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Performance evaluation of Particle Swarm Optimization variants for trajectory tracking of a cable-driven continuum robot: descriptive, parametric, and non-parametric statistical analysis

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2025年第2期138卷 603-615页

作者： Amouri, Ammar Leksir, Yazid Laib Dit Merabti, Halim Belkhiri, Ayman Cherfia, Abdelhakim Freres Mentouri Constantine 1 Univ Dept Mech Engn Lab Mech BP 325 Ain Bey Rd Constantine 25017 Algeria Univ Larbi Ben Mhidi Lab Act Components & Mat BP 358 Constantine Rd Oum El Bouaghi 04000 Algeria Res Ctr Ind Technol CRTI POB 64 Algiers 16014 Algeria

This paper presents a comprehensive evaluation of Particle Swarm Optimization (PSO) variants for trajectory tracking of a cable-driven continuum robot, utilizing descriptive statistical metrics along with parametric and non-parametric methods for performance assessment. The forward kinematic model of the robot was derived using the constant curvature approach, and the trajectory tracking problem was formulated as an optimization task. Five PSO variants, namely Standard PSO (S-PSO), Weighted PSO (W-PSO), Quantum PSO (Q-PSO), Sine-Cosine PSO (SC-PSO), and Constricted PSO (C-PSO), were reviewed and applied to two optimization scenarios: achieving a target point without considering end-tip orientation as a basic optimization problem and achieving both position and orientation as a more complex optimization problem. To evaluate their effectiveness and robustness, each algorithm was run 30 times per scenario to optimize the arc parameters necessary for tracking 500 randomly selected end-tip poses within the robot's workspace. Descriptive statistics, as well as parametric and non-parametric statistical tests, including one-way ANOVA, Kruskal-Wallis, and Dunn's post hoc test with Holm-Bonferroni correction, were used to compare the PSO variants based on tracking error, execution time, and number of iterations. The analysis showed that for simpler trajectory tracking problems, S-PSO and W-PSO were preferred, but as task complexity increased, these variants became less effective, with Q-PSO and SC-PSO performing better in more complex scenarios. Meanwhile, C-PSO consistently underperformed across all scenarios.

关键词： continuum robot cable-driven continuum robot Trajectory tracking Particle Swarm Optimization Descriptive statistics Parametric and non-parametric statistical analysis

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An Accuracy Enhancement Method for a cable-driven continuum robot With a Flexible Backbone

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IEEE ACCESS 2020年 8卷 37474-37481页

作者： Shen, Wenjun Yang, Guilin Zheng, Tianjiang Wang, Yi Yang, Kaisheng Fang, Zaojun Chinese Acad Sci Ningbo Inst Mat Technol & Engn Zhejiang Key Lab Robot & Intelligent Mfg Equipmet Ningbo 315201 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China Zhejiang Marine Dev Res Inst Zhoushan 316021 Peoples R China

In this paper, an integrated accuracy enhancement method based on both the kinematic model and the data-driven Gaussian Process Regression (GPR) technique is proposed for a cable-driven continuum robot (CDCR) with a flexible backbone. Different from the conventional continuum robots driven by pneumatic actuators, a segmented CDCR is developed in this work, which is a modular manipulator composed by a number of consecutive cable-driven Segments (CDSs). Based on the unique design of the backbone structure which merely allows 2-DOF bending motions, a two-variable Product-of-Exponential (POE) formula is employed to formulate the kinematic model of the CDCR. However, such an analytic kinematic model is unable to accurately describe the actual deflections of the backbone structure. Therefore, GPR is proposed to compensate the tip error of a CDCR. Compared with other machine learning methods, GPR requires less learning parameters and training data, which makes the learning process computationally efficient. To validate the effectiveness of the proposed integrated accuracy enhancement method, experiments on the actual testbed are conducted. Experimental results show that the CDCR's position and orientation errors are reduced by 68.72% and 51.74%, respectively.

关键词： cable-driven continuum robot kinematic modeling tip error compensation Gaussian process regression

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

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JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING 2023年第5期45卷 1-17页

作者： Amouri, Ammar Cherfia, Abdelhakim Belkhiri, Ayman Merabti, Halim Freres Mentouri Constantine 1 Univ Dept Mech Engn Lab Mech BP 325Ain Bey Rd Constantine 25017 Algeria CRTI Res Ctr Ind Technol POB 64 Algiers 16014 Algeria

In recent years, research on continuum robots has advanced significantly to overcome the limitations of rigid-link robots that particularly suffer when working in a confined environment and have some insecure interaction. To address these issues, this paper proposes a design of a novel cable-driven continuum robot (CDCR) serially formed by dual-cross-module sections inspired by a fish bone-like structure. The proposed design combines multiple features of lightweight, flexibility, rigid structural stability, and asymmetric-shaped workspace. Furthermore, based on the famous Constant Curvature Kinematic Approach, the paper develops the forward and inverse kinematics of the proposed CDCR. The Forward Kinematics (FKs) are analytically developed, whereas the Inverse Kinematics (IKs) are numerically calculated. The IK of a single CDCR's section, i.e., dual-cross-module CDCR's section, is computed using polynomial functions fitting. Knowing the end-tip coordinates of each CDCR's section, which are determined using Particle Swarm Optimization algorithm, the IK of multi-section CDCR is iteratively derived using a modular and IK-based concept of a single CDCR's section. Besides, the CDCR's workspace is analyzed and compared to that with a cylindrical backbone. Finally, in order to validate the proposed approaches, simulation examples via Matlab software for point-to-point trajectory tracking in free environment, are carried out. In addition, experimental measurements are conducted using a single CDCR's section in order to evaluate the kinematic models and to analyze the design principle in terms of load capacity.

关键词： continuum robot cable-driven continuum robot Design Kinematics modeling Workspace analysis

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

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WORLD JOURNAL OF ENGINEERING 2023年第4期20卷 631-640页

作者： Bousbia, Leila Amouri, Ammar Cherfia, Abdelhakim Univ Freres Mentouri Constantine 1 Dept Genie Mecan Lab Mecan Constantine Algeria

Purpose continuum 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/approach First, 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. Findings Numerical 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/value To 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.

关键词： Dynamic cable-driven continuum robot continuum robot Elasticity modulus identification Static equilibrium

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Optimal cable Arrangement Design for A cable-driven continuum robot with the Flexible Backbone 19

Optimal Cable Arrangement Design for A Cable-driven Continuu...

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IEEE 19th Conference on Industrial Electronics and Applications (ICIEA)

作者： Shen, Wenjun Yang, Guilin Zhang, Hao Fang, Zaojun Bai, Haotian Zhou, Jianwei Chinese Acad Sci Ningbo Inst Mat Technol & Engn Ningbo Peoples R China Zhejiang Key Lab Robot & Intelligent Mfg Equipmen Ningbo Peoples R China Univ Chinese Acad Sci Beijing Peoples R China

ISBN: (纸本)9798350360875;9798350360868

cable-driven continuum robots (CDCRs) with flexible backbones have been developed to perform dexterous manipulation tasks in various confined spaces due to their high flexibility and environment adaptability. A CDCR normally consists of a number of serially-connected identical cable-driven continuum Joint Modules (CDCJMs). To produce large bending movements, a CDCJM often employs a parallel cable arrangement scheme, i.e., all of its driving cables are parallel to each other in its initial pose. However, such a CDCJM will suffer form the kinematics singularity in its initial pose, in which its flexible backbone will likely produce uncontrollable s-shaped deflection curves. To overcome such difficulties, this paper proposes a tilted cable arrangement scheme for the CDCJM. Considering symmetric arrangements of driving cables, a total of six tilted cable arrangement cases are investigated. Based on the structure matrices, the statics equilibrium equations are developed for the CDCJMs. To maximize the lateral force that the cable tensions of the CDCJM can sustain, the number of driving cables and the positions of cable attachment points are optimized. The simulation results indicate that the 2-2 cable arrangement is the optimal cable arrangement for the CDCJM.

关键词： cable-driven continuum robot cable arrangement scheme kinetostatic analysis design optimization

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Shape Sensing and Kinematic Control of a cable-driven continuum robot Based on Stretchable Capacitive Sensors

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SENSORS 2024年第11期24卷 3385页

作者： Shen, Wenjun He, Jianhui Yang, Guilin Kong, Xiangjie Bai, Haotian Fang, Zaojun Chinese Acad Sci Ningbo Inst Mat Technol & Engn Zhejiang Key Lab Robot & Intelligent Mfg Equipment Ningbo 315201 Peoples R China Univ Chinese Acad Sci Coll Mat Sci & Optoelect Technol Beijing 100049 Peoples R China Univ Nottingham Nottingham Ningbo China Beacons Excellence Res & I Sch Comp Sci Ningbo 315199 Peoples R China

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

关键词： cable-driven continuum robot stretchable capacitive sensors shape-sensing model closed-loop control

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Composite Motion Control of cable-driven continuum robots: An Auxiliary-System Based Compensation Method

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2025年

作者： Zhang, Kuan Liu, Yanhong Huo, Benyan Wu, Zhenlong Yu, Hongnian Zhengzhou Univ Sch Elect Engn Zhengzhou 450001 Peoples R China Edinburgh Napier Univ Sch Engn & Built Environm Edinburgh EH14 1DJ Scotland

High-performance motion control of cable-driven continuum robots is challenging due to the inherent model uncertainties, actuator saturation, and measurement delays. Inthis article,we utilize the idea of auxiliary systemto reveal the dynamics of the model uncertainties, actuator saturation, andmeasurement delays, and design a composite motion control strategy to compensate themsimultaneously. First, a time-delay auxiliary system is designed using Pade approximation technique to approximate the saturated time delay, thereby transforming the saturated continuum robot system with time delay into one without time delay. A disturbance auxiliary system and a saturated auxiliary system are also designed to estimate model uncertainties and address actuator saturation, respectively. Second, based on the designed auxiliary systems, a feedback controller is proposed to compensate the model uncertainties, actuator saturation, and measurement delays. The stability of the closed loop system under the proposed control scheme is analyzed as well. Finally, the effectiveness of the proposed control scheme is verified by comparative simulations and experiments.

关键词： continuum robots Uncertainty Delays Actuators Measurement uncertainty Motion control Delay effects Closed loop systems Tracking Springs Actuator saturation auxiliary system cable-driven continuum robot measurement delays model uncertainties motion control

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A Preprogrammable continuum robot Inspired by Elephant Trunk for Dexterous Manipulation

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SOFT robotICS 2023年第3期10卷 636-646页

作者： Zhang, Jie Li, You Kan, Ziyun Yuan, Qiufeng Rajabi, Hamed Wu, Zhigang Peng, Haijun Wu, Jianing Sun Yat Sen Univ Sch Aeronaut & Astronaut Shenzhen Peoples R China Dalian Univ Technol Sch Mech Engn Dalian Peoples R China China Univ Geosci Sch Engn & Technol Beijing Peoples R China London South Bank Univ Sch Engn Div Mech Engn & Design London England London South Bank Univ Bioengn Res Ctr BERC Sch Engn Mech Intelligence Res Grp London England Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian Peoples R China Sun Yat Sen Univ Sch Adv Mfg Shenzhen Peoples R China Sun Yat Sen Univ Sch Aeronaut & Astronaut Shenzhen 518107 Peoples R China Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 518107 Peoples R China

cable-driven continuum robots with hyper-redundant deformable backbones show great promise in applications, such as inspection in unstructured environments, where traditional rigid robots with discrete links and joints fail to operate. However, the motion of existing continuum robots is still constrained by their homogeneous backbones, and limited to environments with modest geometrical complexity. In this study, inspired by highly deformable elephant trunks, we presented a modular tensegrity structure with preprogrammable stiffness for continuum robots. Then we derived a mechanical model based on a positional formulation finite element method for predicting the configuration of the structure in different deformation scenarios. Theoretical predictions revealed that the curvature of each segment could be regulated by preprogramming their spring stiffness. Hence, our customizable design could offer an effective route for efficient robotic interactions. We further fabricated a continuum robot consisting of 12 modules, and showcased its deformation patterns under multiple scenarios. By regulating the distribution of spring stiffness, our robot could move through channels with varying curvatures, exhibiting its potential for applications where varying curvature, and conformal and efficient interactions are needed. Leveraging the inherent intelligence, this robotic system could simplify the complexity of the required actuation and control systems.

关键词： preprogrammable stiffness cable-driven continuum robot modular tensegrity structure varying curvatures morphing

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