Cable-driven Continuum Robot Research Articles

Design optimization and simulation of a 3D printed cable-driven continuum robot using IKM-ANN and nTop software

The first aspect of the paper focuses on presenting the innovative design of a new continuum robot, which was initially conceptualized using SolidWorks and then brought to life through 3D printing. This section illustrates the construction process, detailing the wiring method and the separator between each section of the robot. A key feature of the newly proposed design is the ball-like shape on the upper side of each disk, allowing each disk to rotate freely and gracefully in conjunction with the next one. To further enhance the design, the disk was optimized using nTopology software, an AI-based solution that reduces weight while maintaining performance. This modern engineering tool proved to be instrumental in addressing engineering challenges effectively. Subsequently, both the original and optimized disks were fabricated using 3D printing technology. In addition to the physical construction, the study employed an Artificial Neural Network (ANN) coupled with Particle Swarm Optimization (PSO) to simulate the developed model by solving its inverse kinematic model. The findings from this research have paved the way for a new continuum robot design that can be trained using the ANN-PSO method. Furthermore, the powerful nTopology tool was demonstrated to be capable of skillfully optimizing any given components without sacrificing performance.

Enhancing Surgical Robotics: A Dynamic Model and Optimized Control Strategy for Cable-Driven Continuum Robots

Abstract This paper tackles the challenges encountered in surgical continuum robotics by introducing a dynamic model tailored for a cable-driven continuum robot. The intricacies of dynamic modeling and control frequently lead to suboptimal outcomes. Prior studies have often lacked comprehensive descriptions of individual robot component movements, thereby impeding control processes, especially in the presence of external disturbances. Although machine learning-based models show promise across different domains, they face hurdles in continuum robotics due to the complexity of the systems involved. Traditional mathematical models, in contrast, offer explicit equations, providing better interpretability, unlike machine learning models that may struggle with generalization, especially in highly nonlinear systems like continuum robots. The developed model adeptly captures the kinematic and dynamic constraints of various robot segments, serving as the foundation for a robust optimized control strategy. This strategy, which integrates computed torque control and particle swarm optimization (PSO-CTC), enables real-time computation of joint torques based on feedback, ensuring precise and stable task execution even amidst external perturbations. Comparative analysis with an optimized proportional integral derivative (OPID) controller unequivocally demonstrates the superiority of the optimized computed torque controller (OCTC) in settling time, overshoot, and robustness against disturbances. This advancement represents a noteworthy contribution to robotics, with the potential to significantly enhance continuum robot performance in surgical and inspection applications, thereby fostering innovative advancements across various fields.

Shape Sensing and Kinematic Control of a Cable-Driven Continuum Robot Based on Stretchable Capacitive Sensors.

A Cable-Driven Continuum Robot (CDCR) that consists of a set of identical Cable-Driven Continuum Joint Modules (CDCJMs) is proposed in this paper. The CDCJMs merely produce 2-DOF bending motions by controlling driving cable lengths. In each CDCJM, a pattern-based flexible backbone is employed as a passive compliant joint to generate 2-DOF bending deflections, which can be characterized by two joint variables, i.e., the bending direction angle and the bending angle. However, as the bending deflection is determined by not only the lengths of the driving cables but also the gravity and payload, it will be inaccurate to compute the two joint variables with its kinematic model. In this work, two stretchable capacitive sensors are employed to measure the bending shape of the flexible backbone so as to accurately determine the two joint variables. Compared with FBG-based and vision-based shape-sensing methods, the proposed method with stretchable capacitive sensors has the advantages of high sensitivity to the bending deflection of the backbone, ease of implementation, and cost effectiveness. The initial location of a stretchable sensor is generally defined by its two endpoint positions on the surface of the backbone without bending. A generic shape-sensing model, i.e., the relationship between the sensor reading and the two joint variables, is formulated based on the 2-DOF bending deflection of the backbone. To further improve the accuracy of the shape-sensing model, a calibration method is proposed to compensate for the location errors of stretchable sensors. Based on the calibrated shape-sensing model, a sliding-mode-based closed-loop control method is implemented for the CDCR. In order to verify the effectiveness of the proposed closed-loop control method, the trajectory tracking accuracy experiments of the CDCR are conducted based on a circle trajectory, in which the radius of the circle is 55mm. The average tracking errors of the CDCR measured by the Qualisys motion capture system under the open-loop and the closed-loop control are 49.23 and 8.40mm, respectively, which is reduced by 82.94%.

Design and Kinematics of a Novel Continuum Robot Connected by Unique Offset Cross Revolute Joints

Abstract Continuum robots have continuous structures and inherent compliance, which can be used for accessing unstructured and confined space in many fields, such as minimally invasive surgery and aero-engine in-situ inspection. A novel cable-driven continuum robot connected by unique offset cross revolute joints is proposed in this paper, which has excellent bending capacity and appropriate torsional stiffness compared with continuum robots connected by revolute joints and spherical joints, respectively. Furthermore, the kinematic modeling and analysis are carried out. The mappings among robot's actuator space, joint space and task space are established step by step. Particularly, an improved inverse kinematics algorithm is proposed by combining the constant curvature method with the numerical iterative method. This combined inverse kinematics algorithm can effectively reduce the error of approximate solution derived by the traditional constant curvature method. Numerical simulations are conducted to verify the proposed algorithm and analyze workspace of the continuum robot. Finally, experimental prototype of the robot is built to verify its excellent bending capacity and the correctness of the proposed kinematic model.

Collision-free path planning for cable-driven continuum robot based on improved artificial potential field

AbstractContinuum robot has become a research hotspot due to its excellent dexterity, flexibility and applicability to constrained environments. However, the effective, secure and accurate path planning for the continuum robot remains a challenging issue, for that it is difficult to choose a suitable inverse kinematics solution due to its redundancy in the confined environment. This paper presents a collision-free path planning method based on the improved artificial potential field (APF) for the cable-driven continuum robot, in which the beetle antennae search algorithm is adopted to deal with the optimal problem of APF without the necessary for velocity kinematics. In addition, the local optimum problem of traditional APF is solved by the randomness of the antennae’s direction vector which can make the algorithm easily jump out of local minima. The simulation and experimental results verify the efficiency of the proposed path planning method.

Stability assessment method based on actual measurements for a cable-driven continuum robot

Stability assessment method based on actual measurements for a cable-driven continuum robot

Comprehensive kinetostatic modeling and morphology characterization of cable-driven continuum robots for in-situ aero-engine maintenance

In-situ maintenance is of great significance for improving the efficiency and ensuring the safety of aeroengines. The cable-driven continuum robot (CDCR) with twin-pivot compliant mechanisms, which is enabled with flexible deformation capability and confined space accessibility, has emerged as a novel tool that aims to promote the development of intelligence and efficiency for in-situ aero-engine maintenance. The high-fidelity model that describes the kinematic and morphology of CDCR lays the foundation for the accurate operation and control for in-situ maintenance. However, this model was not well addressed in previous literature. In this study, a general kinetostatic modeling and morphology characterization methodology that comprehensively contains the effects of cable-hole friction, gravity, and payloads is proposed for the CDCR with twin-pivot compliant mechanisms. First, a novel cable-hole friction model with the variable friction coefficient and adaptive friction direction criterion is proposed through structure optimization and kinematic parameter analysis. Second, the cable-hole friction, all-component gravities, deflection-induced center-of-gravity shift of compliant joints, and payloads are all considered to deduce a comprehensive kinetostatic model enabled with the capacity of accurate morphology characterization for CDCR. Finally, a compact continuum robot system is integrated to experimentally validate the proposed kinetostatic model and the concept of in-situ aero-engine maintenance. Results indicate that the proposed model precisely predicts the morphology of CDCR and outperforms conventional models. The compact continuum robot system could be considered a novel solution to perform in-situ maintenance tasks of aero-engines in an invasive manner.

Design and Control of a Multiple-Section Continuum Robot With a Hybrid Sensing System

After decades of development, the technology of continuum robots continues to mature gradually and is used for various applications, e.g., inspection and repair in high-value-added industries, such as aerospace and nuclear. However, such robots are invariably designed with a hyper-redundant structure which causes condition-dependent uncertainties and errors in practical operations. In this article, a hybrid sensing solution—consisting of a dual displacement sensor system (linear and rotary encoders) and a self-carried visual tracking system—is presented to improve the control performance of a multisection cable-driven continuum robot. The dual displacement sensor system works to measure the cable-displacement error at the proximal end of the arm and predicts the cable elongation in the arm to eliminate the control error of the robot in joint-space via a new two-stage cable-displacement control approach. Simultaneously, the self-carried visual system provides real-time section-by-section tip tracking to improve the controllability of the arm in the task space. This feedback is then integrated with a two-level closed-loop controller to achieve accurate tip-positioning control. A series of validation experiments are carried out to validate the approach. Compared with an off-the-shelf position tracking system, the measurement error of the proposed self-carried visual tracking system is smaller than 2 mm, with a mean error of 0.67 mm, within the workspace of a single-section continuum robot. The distal-tip control accuracy of a two-section robot can achieve 1.72 mm under the closed-loop controller supported by the hybrid sensing system.

Distilled neural state-dependent Riccati equation feedback controller for dynamic control of a cable-driven continuum robot

This article presents a novel learning-based optimal control approach for dynamic control of continuum robots. Working and interacting with a confined and unstructured environment, nonlinear coupling, and dynamic uncertainty are only some of the difficulties that make developing and implementing a continuum robot controller challenging. Due to the complexity of the control design process, a number of researchers have used simplified kinematics in the controller design. The nonlinear optimal control technique presented here is based on the state-dependent Riccati equation and developed with consideration of the dynamics of the continuum robot. To address the high computational demand of the state-dependent Riccati equation controller, the distilled neural technique is adopted to facilitate the real-time controller implementation. The efficiency of the control scheme with different neural networks is demonstrated using simulation results.

Bio-inspired a novel dual-cross-module sections cable-driven continuum robot: design, kinematics modeling and workspace analysis

Bio-inspired a novel dual-cross-module sections cable-driven continuum robot: design, kinematics modeling and workspace analysis

Morphology and Tension Perception of Cable-Driven Continuum Robots

The operation and control of the cable-driven continuum robot (CDCR) is directly determined by the actuation of cables, and the relationship between the driving length and the tension as well as the morphology of the CDCR has not been deeply researched in previous literature. In this article, a novel methodology for perceiving the morphology, tension, and driving state of the robot is proposed, which can be calculated only by the dynamic driving length/speed of cables without using shape sensors and tension sensors. First, a model of the tension distribution along with the cable path is deduced, which takes into account the influence of the sliding friction. Second, a rigid-flexible coupling dynamic model considering the strain of the cable is established. Then, a nonlinear complementary model between the driving state and the tensions of cables is constructed based on the mechanism of cable actuation, and an efficient solution algorithm is presented. Experiments of a single arm driven by two cables and a three-tandem arm driven by multiple cables were conducted to validate the proposed method. The average errors of the perceiving morphology and tension are 1.85% and 7.26%, respectively, and the transaction between the slack and tensional state of the driving cable is accurately captured. In addition, the hysteresis behavior of the cable actuation is also perceived.

Dizajn pid kontrolera frakcionog reda za kontrolu praćenja putanje kontinualnih robota

Continuum robots are the behavioral extension of hyper-redundant robots usually inspired by living biological organs. These robots outperform their rigid counterparts regarding high flexibility, dexterity, and most importantly safe interaction. On the flip side, they are kinematically redundant, highly nonlinear, and multi-input, and consequently, their controlling remains a complex and challenging task. To this end, this paper proposes a Fractional-Order Proportional-Integral-Derivative (FOPID) controller to control the continuum robot's end-tip. The proposed controller is designed to control the inputs of a class of continuum robots, namely the Cable-Driven Continuum Robot (CDCR). To design the controller satisfactorily, the Particle Swarm Optimization (PSO) algorithm extracts the optimal values of the controller's parameters. The proposed FOPID controller's efficiency and control performance are demonstrated through two simulation examples: set-point tracking and point-to-point trajectory tracking. In addition, the obtained simulation results are compared to those provided by classical and Optimized PID controllers and to some available schemes. Given the obtained results, it is clear that the performances of the proposed FOPID controller are superior in tracking accuracy and smoothness in control signals.

Modeling and control of cable-driven continuum robot used for minimally invasive surgery.

Continuum robot has great advantages in minimally invasive surgery (MIS) due to the slenderness and dexterity. But the friction and backlash result in the low trajectory tracking accuracy. This paper aims to study the transmission process of the driving force and the error compensation method. The statics is performed considering the frictional transmission process, and the variation of friction force with driving force is revealed by the model. The hysteresis effect of the tip trajectory is revealed. Then the relationship between the load history and the robot shape is studied, next, the deflection of the robot subject to the different loading forces can be predicted. The correctness of the mechanical model is verified by numerical simulation and experiments. Furthermore, the control methods according to the cable length and the driving force are compared respectively, and a method of error compensation according to the cable length is worked out considering the mechanical model. The rationality of the compensation method is validated by experiment. The results show that the compensation method based on cable length greatly improves the control accuracy, and the maximum deviation is 1.08 mm. The established model and compensation method create conditions for clinical application of the proposed continuum robot.

Closed-Loop Trajectory Tracking Control of a Cable-Driven Continuum Robot With Integrated Draw Tower Grating Sensor Feedback

Abstract Due to the inherent deformability of continuum robots (CRs), closed-loop control strategies of CRs come with some challenges, including sensor integration within a limited dimension and uncertainties with the CR system. In this paper, to obtain the spatial shape information and tip position of a cable-driven CR, a draw tower grating (DTG) sensor is integrated. A shape sensing algorithm is proposed to reconstruct the shape of the CR based on the relation between the DTG sensor and the CR centerline. Then, with the feedback information of the DTG sensor, a damped least-squares (DLS)-based closed-loop controller is implemented to improve the trajectory tracking performance of the CR. To verify the effectiveness of the proposed scheme, comparative experiments are performed.

Novel Design of a Cable-Driven Continuum Robot With Multiple Motion Patterns

Cable-driven continuum robots exhibit accessing and manipulation capabilities in constrained and cluttered environments that are unachievable for traditional robots composing of discrete links and joints. However, the existing continuum robots structured by non-scalable backbones are monofunctional, merely capable of providing bending degree of freedom, not allowing regional elongation that is necessary for dexterous manipulation. In this paper, we present a particular tensegrity topology for the continuum robotic design with an additional stretching degree of freedom, by which the robot can achieve high flexibility in both bending and contraction motion patterns for more configurable operations. To quantify kinematics of the robot under various motion patterns, we build a mechanical model following a positional formulation finite element method. Guided by the theoretical results, a triple-segmented continuum robot is designed and fabricated. To reduce the control complexity, we regulate the individual stiffness of each segment, by which the motion coupling among the segments can be eliminated. Moreover, we also demonstrate the potential applications of this robotic design in tasks of traveling through holes and avoiding obstacles.

Cable‐Driven Continuum Robot Perception Using Skin‐Like Hydrogel Sensors

AbstractThe cable‐driven continuum robot (CDCR) is a highly significant soft robot that exhibits a lightweight structure, intrinsic safety properties, and a considerable degree of freedom; therefore, it can work well in confined and complex environments. However, commonly used fiber Bragg grating sensors in CDCR systems are ultra‐stiff, extremely low in elongation, and lack an adhesion mechanism; this significantly restricts the movement of the robot and tends to delaminate from it, which makes it unsuitable for integrated systems. In this study, a new strategy is developed to enable CDCR perception via skin‐like hydrogel sensors made from ionic conductive polyacrylamide/alginate/nanoclay polymeric composite hydrogels; it exhibits a fracture strain of 1840% and adheres to a CDCR backbone with an adhesion strength of 6.6 kPa. The sensors are sensitive, stable, and reliable, and they can be manually operated to draw portraits using sensing curves as painted lines. Through these sensors, the CDCR acquires proprioception for sensing movements and exteroception for sensing barriers and traps. The hydrogel sensors are further employed to build a closed‐loop control system for regulating the bending of the CDCR. This study establishes effective routes for designing sensors and closed‐loop systems that can be applied to soft robots.

Dynamics modeling of a 2-DoFs cable-driven continuum robot

PurposeContinuum robots modeling, be it from a hard or soft class, is giving rise to several challenges compared with rigid robots. These challenges are mainly due to kinematic redundancy, dynamic nonlinearity and high flexibility. This paper aims initially at designing a hard class of continuum robots, namely, cable-driven continuum robot (CDCR) and equally at developing their kinematic and dynamic models.Design/methodology/approachFirst, the CDCR prototype is constructed, and its description is made. Second, kinematic models are established based on the constant curvature assumption and inextensible bending section. Third, by using the Lagrange method, the dynamic model is derived under some simplifications and based on the kinematic equations, in which the flexible backbone’s elasticity modulus was identified experimentally. Finally, the static model of the CDCR is also derived based on the dynamic model.FindingsNumerical examples are carried out using Matlab software to verify the static and dynamic models. Moreover, the static model is validated by comparing the simulation’s results to the real measurements that have been provided with satisfactory results.Originality/valueTo reduce the complexity of the dynamic model’s expressions and avoid the numerical singularity when the bending angle is close to zero, some simplifications have been taken, especially for the kinetic energy terms, by using the nonlinear functions approximation. Hence, the main advantage of this analytical-approximate solution is that it can be applied in the bending angle that ranges up to 2p with reasonable errors, unlike the previously proposed techniques. Furthermore, the resulting dynamic model has, to some extent, the proprieties of simplicity, accuracy and fast computation time. Ultimately, the obtained results from the simulations and real measurements demonstrate that the considered CDCR’s static and dynamic models are feasible.

Prediktivna kontrola nelinearnog modela klase kontinualnih robota koristeći kinematske i dinamičke modele

Controlling continuum robots with precision is particularly a challenging task due to the complexity of their mathematical models and inaccuracies in modeling approaches. Therefore, most advanced control schemes have shown poor performances, especially in trajectory tracking accuracy. This paper presents a proposed Nonlinear Model Predictive Control (NMPC) scheme to solve the trajectory tracking of a class of continuum robots, namely Cable-Driven Continuum Robot (CDCR). However, since NMPC schemes are often limited by the computational burden associated with the optimization algorithms to be solved at each sampling time, the Particle Swarm Optimization (PSO) algorithm is used to solve the arising optimization problem NMPC, thanks to its simplicity and fast convergence. The proposed NMPC-PSO scheme is applied to the developed kinematic and dynamic models of the considered CDCR. Based on the kinematic and dynamic model, the two proposed controllers have been validated against numerical simulations of two-dimensional CDCR with two bending sections for set-point stabilization and point-to-point trajectory tracking. For both controllers, the performance of tracking accuracy and computation time is analyzed and compared. Moreover, the obtained simulation results are compared to the available literature works. In view of the results obtained on the considered CDCR, the proposed NMPC-PSO scheme can track in real-time the desired trajectory with high accuracy and much less execution time than other advanced control schemes, which makes it an alternative for real-time applications.

Cable Decoupling and Cable-Based Stiffening of Continuum Robots

Cable-driven continuum robots, which are robots with a continuously flexible backbone and no identifiable joints that are actuated by cables, have shown great potential for many applications in unstructured, uncertain environments. However, the standard design for a cable-driven continuum robot segment, which bends a continuous backbone along a circular arc, has many compliant modes of deformation which are uncontrolled, and which may result in buckling or other undesirable behaviors if not ameliorated. In this paper, we detail an approach for using additional cables to selectively stiffen planar cable-driven robots without substantial coupling to the actuating cables. A mechanics-based model based on the planar Cosserat equations is used to find the design conditions under which additional cables can be routed without coupling of the cable lengths for small deformations. Simulations show that even for relatively large deformations, coupling remains small. A prototype is evaluated, and it is demonstrated that the compliance of the robot is substantially modified relative to the same robot without stiffening cables. Additional stiffening cables are shown to increase the end-effector output stiffness by a factor of approximately 10 over a typical design with actuating cables.

Development of a cable-driven continuum robot having a large workspace (Mechanism design of a one-segment continuum robot focused on orientation workspace)

Development of a cable-driven continuum robot having a large workspace (Mechanism design of a one-segment continuum robot focused on orientation workspace)