Tendon-driven Continuum Robot Research Articles

Wrench Estimation and Friction Compensation Using Multiple Shooting Method for Tether Units Augmented to Remote Tendon-Driven Continuum Robots

Abstract Remote-actuated mechanisms that employ tendon sheaths or tether units can transmit mechanical force without directly connecting the actuators to the mechanism, but suffer from undesirable side effects like mechanical friction and induced external wrench disturbances on the distal side of the mechanism. In this work, a multiple shooting method is proposed as a superior method to the single shooting method to solve the Cosserat rod boundary value problems, to obtain the states of the system. With that, numerical experiments are provided to demonstrate the difficulty of solving these boundary value problems, simultaneously showing the validity of the proposed approach. 2D reconstruction experiments were conducted to show shape reconstruction capabilities. In addition, friction loss and 6-degree-of-freedom wrench estimations were also experimentally validated with the proposed mathematical model with 0.1679N and 0.0401Nm for root-mean-squared error (RMSE) force estimation and torque estimation error, respectively, while achieving a 3% mean absolute percentage steady-state friction estimation error. Finally, a modified resolved rate controller was applied to steer a remote tendon-driven continuum robot to compensate for friction loss for 3.1-m long tether units.

Shared Control of Tendon-Driven Continuum Robots Using Visibility-Guaranteed Optimization for Endoscopic Surgery

Shared Control of Tendon-Driven Continuum Robots Using Visibility-Guaranteed Optimization for Endoscopic Surgery

Model-based trajectory tracking of a compliant continuum robot.

Introduction: Compliant mechanisms, especially continuum robots, are becoming integral to advancements in minimally invasive surgery due to their ability to autonomously navigate natural pathways, significantly reducing collision severity. A major challenge lies in developing an effective control strategy to accurately reflect their behavior for enhanced operational precision. Methods: This study examines the trajectory tracking capabilities of a tendon-driven continuum robot at its tip. We introduce a novel feedforward control methodology that leverages a mathematical model based on Cosserat rod theory. To mitigate the computational challenges inherent in such models, we implement an implicit time discretization strategy. This approach simplifies the governing equations into space-domain ordinary differential equations, facilitating real-time computational efficiency. The control strategy is devised to enable the robot tip to follow a dynamically prescribed trajectory in two dimensions. Results: The efficacy of the proposed control method was validated through experimental tests on six different demand trajectories, with a motion capture system employed to assess positional accuracy. The findings indicate that the robot can track trajectories with an accuracy within 9.5%, showcasing consistent repeatability across different runs. Discussion: The results from this study mark a significant step towards establishing an efficient and precise control methodology for compliant continuum robots. The demonstrated accuracy and repeatability of the control approach significantly enhance the potential of these robots in minimally invasive surgical applications, paving the way for further research and development in this field.

A ball-jointed tendon-driven continuum robot with multi-directional operability for grasping objects

A continuum robot, inspired by biological features, flexibly bends its body and conforms to various shapes. The high compliance and low stiffness, however, causes low rigidity and ambiguity in control when it is applied to grasping and manipulating an object. In this study, we develop a ball-jointed tendon-driven continuum robot that can bend to arbitrary directions for manipulating and grasping an object. Discs are connected by ball joints, together with coil springs coupled with tendon threads, and form a backbone of the robotic body. The continuum robot is operated to bend to an arbitrary direction by pulling the tendons using three servomotors, and returns to the original straight shape by releasing the pulling force of the contracted coil springs. The robot is constructed by using 3D-printed parts. In the experiment, the ability of the multi-directional operation was tested by bending the continuum body to specific directions, and then performing arc-following motion. Furthermore, the manipulator's grasping performance was demonstrated by preparing five objects that have various shapes, sizes, and softness. The robot successfully grasped all the objects by wrapping around them and adapting its shape to the object's shapes. The experiments verified the satisfactory operability of the continuum robot.

A Self-Assembling Extendable Tendon-Driven Continuum Robot With Variable Length

A Self-Assembling Extendable Tendon-Driven Continuum Robot With Variable Length

An analytical differential kinematics-based method for controlling tendon-driven continuum robots

Generic and high-performance feedback control is still challenging for tendon-driven continuum robots. Conventional model-based controllers, based on the piecewise constant curvature (PCC) assumption, explicitly require the arc parameters (bending angle and direction angle) to link the task (in Cartesian coordinates) and actuation spaces. However, the approaches' effectiveness remains to be explored when robot shapes deviate from circular arcs. This paper proposed a hybrid scheme for novel kinematic control of continuum robots. The error led by the slack state has been avoided through tension supervision, while analytical differential kinematics is further developed to avoid the explicit call of arc parameters by importing Cylindrical coordinates into task space and applying accurate piecewise linear approximation. Comparison between a conventional PCC-based controller and the proposed controller has been done by implementing them in a twin-pivot joint-based continuum section. An overall tip positioning accuracy of ±0.35mm has been reached, and a result of root-mean-square-error (RMSE): 0.3mm and Max error: 0.97mm has been observed when running two predefined path tracking. Further, in order to evaluate the versatility of the proposed controller, a dual-revolute joint-based and a 3D-printed continuum section were used to test for path tracking to prove the effectiveness of the controller on a wide range of continuum robotic systems.

Hapstick: A Soft Flexible Joystick for Stiffness Rendering via Fiber Jamming

Continuum robots are well-suited for applications in delicate and constrained environments, such as minimally invasive surgery, due to their inherent compliance and ability to conform to highly curved paths. Yet the kinematic dissimilarity between continuum robots and conventional, off-the-shelf input devices, along with the general lack of haptic feedback available with such devices, can lead to non-intuitive control. In this work, we present Hapstick — a soft, flexible haptic joystick that uses fiber jamming to modulate its stiffness and provide feedback to users during teleoperation tasks. We characterize the performance of Hapstick, showing that the bending stiffness increases linearly with the increase in applied vacuum load. A psychophysical study is also conducted to obtain the just noticeable difference in stiffness that users can perceive using Hapstick. Lastly, we perform a study in which participants use Hapstick to teleoperate a physical tendon-driven continuum robot in a simulated colorectal cancer screening task. Users correctly identify the position and development stages of cancerous tissues in 25 out of 27 trials, illustrating the potential of jamming-based mechanisms as bidirectional interfaces capable of providing effective haptic feedback.

Modeling and Analysis of Tendon-Driven Continuum Robots for Rod-Based Locking

Various design modifications have been proposed for tendon-driven continuum robots to improve their stiffness and workspace. One of them is using locking mechanisms to constrain the lengths of rods or passive backbones along the robot. However, physics-based models used to predict these robots' behaviour commonly assume that the curvature of the locked portion does not change during robot actuation or that the effects of friction and gravity are negligible. In addition, these models do not consider the variations in twist on force application. In this letter, we propose a 3D static model for tendon-driven continuum robots experiencing locking due to length constraints on rods along their backbone. The proposed model is evaluated on prototypes of length 240 mm, with up to three locking mechanisms and has an accuracy of 3.63% w.r.t. length. Using the proposed model, a compliance analysis is performed studying the evolution of the robot compliance with the position of the locking mechanisms. An actuation strategy is proposed that can allow the robot to achieve the same shape with different compliance.

Modeling and analysis of a modular-structured tendon-driven continuum robot for the three-dimensional end effector coordinate

This article introduces the design and control of a tendon-driven continuum robot (CR) segment with a modular structure consisting of a series of backbone discs connected in series. Thanks to this developed design; The backbone length can be changed by increasing or decreasing the number of discs, the number of segments can be increased thanks to the hollow flexible central backbone, and additional apparatus such as a camera or holder can be sent to the end effector. Multi-part and multi-degree-of-freedom CRs are difficult to control because their kinematics and dynamics are non-linear. To overcome this challenge, the development of a finite element method (FEM) based model is presented. In this framework, a nonlinear FEM formulation was applied to model large displacements and contact problems in CRs with motion control by a tendon driven mechanism. The study was supported by a series of experiments to evaluate the accuracy and performance of the developed model. A Feed-forward Artificial Neural Network (FNN) model was developed using the data obtained from the FEM model. The FNN model predicts the X, Y, Z coordinates of the end effector in the 3D plane, based on the tendon drive distance of the CR. The results demonstrated the accuracy and reliability of the proposed nonlinear FEM formulation. At the same time, the FNN algorithm developed with optimum parameters demonstrated that the X, Y and Z position of the end effector has a high estimation accuracy of R=0.9995 on average, depending on the amount of tendon drive.

Modelling of Tendon-Driven Continuum Robot Based on Constraint Analysis and Pseudo-Rigid Body Model

Quasi-static models of tendon-driven continuum robots (TDCR) require consideration of both the kinematic and static conditions simultaneously. While the Pseudo-Rigid Body (PRB-3R) model has been demonstrated to be efficient, existing works ignore the mechanical effect of the tendons such as elongation. In addition, the static equilibrium equations for the partially constrained tendons have been expressed in different forms within the literature. This leads to inconsistent simulation results which have not been validated by experimental data when external loads are applied. Furthermore, the inverse problem for solving the required inputs for a prescribed end effector pose has not been studied for the PRB-3R model. In this work, we introduce a new modelling approach based on constraint analysis (CA) of a multi-body system and Lagrange multipliers to systematically derive all the relevant governing equations required for a planar TDCR. This method can include tendon mechanics and efficiently solve for the direct and inverse kinetostatic models with either forces or displacements as the actuation inputs. We validate the proposed CA method using numerical simulation of a benchmark model and experimental data.

Design and control of an aerial-ground tethered tendon-driven continuum robot with hybrid routing

Combining aerial and continuum robots harnesses both their flexibility and manoeuvrability to potentially perform dangerous maintenance tasks. However, such systems require heavy payloads to interact with its environment. An aerial-ground tethered tendon-driven continuum robot is thus proposed to tackle the limitations of on-board payload aerial systems and the underactuation of multirotors. Due to the natural limitation on the tendons used in the implementation of aerial ground tethered continuum robots, we explore the use of hybrid polynomial and parallel routes to achieve desired workspace profiles, while providing intuition on choosing suitable tendon routes. In this work, we leverage on geometrically exact methods to derive the differential kinematics of the aerial continuum robot using actuation sensors particularly for polynomial tendon routes. We demonstrate that both position and orientation can be controlled using a single stage continuum robot with hybrid tendon routing. Finally, a simple manoeuvre is executed by the aerial continuum robot prototype to validate the proposed proof of concept.

Multiple aspects grasp quality evaluation in underactuated grasp of tendon-driven continuum robots

Multiple aspects grasp quality evaluation in underactuated grasp of tendon-driven continuum robots

Estimating Forces Along Continuum Robots

Continuum robots can be slender and flexible to navigate through complex environments, such as passageways in the human body. In order to control the forces that continuum robots apply during navigation and manipulation, we would like to detect the location, direction, and magnitude of contact forces distributions as they arise. In this paper, we present a model-based framework for sensing distributed loads along continuum robots. Using sensed positions along the robot, we use a nonlinear optimization algorithm to estimate the loading which fits the model-predicted robot shape to the data. We propose that Gaussian load distributions provide a seamless way to account for a wide range of loadings, including approximate point loads and uniform distributed loads, while avoiding the ill-conditioning associated with highly resolved force distributions. In addition, we gain computational efficiency by re-framing the problem as unconstrained weighted least-squares minimization and by solving this problem with an Extended Kalman-filter framework. We validate the approach on two prototype tendon-driven continuum robots in multiple 3D loading scenarios, displaying a mean error of 0.58 N in load magnitude and 7% mean error in load location with respect to the length of the respective robot.

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.