introduced in this paper to regulate axial loading and suppress co-activation compression. The framework is validated across circular, pentagonal, and square trajectories, demonstrating smooth convergence, stable tension evolution, and sub-millimeter steady-state accuracy without any model calibration or parameter identification. These results establish the proposed controller as a scalable alternative to model-dependent continuum manipulation in a constrained environment.

This letter describes the manufacturing and experimental characterization of novel stretchable strain sensors for continuum robots. The overarching goal of this research is to provide a new solution for the shape sensing of these devices. The sensors are fabricated via direct ink writing, an extrusion-based additive manufacturing technique. Electrically conductive material (i.e., the \textit{ink}) is printed into traces whose electrical resistance varies in response to mechanical deformation. The principle of operation of stretchable strain sensors is analogous to that of conventional strain gauges, but with a significantly larger operational window thanks to their ability to withstand larger strain. Among the different conductive materials considered for this study, we opted to fabricate the sensors with a high-viscosity eutectic Gallium-Indium ink, which in initial testing exhibited high linearity ($R^2 \approx$ 0.99), gauge factor $\approx$ 1, and negligible drift. Benefits of the proposed sensors include (i) ease of fabrication, as they can be conveniently printed in a matter of minutes; (ii) ease of installation, as they can simply be glued to the outside body of a robot; (iii) ease of miniaturization, which enables integration into millimiter-sized continuum robots.

Tendon-sheath mechanisms (TSMs) are widely used in minimally invasive surgical (MIS) applications, but their inherent hysteresis-caused by friction, backlash, and tendon elongation-leads to significant tracking errors. Conventional modeling and compensation methods struggle with these nonlinearities and require extensive parameter tuning. To address this, we propose a vibration-assisted hysteresis compensation approach, where controlled vibrational motion is applied along the tendon's movement direction to mitigate friction and reduce dead zones. Experimental results demonstrate that the exerted vibration consistently reduces hysteresis across all tested frequencies, decreasing RMSE by up to 23.41% (from 2.2345 mm to 1.7113 mm) and improving correlation, leading to more accurate trajectory tracking. When combined with a Temporal Convolutional Network (TCN)-based compensation model, vibration further enhances performance, achieving an 85.2% reduction in MAE (from 1.334 mm to 0.1969 mm). Without vibration, the TCN-based approach still reduces MAE by 72.3% (from 1.334 mm to 0.370 mm) under the same parameter settings. These findings confirm that vibration effectively mitigates hysteresis, improving trajectory accuracy and enabling more efficient compensation models with fewer trainable parameters. This approach provides a scalable and practical solution for TSM-based robotic applications, particularly in MIS.

Origami offers a versatile framework for designing morphable structures and soft robots by exploiting the geometry of folds. Tubular origami structures can act as continuum manipulators that balance flexibility and strength. However, precise control of such manipulators often requires reliance on vision-based systems that limit their application in complex and cluttered environments. Here, we propose a proprioceptive tendon-driven origami manipulator without compromising its flexibility. Using conductive threads as actuating tendons, we multiplex them with proprioceptive sensing capabilities. The change in the active length of the tendons is reflected in their effective resistance, which can be measured with a simple circuit. We correlated the change in the resistance to the lengths of the tendons. We input this information into a forward kinematic model to reconstruct the manipulator configuration and end-effector position. This platform provides a foundation for the closed-loop control of continuum origami manipulators while preserving their inherent flexibility.

Since the shape of industrial endoscopes is passively altered according to the contact around it, manual inspection approaches of aeroengines through the inspection ports have unreachable areas, and it's difficult to traverse multistage blades and inspect them simultaneously, which requires engine disassembly or the cooperation of multiple operators, resulting in efficiency decline and increased costs. To this end, this paper proposes a novel continuum manipulator with push-pull multisection structure which provides a potential solution for the disadvantages mentioned above due to its higher flexibility, passability, and controllability in confined spaces. The ultra-slender design combined with a tendon-driven mechanism makes the manipulator acquire enough workspace and more flexible postures while maintaining a light weight. Considering the coupling between the tendons in multisection, a innovative kinematics decoupling control method is implemented, which can realize real-time control in the case of limited computational resources. A prototype is built to validate the capabilities of mechatronic design and the performance of the control algorithm. The experimental results demonstrate the advantages of our continuum manipulator in the in-situ inspection of aeroengines' multistage blades, which has the potential to be a replacement solution for industrial endoscopes.

Continuum manipulators have gained significant attention as a promising alternative to rigid manipulators, offering notable advantages in terms of flexibility and adaptability within intricate workspace. However, the broader application of high degree-of-freedom (DoF) continuum manipulators in intricate environments with multiple obstacles necessitates the development of an efficient inverse kinematics (IK) solver specifically tailored for such scenarios. Existing IK methods face challenges in terms of computational cost and solution guarantees for high DoF continuum manipulators, particularly within intricate workspace that obstacle avoidance is needed. To address these challenges, we have developed a novel IK solver for continuum manipulators that incorporates obstacle avoidance and other constraints like length, orientation, etc., in intricate environments, drawing inspiration from optimization-based path planning methods. Through simulations, our proposed method showcases superior flexibility, efficiency with increasing DoF, and robust performance within highly unstructured workspace, achieved with acceptable latency.

Abstract-- Cable-Driven Continuum Manipulators (CDCMs) enable scar-free procedures via natural orifices and improve target lesion accessibility through curved paths. This paper introduces an extensible CDCM with a Semi-active Mechanism (SAM) to expand the workspace via translational motion without additional mechanical elements or actuation. We collect a hysteresis dataset using 8 fiducial markers and RGBD sensing. Based on this dataset, we develop a real-time hysteresis compensation control algorithm using the trained Temporal Convolutional Network (TCN) with a 1ms time latency, effectively estimating the manipulator's hysteresis In contrast, Cable-Driven Continuum Manipulators (CDCMs), with their flexible and bendable property, are expected to enable minimally invasive surgery by navigating through complex internal organs [2]-[5]. CDCMs are emerging as a next-generation surgical manipulation technology.

Abstract-- To address the challenges associated with shape sensing of continuum manipulators (CMs) using Fiber Bragg Grating (FBG) optical fibers, we feature a unique shape sensing assembly utilizing solely a single Optical Frequency Domain Reflectometry (OFDR) fiber attached to a flat nitinol wire (NiTi). Integrating this easy-to-manufacture unique sensor with a long and soft CM with 170 mm length, we performed different experiments to evaluate its shape reconstruction ability. Results demonstrate phenomenal shape reconstruction accuracy for both C-shape (< 2 mm tip error, < 1.2 mm shape error) and J-shape (< 3.4 mm tip error, < 2.3 mm shape error) experiments. I. INTRODUCTION Instead of using rigid instrumentation in minimally invasive surgeries that limit access and dexterity of clinicians, continuum manipulators (CMs) have been proposed to provide more flexibility and access within confined and tortuous paths of anatomical spaces [1]. SSA. Figure also shows the SSA structure modeled as a composite Particularly, having an appropriate integrated sensing modality and pertinent algorithm to estimate their shape and end effector position at any time would be of Paramount importance for cannot completely address this poor accuracy and may increase the accurate control of these robots [1], [4].

Continuum Dexterous Manipulators (CDMs) are well-suited tools for minimally invasive surgery due to their inherent dexterity and reachability. Nonetheless, their flexible structure and non-linear curvature pose significant challenges for shape-based feedback control. The use of Fiber Bragg Grating (FBG) sensors for shape sensing has shown great potential in estimating the CDM's tip position and subsequently reconstructing the shape using optimization algorithms. This optimization, however, is under-constrained and may be ill-posed for complex shapes, falling into local minima. In this work, we introduce a novel method capable of directly estimating a CDM's shape from FBG sensor wavelengths using a deep neural network. In addition, we propose the integration of uncertainty estimation to address the critical issue of uncertainty in neural network predictions. Neural network predictions are unreliable when the input sample is outside the training distribution or corrupted by noise. Recognizing such deviations is crucial when integrating neural networks within surgical robotics, as inaccurate estimations can pose serious risks to the patient. We present a robust method that not only improves the precision upon existing techniques for FBG-based shape estimation but also incorporates a mechanism to quantify the models' confidence through uncertainty estimation. We validate the uncertainty estimation through extensive experiments, demonstrating its effectiveness and reliability on out-of-distribution (OOD) data, adding an additional layer of safety and precision to minimally invasive surgical robotics.

Flexible continuum manipulators are valued for minimally invasive surgery, offering access to confined spaces through nonlinear paths. However, cable-driven manipulators face control difficulties due to hysteresis from cabling effects such as friction, elongation, and coupling. These effects are difficult to model due to nonlinearity and the difficulties become even more evident when dealing with long and coupled, multi-segmented manipulator. This paper proposes a data-driven approach based on Deep Neural Networks (DNN) to capture these nonlinear and previous states-dependent characteristics of cable actuation. We collect physical joint configurations according to command joint configurations using RGBD sensing and 7 fiducial markers to model the hysteresis of the proposed manipulator. Result on a study comparing the estimation performance of four DNN models show that the Temporal Convolution Network (TCN) demonstrates the highest predictive capability. Leveraging trained TCNs, we build a control algorithm to compensate for hysteresis. Tracking tests in task space using unseen trajectories show that the proposed control algorithm reduces the average position and orientation error by 61.39% (from 13.7mm to 5.29 mm) and 64.04% (from 31.17{\deg} to 11.21{\deg}), respectively. This result implies that the proposed calibrated controller effectively reaches the desired configurations by estimating the hysteresis of the manipulator. Applying this method in real surgical scenarios has the potential to enhance control precision and improve surgical performance.