Tendon-driven Continuum Robot Research Articles

FAS-A Fully Actuated Segment for Tendon-Driven Continuum Robots.

We propose a segment design that combines two distinct characteristics of tendon-driven continuum robots, i.e. variable length and non-straight tendon routing, into a single segment by enabling rotation of its backbone. As a result, this segment can vary its helical tendon routing and has four degrees-of-freedom, while maintaining a small-scale design with an overall outer diameter of 7 mm thanks to an extrinsic actuation principle. In simulation and on prototypes, we observe improved motion capabilities, as evidenced by position redundancy and follow-the-leader deployment along spatially tortuous paths. To demonstrate the latter on a physical prototype, a simple, yet effective area-based error measure for follow-the-leader deployment is proposed to evaluate the performance. Furthermore, we derive a static model which is used to underpin the observed motion capabilities. In summary, our segment design extends previous designs with minimal hardware overhead, while either archiving similar accuracy in position errors and planar follow-the-leader deployment, or exhibiting superior motion capabilities due to position redundancy and spatial follow-the-leader deployment.

Optimization of Stress Distribution in Tendon-Driven Continuum Robots Using Fish-Tail-Inspired Method

Tendon-driven continuum robots are widely used in different engineering disciplines due to their simple structure and high flexibility. The typical structure of a tendon-driven continuum robot usually contains a series of identical compliant joints in its backbone to achieve large-deflection bending movements. However, with compliant joints of the same geometry, the real bending shape of the robot backbone is an arc with variable curvature, which results in uneven stress distribution along the robot backbone. In the long term, higher stresses in the compliant joints near the fixation base could lead to fatigue or fracture of the entire robot structure. To cope with this problem, we propose a fish-tail-inspired method in this letter to optimize the stress distribution along the serial compliant joints. Several optimization examples were presented to show the performance of the proposed method. Simulation and experimental results have demonstrated that the developed method can effectively reduce the stress differences in serial compliant joints during large-deflection bending movements.

Design and analysis of hybrid-driven origami continuum robots with extensible and stiffness-tunable sections

Tendon-driven continuum robots have increasingly attracted attention these years. Conventionally, such kind of robots utilizes elastic central backbones to hold the structure, which makes the robots inextensible, as well as reduces the dexterity and the workspace. Inspired by the reconfigurable feature of origami structures, this paper presents the design, analysis, and validation of a hybrid-driven continuum robot without an elastic backbone. The fabric-based, soft, and unstretchable origami pneumatic chamber holds the continuum structure and makes the robot exhibit a high extension ratio, low input pressure, and no radial expansion. With the antagonistic actuation of tendon-pulling and air-pushing, the robot can perform 3DoF motion with variable stiffness. The kinetostatics modeling and analysis are developed based on a discretization-based approach to predict the motion behavior and control the proposed robot. To validate the proposed design principle and the modeling method, a prototype is built, on which a series of experiments have been conducted. The results show that, with the proposed kinetostatics model, the prototype possesses acceptable positioning accuracy and tracking performances, while the structural stiffness can also be effectively adjusted.

Constrained visual predictive control of tendon-driven continuum robots

Due to their compliance, continuum robots (CRs) hold great potential for many applications. However, despite intensive recent research, their control poses significant challenges. The nonlinear kinematic behavior, limited actuation channels, and physical and environmental constraints typically associated with CRs hinder the development of effective control strategies. In this paper, a visual predictive position control method for tendon-driven continuum robots is proposed. The developed control approach integrates the advantages of image-based visual servoing and model predictive control techniques to enable direct end-point control in the presence of constraints and improve the control robustness to system uncertainties, sensing noise, and modeling errors. Both simulation and experimental results demonstrate the effectiveness of the method.

How to Model Tendon-Driven Continuum Robots and Benchmark Modelling Performance.

Tendon actuation is one of the most prominent actuation principles for continuum robots. To date, a wide variety of modelling approaches has been derived to describe the deformations of tendon-driven continuum robots. Motivated by the need for a comprehensive overview of existing methodologies, this work summarizes and outlines state-of-the-art modelling approaches. In particular, the most relevant models are classified based on backbone representations and kinematic as well as static assumptions. Numerical case studies are conducted to compare the performance of representative modelling approaches from the current state-of-the-art, considering varying robot parameters and scenarios. The approaches show different performances in terms of accuracy and computation time. Guidelines for the selection of the most suitable approach for given designs of tendon-driven continuum robots and applications are deduced from these results.

Design and Validation of a Novel Fuzzy-Logic-Based Static Feedback Controller for Tendon-Driven Continuum Robots

Continuum robots (CRs) outperform the conventional rigid-link manipulators in aspects of hyper-redundant and compliant features. They provide universal and efficient solutions to access to constrained environments, e.g., aero engines and industrial vessels. In this article, a slender tendon-driven CR (length/diameter: 715/12.7 mm) is introduced for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> maintenance of aero engine combustors. Two control challenges, the piecewise-constant-curvature (PCC) assumption mismatch and sections coupling issues, are discussed to explain the defect of model-based kinematic controllers on specific designs. Then, inspired by the tug of war, a novel local model-less controller utilizing a fuzzy logic algorithm is proposed for the feedback control of a single section. This implements the control policies directly from the task space to the actuation space, avoiding the model mismatch of the PCC assumption owing to the explicit call of arc parameters. Experiments on a single section of the tendon-driven CR, in comparison with PCC-based method, validate the stability and universality of the developed controller, which can reach <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \pm 1 - $</tex-math></inline-formula> mm overall positioning accuracy and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \pm 0.5$</tex-math></inline-formula> <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</b> mm positional accuracy for 75% of the test points in both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> directions. Further, a set of trails on two distal sections of a long robot demonstrate that the controller can also effectively minimize the section coupling issue.

Cosserat Rod-Based Dynamic Modeling of Tendon-Driven Continuum Robots: A Tutorial

This article provides a tutorial on the dynamic modeling of continuum robots. Continuum robots (CRs) have gained popularity in recent years due to their flexible backbone structure. Modeling and control of CRs motivate accurate and efficient dynamic models. Such models will enable simulation of dynamic behavior, improved structural design, and the development of dynamics-based control systems for CRs. As a unified underlying approach, the Cosserat rod-based modeling of tendon-driven CRs is used as the basis of the modeling techniques discussed in this paper. In addition to conventional continuum robot assemblies, new and emerging assemblies such as tendon-bent concentric tube and co-operative robots are also considered. The governing equations of motion for conventional CRs are first summarized and then extended for other tendon-driven CRs. This tutorial also contributes to developing a MATLAB code package for simulation of the dynamic response of these robots. The presented method and codes provide a useful and compact resource for readers and can be used for further development of tendon-driven continuum robots.

Automated 3-D Deformation of a Soft Object Using a Continuum Robot

This study investigates the use of a tendon-driven continuum robot to deform a soft object, whereas the robot body is deformed into an arbitrary shape to adapt to a constrained environment. A dynamic estimator (DE) is developed to approximate the Jacobian matrix that associates the actuator input with the deformed output of the soft object. This helps solve the singularity problem and reduce the effects of noise. Then a visual predictive controller (VPC) with a reference trajectory is developed to ensure a smooth operation. A linear extended-state observer (ESO) is further designed to measure the robot states, such that the controller can compensate for the estimation error. Simulations and experiments are performed to verify the proposed control approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this article is to solve the problem of automatic deformation control of soft objects in restricted environments. The existing soft object deformation control is achieved using rigid robots in an open environment, but rigid robots are difficult to use in specific applications where the environment is restricted (e.g., natural orifice surgery). Flexible continuum robots with mechanical compliance can manipulate soft objects in narrow spaces. However, due to environmental constraints, the robot body may be deformed into any shape regardless of the input of the actuator. To solve the problem, this research provides a new visual servo control strategy that deforms soft objects using a continuum robot in a restricted environment. The proposed method can control a flexible robot to manipulate soft objects while taking into account the change in the robot configuration in a restricted environment.

Force Sensing With 1 mm Fiber Bragg Gratings for Flexible Endoscopic Surgical Robots

This article presents a novel force sensor to detect the distal force of tendon-sheath mechanisms (TSMs) in flexible endoscopic surgical robots. We propose to measure the compression force on the sheath at the distal end so that the tension force on the tendon, which equals the compression force on the sheath, can be obtained. With this approach, a new force sensor made up of a 1 mm fiber Bragg grating attached to a 3 mm long nitinol tube was developed to measure the compression force exerted on the sheath. Mechanics analysis and verification tests were conducted to characterize the relationship between tension and compression on a TSM. Force calibrations, hysteresis study, and temperature compensation verification tests on the sensor were carried out. The force sensor has a measurement error of 0.178 N and a sensitivity of 34.14 pm/N. Applications of the sensor in a TSM-driven robotic grasper and a tendon-driven continuum robot were demonstrated. This force sensor has salient advantages: it is small, structurally simple, electrically passive, temperature-compensated, easy to assemble and disassemble, flexible, and biocompatible. This proposed approach with the new force sensor can also be applied to both TSM-driven systems and tendon-driven systems such as robotic fingers/hands, wearable devices, surgical catheters, and rehabilitation devices.

Tendon-driven continuum robots with extensible sections—A model-based evaluation of path-following motions

Continuum robots are highly miniaturizable, exhibit non-linear shapes with several curves, and are flexible and compliant. In particular, concentric-tube and tendon-driven continuum robots can be designed on a small scale with diameters of below 10 mm. A small diameter-to-length ratio enables insertion of these robots through small entry points in order to reach hardly accessible regions by avoiding obstacles. This scenario can often be found in minimally invasive surgery and technical inspections. However, to reach the target region, a deployment along a narrow tortuous path is often required. Common tendon-driven continuum robots are intrinsically incapable of such deployment and concentric-tube continuum robots require special path conditions and intensive parameter optimization. Other proposed robot types, such as hyper-redundant and pneumatically actuated robots, exhibit less favorable diameter-to-length ratios and are thus not suitable for those tasks. Since the limiting factors are found in the design of continuum robots, we propose a novel tendon-driven continuum robot design, which features an additional degree of freedom in each robot section. The backbone is composed of straight, concentrically arranged tubes, each of which composes a section and is used to adapt its length. We present a three-section continuum robot prototype with a diameter of 7 mm, determine its follow-the-leader capabilities theoretically, and validate the results experimentally using model-based control. For our 165 mm long robot prototype, the repeatability is below 2.38 mm. The model accuracy reaches a median of 3.16% over 25 configurations with respect to robot length. The path-following error over five curvilinear paths results in median errors of 2.59% with respect to robot length.

Modular FBG Bending Sensor for Continuum Neurosurgical Robot.

We present a modular sensing system to measure the deflection of a minimally invasive neurosurgical intracranial robot: MINIR-II. The MINIR-II robot is a tendon-driven continuum robot comprised of multiple spring backbone segments, which has been developed in our prior work. Due to the flexibility of the spring backbone and unique tendon routing configuration, each segment of MINIR-II can bend up to a large curvature (≥100 m-1) in multiple directions. However, the shape measurement of the robot based on tendon displacement is not precise due to friction and unknown external load/disturbance. In this regard, we propose a bending sensor module comprised of a fiber Bragg grating (FBG) fiber, a Polydimethylsiloxane (PDMS) cylinder, and a superelastic spring. The grating segment of the FBG fiber is enclosed inside a PDMS cylinder (1 mm in diameter), and the PDMS cylinder is bonded with the superelastic spring in series. The deflection or bending of the robot backbone segment is translated into an axial loading in the superelastic spring, which applies tension to the FBG; therefore, by measuring the peak wavelength shift of the FBG, the bending angle can be estimated. This paper describes the design, fabrication, and kinematic aspects of the sensor module in detail. To evaluate the proposed concept, one such sensor module has been tested and evaluated on the MINIR-II robot.

An Analytical Loading Model for &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$n$&lt;/tex-math&gt; &lt;/inline-formula&gt;-Tendon Continuum Robots

One of the key design parameters in tendon-driven continuum robots is the number of tendons and the tendon loading distribution. A load model is also helpful for avoiding slack in tendons that causes control inefficiency and inaccuracy. A quasi-static model of $n$ -tendon continuum robots is derived using the Euler–Lagrange formulation. The model is employed to derive an analytical loading model for equidistant tendon tensions for any given beam configuration within the workspace. The model accounts for the bending and axial compliance of the manipulator as well as tendon compliance. Features of the proposed model are discussed and some of the potential applications are explained. Based on the proposed model, a slack avoidance algorithm with analytical formulation is developed to dynamically optimize the tendon loads while preventing slack in tendons for a given configuration. The proposed model is experimentally validated in a multitendon continuum robot system for four case studies of three- to six-tendon arrangements in open-loop control architecture. A stereo vision-based three-dimensional reconstruction system measures the beam configuration and properties for each of the three- to six-tendon continuum robots. The effect of number of tendons on the tension loads in $n$ -tendon continuum robots is studied. A quantitative dimensionless relationship between the number of tendons, the maximum tendon loads, and the bending angles is developed that may be used as a design tool for tradeoff among the complexity and required force and size.

Toward a Flexible Variable Stiffness Endoport for Single-Site Partial Nephrectomy.

Laparoscopic partial nephrectomy for localized renal tumors is an upcoming standard minimally invasive surgical procedure. However, a single-site laparoscopic approach would be even more preferable in terms of invasiveness. While the manual approach offers rigid curved tools, robotic single-site systems provide high degrees of freedom manipulators. However, they either provide only a straight deployment port, lack of instrument integration, or cannot be reconfigured. Therefore, the current main shortcomings of single-site surgery approaches include limited tool dexterity, visualization, and intuitive use by the surgeons. For partial nephrectomy in particular, the accessibility of the tumors remains limited and requires invasive kidney mobilization (separation of the kidney from the surrounding tissue), resulting in patient stress and prolonged surgery. We address these limitations by introducing a flexible, robotic, variable stiffness port with several working channels, which consists of a two-segment tendon-driven continuum robot with integrated granular and layer jamming for stabilizing the pose and shape. We investigate biocompatible granules for granular jamming and demonstrate the stiffening capabilities in terms of pose and shape accuracy with experimental evaluations. Additionally, we conduct in vitro experiments on a phantom and prove that the visualization of tumors at various sites is increased up to 38% in comparison to straight endoscopes.

Workspace Analysis of Tendon-Driven Continuum Robots Based on Mechanical Interference Identification

Continuum robots have excited increasing attention and efforts from the robotic community due to their high dexterity and safety. This paper proposes a design for a type of multimodule continuum robot equipped with an elastic backbone structure and tendon-driven actuation system. The kinematic model of the robot is formulated where the maximum bending angle of a module is obtained by identifying the interference between the backbone structure and the tendons. A superposition method is then used to determine the configuration space of the robotic module. Finally, an approximation method is presented to estimate the workspace of the tendon-driven continuum robot that reduces the computational complexity in comparison with the previously used scanning method. Experiments are provided to validate the proposed methods.

Design and control of a tendon-driven continuum robot

Continuum robots are suitable for operating in unstructured environments owing to their intrinsic compliance. This paper presents a novel tendon-driven continuum robot equipped with two modules and a compliant backbone formed by helical springs. Each module is driven by four parallel arranged tendons to implement a redundant actuation system that guarantees dexterous motions of the robot. A position feedback controller for the continuum robot is then developed, and a quadratic programming algorithm is incorporated into the controller to achieve a smooth configuration of the robot. Experiments results show that the control method has good trajectory tracking performance against external disturbances.

Tendon-driven continuum robot for neuroendoscopy: validation of extended kinematic mapping for hysteresis operation.

The hysteresis operation is an outstanding issue in tendon-driven actuation--which is used in robot-assisted surgery--as it is incompatible with kinematic mapping for control and trajectory planning. Here, a new tendon-driven continuum robot, designed to fit existing neuroendoscopes, is presented with kinematic mapping for hysteresis operation. With attention to tension in tendons as a salient factor of the hysteresis operation, extended forward kinematic mapping (FKM) has been developed. In the experiment, the significance of every component in the robot for the hysteresis operation has been investigated. Moreover, the prediction accuracy of postures by the extended FKM has been determined experimentally and compared with piecewise constant curvature assumption. The tendons were the most predominant factor affecting the hysteresis operation of the robot. The extended FKM including friction in tendons predicted the postures in the hysteresis operation with improved accuracy (2.89 and 3.87 mm for the single and the antagonistic-tendons layouts, respectively). The measured accuracy was within the target value of 5 mm for planning of neuroendoscopic resection of intraventricle tumors. The friction in tendons was the most predominant factor for the hysteresis operation in the robot. The extended FKM including this factor can improve prediction accuracy of the postures in the hysteresis operation. The trajectory of the new robot can be planned within target value for the neuroendoscopic procedure by using the extended FKM.

Tendon-Driven Continuum Robot for Endoscopic Surgery: Preclinical Development and Validation of a Tension Propagation Model.

In this paper, we present a tendon-driven continuum robot for endoscopic surgery. The robot has two sections for articulation actuated by tendon wires. By actuating the two sections independently, the robot can generate a variety of tip positions while maintaining the tip direction. This feature offers more flexibility in positioning the tip for large viewing angles of up to 180 degrees than does a conventional endoscope. To accurately estimate the tip position at large viewing angles, we employed kinematic mapping with a tension propagation model including friction between the tendon wires and the robot body. In a simulation study using this kinematic-mapping, the two-section robot at a target scale (outer diameter 1.7 mm and length 60 mm) produced a variety of tip positions within 50-mm ranges at the 180°-angle view. In the experimental validation, a 10:1 scale prototype performed three salient postures with different tip positions at the 180°-angle view. The proposed forward kinematic mapping (FKM) predicted the tip position within a tip-to-tip error of 6 mm over the 208-mm articulating length. The tip-to-tip error by FKM was significantly less than the one by conventional piecewise-constant-curvature approximation (PCCA) (FKM: 5.9 ± 2.9 mm vs. PCCA: 23.7 ± 3.6 mm, n=15, P < 0.01).