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Journal articles on the topic 'Concentric tubes robots'

Author: Grafiati

Published: 1 March 2025

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1

Liu, Tianxiang, Gang Zhang, Peng Zhang, Tianyu Cheng, Zijie Luo, Shengsong Wang, and Fuxin Du. "Modeling of and Experimenting with Concentric Tube Robots: Considering Clearance, Friction and Torsion." Sensors 23, no. 7 (April 3, 2023): 3709. http://dx.doi.org/10.3390/s23073709.

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Concentric tube robots (CTRs) are a promising prospect for minimally invasive surgery due to their inherent compliance and ability to navigate in constrained environments. Existing mechanics-based kinematic models typically neglect friction, clearance, and torsion between each pair of contacting tubes, leading to large positioning errors in medical applications. In this paper, an improved kinematic modeling method is developed. The effect of clearance on tip position during concentric tube assembly is compensated by the database method. The new kinematic model is mechanic-based, and the impact of friction moment and torsion on tubes is considered. Integrating the infinitesimal torsion of the concentric tube robots eliminates the errors caused by the interaction force between the tubes. A prototype is built, and several experiments with kinematic models are designed. The results indicate that the error of tube rotations is less than 2 mm. The maximum error of the feeding experiment does not exceed 0.4 mm. The error of the new modeling method is lower than that of the previous kinematic model. This paper has substantial implications for the high-precision and real-time control of concentric tube robots.

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2

Garriga-Casanovas, Arnau, and Ferdinando Rodriguez y Baena. "Complete follow-the-leader kinematics using concentric tube robots." International Journal of Robotics Research 37, no. 1 (December 28, 2017): 197–222. http://dx.doi.org/10.1177/0278364917746222.

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Concentric tube robots offer the capability of follow-the-leader motion, which is desirable when navigating in cluttered environments, such as in minimally invasive surgery or in-situ inspections. The follow-the-leader capabilities identified in the existing literature, however, are limited to trajectories with piecewise constant-curvature segments or piecewise helical segments. A complete study of follow-the-leader kinematics is, therefore, relevant to determine the full potential of these robots, and clarify an open question. In this paper, a general analysis of follow-the-leader motion is presented, and a closed-form solution to the complete set of trajectories where follow-the-leader is possible under the assumption of no axial torsion of the tubes composing the robot is derived. For designs with constant-stiffness tubes, the precurvatures required are found to be either circumference arcs, helices, or deformed helices with exponentially varying curvature magnitude. The analysis developed also elucidates additional motions of interest, such as the combination of follow-the-leader motion in a robot segment with general maneuvers in another part. To determine the applicability of the assumption regarding the tubes’ torsion, the general equilibrium of the robot designs of interest is considered, and a closed-form solution to torsion in two-tube robots with helical precurvatures is derived. Criteria to select a desired torsional behavior are then extracted. This enables one to identify stable trajectories where follow-the-leader is possible, for potential application to minimally invasive surgery. An illustrative case study involving simulation and experiment is conceived using one of these trajectories, and the results are reported, showcasing the research.

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3

Ha, Junhyoung, and Pierre E. Dupont. "Designing Stable Concentric Tube Robots Using Piecewise Straight Tubes." IEEE Robotics and Automation Letters 2, no. 1 (January 2017): 298–304. http://dx.doi.org/10.1109/lra.2016.2606656.

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4

Bruns, Trevor L., Andria A. Remirez, Maxwell A. Emerson, Ray A. Lathrop, Arthur W. Mahoney, Hunter B. Gilbert, Cindy L. Liu, et al. "A modular, multi-arm concentric tube robot system with application to transnasal surgery for orbital tumors." International Journal of Robotics Research 40, no. 2-3 (February 2021): 521–33. http://dx.doi.org/10.1177/02783649211000074.

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In the development of telemanipulated surgical robots, a class of continuum robots known as concentric tube robots has drawn particular interest for clinical applications in which space is a major limitation. One such application is transnasal surgery, which is used to access surgical sites in the sinuses and at the skull base. Current techniques for performing these procedures require surgeons to maneuver multiple rigid tools through the narrow confines of the nasal passages, leaving them with limited dexterity at the surgical site. In this article, we present a complete robotic system for transnasal surgery featuring concentric tube manipulators. It illustrates a bagging concept for sterility, and intraoperatively interchangeable instruments that work in conjunction with it, which were developed with operating room workflow compatibility in mind. The system also includes a new modular, portable surgeon console, a variable view-angle endoscope to facilitate surgical field visualization, and custom motor control electronics. Furthermore, we demonstrate elastic instability avoidance for the first time on a physical prototype in a geometrically accurate surgical scenario, which facilitates use of higher curvature tubes than could otherwise be used safely in this application. From a surgical application perspective, this article presents the first robotic approach to removing tumors growing behind the eyes in the orbital apex region, which has not been attempted previously with a surgical robot.

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5

Modes, Vincent, and Jessica Burgner-Kahrs. "Calibration of Concentric Tube Continuum Robots: Automatic Alignment of Precurved Elastic Tubes." IEEE Robotics and Automation Letters 5, no. 1 (January 2020): 103–10. http://dx.doi.org/10.1109/lra.2019.2946060.

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6

Swaney, Philip J., Arthur W. Mahoney, Bryan I. Hartley, Andria A. Remirez, Erik Lamers, Richard H. Feins, Ron Alterovitz, and Robert J. Webster. "Toward Transoral Peripheral Lung Access: Combining Continuum Robots and Steerable Needles." Journal of Medical Robotics Research 02, no. 01 (February 26, 2017): 1750001. http://dx.doi.org/10.1142/s2424905x17500015.

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Lung cancer is the most deadly form of cancer in part because of the challenges associated with accessing nodules for diagnosis and therapy. Transoral access is preferred to percutaneous access since it has a lower risk of lung collapse, yet many sites are currently unreachable transorally due to limitations with current bronchoscopic instruments. Toward this end, we present a new robotic system for image-guided trans-bronchoscopic lung access. The system uses a bronchoscope to navigate in the airway and bronchial tubes to a site near the desired target, a concentric tube robot to move through the bronchial wall and aim at the target, and a bevel-tip steerable needle with magnetic tracking to maneuver through lung tissue to the target under closed-loop control. In this work, we illustrate the workflow of our system and show accurate targeting in phantom experiments. Ex vivo porcine lung experiments show that our steerable needle can be tuned to achieve appreciable curvature in lung tissue. Lastly, we present targeting results with our system using two scenarios based on patient cases. In these experiments, phantoms were created from patient-specific computed tomography information and our system was used to target the locations of suspicious nodules, illustrating the ability of our system to reach sites that are traditionally inaccessible transorally.

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7

Jabari, Mohammad, Manizhe Zakeri, Farrokh Janabi-Sharifi, and Somayeh Norouzi-Ghazbi. "Inverse Kinematics of Concentric Tube Robots in the Presence of Environmental Constraints." Applied Bionics and Biomechanics 2021 (August 14, 2021): 1–12. http://dx.doi.org/10.1155/2021/4107732.

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Inverse kinematics (IK) of concentric tube continuum robots (CTRs) is associated with two main problems. First, the robot model (e.g., the relationship between the configuration space parameters and the robot end-effector) is not linear. Second, multiple solutions for the IK are available. This paper presents a general approach to solve the IK of CTRs in the presence of constrained environments. It is assumed that the distal tube of the CTR is inserted into a cavity while its proximal end is placed inside a tube resembling the vessel enabling the entry to the organ cavity. The robot-tissue interaction at the beginning of the organ-cavity imposed displacement and force constraints to the IK problem to secure a safe interaction between the robot and tissue. The IK in CTRs has been carried out by treating the problem as an optimization problem. To find the optimized IK of the CTR, the cost function is defined to be the minimization of input force into the body cavity and the occupied area by the robot shaft body. The optimization results show that CTRs can keep the safe force range in interaction with tissue for the specified trajectories of the distal tube. Various simulation scenarios are conducted to validate the approach. Using the IK obtained from the presented approach, the tracking accuracy is achieved as 0.01 mm which is acceptable for the application.

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8

Rucker, Caleb, Jake Childs, Parsa Molaei, and Hunter B. Gilbert. "Transverse Anisotropy Stabilizes Concentric Tube Robots." IEEE Robotics and Automation Letters 7, no. 2 (April 2022): 2407–14. http://dx.doi.org/10.1109/lra.2022.3140441.

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9

Rucker, D. Caleb, Robert J. Webster, Gregory S. Chirikjian, and Noah J. Cowan. "Equilibrium Conformations of Concentric-tube Continuum Robots." International Journal of Robotics Research 29, no. 10 (April 2010): 1263–80. http://dx.doi.org/10.1177/0278364910367543.

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10

Till, John, Vincent Aloi, Katherine E. Riojas, Patrick L. Anderson, Robert James Webster III, and Caleb Rucker. "A Dynamic Model for Concentric Tube Robots." IEEE Transactions on Robotics 36, no. 6 (December 2020): 1704–18. http://dx.doi.org/10.1109/tro.2020.3000290.

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11

Dupont, P. E., J. Lock, B. Itkowitz, and E. Butler. "Design and Control of Concentric-Tube Robots." IEEE Transactions on Robotics 26, no. 2 (April 2010): 209–25. http://dx.doi.org/10.1109/tro.2009.2035740.

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12

Morimoto, Tania K., and Allison M. Okamura. "Design of 3-D Printed Concentric Tube Robots." IEEE Transactions on Robotics 32, no. 6 (December 2016): 1419–30. http://dx.doi.org/10.1109/tro.2016.2602368.

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13

Kuntz, Alan, Armaan Sethi, Robert J. Webster, and Ron Alterovitz. "Learning the Complete Shape of Concentric Tube Robots." IEEE Transactions on Medical Robotics and Bionics 2, no. 2 (May 2020): 140–47. http://dx.doi.org/10.1109/tmrb.2020.2974523.

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14

Baek, Changyeob, Kyungho Yoon, and Do-Nyun Kim. "Finite element modeling of concentric-tube continuum robots." Structural Engineering and Mechanics 57, no. 5 (March 10, 2016): 809–21. http://dx.doi.org/10.12989/sem.2016.57.5.809.

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15

Granna, Josephine, Yi Guo, Kyle D. Weaver, and Jessica Burgner-Kahrs. "Comparison of Optimization Algorithms for a Tubular Aspiration Robot for Maximum Coverage in Intracerebral Hemorrhage Evacuation." Journal of Medical Robotics Research 02, no. 01 (February 26, 2017): 1750004. http://dx.doi.org/10.1142/s2424905x17500040.

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Intracerebral hemorrhage evacuation (ICH) using a tubular aspiration robot promises benefits over conventional approaches to release the pressure of an hemorrhage within the brain. The blood of the hemorrhage is evacuated through preplanned, coordinated motion of a flexible, curved, concentric tube that aspirates from within the hemorrhage. To achieve maximum decompression, the curvature of the inner aspirator tube has to be selected such that its workspace covers the hemorrhage. As the use of multiple aspiration tubes sequentially is advisable, one can perform an exhaustive search over all possible aspiration tube shapes as has been previously proposed in the literature. In this paper, we introduce a new optimization algorithm which is computationally more efficient and thus allows for quick optimization during surgery. To demonstrate its performance and compare it to the previously proposed exhaustive search algorithm, we present experimental evaluation results on 175 simulated patient trials.

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16

Ai Xin Jue Luo, Kevin, Jongwoo Kim, Thomas Looi, and James Drake. "Design Optimization for the Stability of Concentric Tube Robots." IEEE Robotics and Automation Letters 6, no. 4 (October 2021): 8309–16. http://dx.doi.org/10.1109/lra.2021.3102306.

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17

Lee, Dae-Young, Jongwoo Kim, Ji-Suk Kim, Changyeob Baek, Gunwoo Noh, Do-Nyun Kim, Keri Kim, Sungchul Kang, and Kyu-Jin Cho. "Anisotropic Patterning to Reduce Instability of Concentric-Tube Robots." IEEE Transactions on Robotics 31, no. 6 (December 2015): 1311–23. http://dx.doi.org/10.1109/tro.2015.2481283.

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18

Vandini, Alessandro, Christos Bergeles, Ben Glocker, Petros Giataganas, and Guang-Zhong Yang. "Unified Tracking and Shape Estimation for Concentric Tube Robots." IEEE Transactions on Robotics 33, no. 4 (August 2017): 901–15. http://dx.doi.org/10.1109/tro.2017.2690977.

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19

Riojas, Katherine E., Richard J. Hendrick, and Robert J. Webster. "Can Elastic Instability Be Beneficial in Concentric Tube Robots?" IEEE Robotics and Automation Letters 3, no. 3 (July 2018): 1624–30. http://dx.doi.org/10.1109/lra.2018.2800779.

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20

Kudryavtsev, Andrey V., Mohamed Taha Chikhaoui, Aleksandr Liadov, Patrick Rougeot, Fabien Spindler, Kanty Rabenorosoa, Jessica Burgner-Kahrs, Brahim Tamadazte, and Nicolas Andreff. "Eye-in-Hand Visual Servoing of Concentric Tube Robots." IEEE Robotics and Automation Letters 3, no. 3 (July 2018): 2315–21. http://dx.doi.org/10.1109/lra.2018.2807592.

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21

Zhang, Gang, Fuxin Du, Shaowei Xue, Hao Cheng, Xingyao Zhang, Rui Song, and Yibin Li. "Design and Modeling of a Bio-Inspired Compound Continuum Robot for Minimally Invasive Surgery." Machines 10, no. 6 (June 11, 2022): 468. http://dx.doi.org/10.3390/machines10060468.

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The continuum robot is a new type of bionic robot which is widely used in the medical field. However, the current structure of the continuum robot limits its application in the field of minimally invasive surgery. In this paper, a bio-inspired compound continuum robot (CCR) combining the concentric tube continuum robot (CTR) and the notched continuum robot is proposed to design a high-dexterity minimally invasive surgical instrument. Then, a kinematic model, considering the stability of the CTR part, was established. The unstable operation of the CCR is avoided. The simulation of the workspace shows that the introduction of the notched continuum robot expands the workspace of CTR. The dexterity indexes of the robots are proposed. The simulation shows that the dexterity of the CCR is 1.472 times that of the CTR. At last, the length distribution of the CCR is optimized based on the dexterity index by using a fruit fly optimization algorithm. The simulations show that the optimized CCR is more dexterous than before. The dexterity of the CCR is increased by 1.069 times. This paper is critical for the development of high-dexterity minimally invasive surgical instruments such as those for the brain, blood vessels, heart and lungs.

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22

Ha, Junhyoung, Frank C. Park, and Pierre E. Dupont. "Optimizing Tube Precurvature to Enhance the Elastic Stability of Concentric Tube Robots." IEEE Transactions on Robotics 33, no. 1 (February 2017): 22–37. http://dx.doi.org/10.1109/tro.2016.2622278.

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23

Renda, Federico, Conor Messer, Caleb Rucker, and Frederic Boyer. "A Sliding-Rod Variable-Strain Model for Concentric Tube Robots." IEEE Robotics and Automation Letters 6, no. 2 (April 2021): 3451–58. http://dx.doi.org/10.1109/lra.2021.3063704.

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24

Ha, Junhyoung, Frank C. Park, and Pierre E. Dupont. "Elastic Stability of Concentric Tube Robots Subject to External Loads." IEEE Transactions on Biomedical Engineering 63, no. 6 (June 2016): 1116–28. http://dx.doi.org/10.1109/tbme.2015.2483560.

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25

Girerd, Cedric, Andrey V. Kudryavtsev, Patrick Rougeot, Pierre Renaud, Kanty Rabenorosoa, and Brahim Tamadazte. "SLAM-Based Follow-the-Leader Deployment of Concentric Tube Robots." IEEE Robotics and Automation Letters 5, no. 2 (April 2020): 548–55. http://dx.doi.org/10.1109/lra.2019.2963821.

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26

Flaßkamp, K., K. Worthmann, J. Mühlenhoff, C. Greiner-Petter, C. Büskens, J. Oertel, D. Keiner, and T. Sattel. "Towards optimal control of concentric tube robots in stereotactic neurosurgery." Mathematical and Computer Modelling of Dynamical Systems 25, no. 6 (November 2, 2019): 560–74. http://dx.doi.org/10.1080/13873954.2019.1690004.

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27

Pourafzal, Mahdi, Ali Talebi, and Kanty Rabenorosoa. "Stochastic model-based contact force estimation for concentric tube robots." Mechanism and Machine Theory 180 (February 2023): 105135. http://dx.doi.org/10.1016/j.mechmachtheory.2022.105135.

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28

Uthayasooriyan, Anuraj, Fernando Vanegas, Amir Jalali, Krishna Manaswi Digumarti, Farrokh Janabi-Sharifi, and Felipe Gonzalez. "Tendon-Driven Continuum Robots for Aerial Manipulation—A Survey of Fabrication Methods." Drones 8, no. 6 (June 17, 2024): 269. http://dx.doi.org/10.3390/drones8060269.

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Aerial manipulators have seen a rapid uptake for multiple applications, including inspection tasks and aerial robot–human interaction in building and construction. Whilst single degree of freedom (DoF) and multiple DoF rigid link manipulators (RLMs) have been extensively discussed in the aerial manipulation literature, continuum manipulators (CMs), often referred to as continuum robots (CRs), have not received the same attention. This survey seeks to summarise the existing works on continuum manipulator-based aerial manipulation research and the most prevalent designs of continuous backbone tendon-driven continuum robots (TDCRs) and multi-link backbone TDCRs, thereby providing a structured set of guidelines for fabricating continuum robots for aerial manipulation. With a history spanning over three decades, dominated by medical applications, CRs are now increasingly being used in other domains like industrial machinery and system inspection, also gaining popularity in aerial manipulation. Fuelled by diverse applications and their associated challenges, researchers have proposed a plethora of design solutions, primarily falling within the realms of concentric tube (CT) designs or tendon-driven designs. Leveraging research works published in the past decade, we place emphasis on the preparation of backbones, support structures, tendons, stiffness control, test procedures, and error considerations. We also present our perspectives and recommendations addressing essential design and fabrication aspects of TDCRs in the context of aerial manipulation, and provide valuable guidance for future research and development endeavours in this dynamic field.

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29

Nguyen, D. V. A., C. Girerd, Q. Boyer, P. Rougeot, O. Lehmann, L. Tavernier, J. Szewczyk, and K. Rabenorosoa. "A Hybrid Concentric Tube Robot for Cholesteatoma Laser Surgery." IEEE Robotics and Automation Letters 7, no. 1 (January 2022): 462–69. http://dx.doi.org/10.1109/lra.2021.3128685.

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30

Webster, Robert J., and Daniel Caleb Rucker. "Parsimonious Evaluation of Concentric-Tube Continuum Robot Equilibrium Conformation." IEEE Transactions on Biomedical Engineering 56, no. 9 (September 2009): 2308–11. http://dx.doi.org/10.1109/tbme.2009.2025135.

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31

Pourafzal, Mahdi, Heidar Ali Talebi, and Kanty Rabenorosoa. "Piecewise constant strain kinematic model of externally loaded concentric tube robots." Mechatronics 74 (April 2021): 102502. http://dx.doi.org/10.1016/j.mechatronics.2021.102502.

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32

Gilbert, Hunter B., Joseph Neimat, and Robert J. Webster. "Concentric Tube Robots as Steerable Needles: Achieving Follow-the-Leader Deployment." IEEE Transactions on Robotics 31, no. 2 (April 2015): 246–58. http://dx.doi.org/10.1109/tro.2015.2394331.

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33

Khadem, Mohsen, John O'Neill, Zisos Mitros, Lyndon da Cruz, and Christos Bergeles. "Autonomous Steering of Concentric Tube Robots via Nonlinear Model Predictive Control." IEEE Transactions on Robotics 36, no. 5 (October 2020): 1595–602. http://dx.doi.org/10.1109/tro.2020.2991651.

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34

Rucker, D. Caleb, Bryan A. Jones, and Robert J. Webster III. "A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots." IEEE Transactions on Robotics 26, no. 5 (October 2010): 769–80. http://dx.doi.org/10.1109/tro.2010.2062570.

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35

Cen, Guangdu, Chao Zhang, Xing Yang, Ang Zhang, Jiaole Wang, and Shuang Song. "A Dual-Arm Concentric-Tube Robot System for Transnasal Surgery." Procedia Computer Science 209 (2022): 76–83. http://dx.doi.org/10.1016/j.procs.2022.10.101.

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36

Gilbert, Hunter B., Richard J. Hendrick, and Robert J. Webster III. "Elastic Stability of Concentric Tube Robots: A Stability Measure and Design Test." IEEE Transactions on Robotics 32, no. 1 (February 2016): 20–35. http://dx.doi.org/10.1109/tro.2015.2500422.

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37

Leibrandt, Konrad, Christos Bergeles, and Guang-Zhong Yang. "Concentric Tube Robots: Rapid, Stable Path-Planning and Guidance for Surgical Use." IEEE Robotics & Automation Magazine 24, no. 2 (June 2017): 42–53. http://dx.doi.org/10.1109/mra.2017.2680546.

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38

Alfalahi, Hessa, Federico Renda, and Cesare Stefanini. "Concentric Tube Robots for Minimally Invasive Surgery: Current Applications and Future Opportunities." IEEE Transactions on Medical Robotics and Bionics 2, no. 3 (August 2020): 410–24. http://dx.doi.org/10.1109/tmrb.2020.3000899.

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39

Liu, Shao T., and Chao Chen. "Framework of modelling concentric tube robot and comparison on computational efficiency." Meccanica 52, no. 9 (October 31, 2016): 2201–17. http://dx.doi.org/10.1007/s11012-016-0564-2.

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40

Iyengar, Keshav, George Dwyer, and Danail Stoyanov. "Investigating exploration for deep reinforcement learning of concentric tube robot control." International Journal of Computer Assisted Radiology and Surgery 15, no. 7 (June 6, 2020): 1157–65. http://dx.doi.org/10.1007/s11548-020-02194-z.

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41

Mayer, Juliane, Marcel Dumancic, and Peter P. Pott. "Symmetric single-input eccentric tube robot (ETR) for manual use." Current Directions in Biomedical Engineering 10, no. 2 (September 14, 2024): 103–6. http://dx.doi.org/10.1515/cdbme-2024-1078.

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Abstract Concentric tube robots (CTR) have gained popularity in robotic research due to their potential for smaller instrument sizes, enhanced dexterity and reduced trauma. However, CTR control can be complex, with tip direction and curvature being kinematically coupled. To address this, a symmetric eccentric tube robot (ETR) is presented, where three identical pre-curved wires are arranged in parallel and constrained by an outer sheath. Instrument curvature is controlled by a single input angle. This study aims to demonstrate the suitability as manually actuated instrument. A model for curvature as a function of input angle is presented, and a prototype ETR with an outer diameter of 1 mm is assembled and evaluated. The results show that the ETR follows the expected shape, the curvature decreasing with the separation angle in an almost linear way that may be perceived as intuitive and predictable by the human user. However, some unsteady behavior (snapping) is observed, which may be addressed by preventing torsion of the wires through mechanical means. The simplified model neglecting the sheath stiffness provides precise enough predictions for the working space of a manual ETR. The findings suggest that manual ETRs have potential applications in superficial interventions, such as injections, arthroscopy, or ophthalmic surgery, where their curved section can be beneficial in comparison to current straight needles. Further research could explore interlocking mechanical designs to prevent torsion or modular setups for enhanced functionality.

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42

Gilbert, Hunter, Robert Webster, Paul Russell, Kyle Weaver, and Philip Swaney. "Endonasal Skull Base Tumor Removal Using Concentric Tube Continuum Robots: A Phantom Study." Journal of Neurological Surgery Part B: Skull Base 76, no. 02 (November 7, 2014): 145–49. http://dx.doi.org/10.1055/s-0034-1390401.

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43

Donat, Heiko, Sven Lilge, Jessica Burgner-Kahrs, and Jochen J. Steil. "Estimating Tip Contact Forces for Concentric Tube Continuum Robots Based on Backbone Deflection." IEEE Transactions on Medical Robotics and Bionics 2, no. 4 (November 2020): 619–30. http://dx.doi.org/10.1109/tmrb.2020.3034258.

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44

Hoffmann, Matthias K., Willem Esterhuizen, Karl Worthmann, and Kathrin Flaßkamp. "Path Planning for Concentric Tube Robots: A Toolchain with Application to Stereotactic Neurosurgery." IFAC-PapersOnLine 56, no. 2 (2023): 2871–76. http://dx.doi.org/10.1016/j.ifacol.2023.10.1403.

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45

Wei, Hangxing, Gang Zhang, Shengsong Wang, Peng Zhang, Jing Su, and Fuxin Du. "Coupling Analysis of Compound Continuum Robots for Surgery: Another Line of Thought." Sensors 23, no. 14 (July 14, 2023): 6407. http://dx.doi.org/10.3390/s23146407.

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The compound continuum robot employs both concentric tube components and cable-driven continuum components to achieve its complex motions. Nevertheless, the interaction between these components causes coupling, which inevitably leads to reduced accuracy. Consequently, researchers have been striving to mitigate and compensate for this coupling-induced error in order to enhance the overall performance of the robot. This paper leverages the coupling between the components of the compound continuum robot to accomplish specific surgical procedures. Specifically, the internal concentric tube component is utilized to induce motion in the cable-driven external component, which generates coupled motion under the constraints of the cable. This approach enables the realization of high-precision surgical operations. Specifically, a kinematic model for the proposed robot is established, and an inverse kinematic algorithm is developed. In this inverse kinematic algorithm, the solution of a highly nonlinear system of equations is simplified into the solution of a single nonlinear equation. To demonstrate the effectiveness of the proposed approach, simulations are conducted to evaluate the efficiency of the algorithm. The simulations conducted in this study indicate that the proposed inverse kinematic (IK) algorithm improves computational speed by a significant margin. Specifically, it achieves a speedup of 2.8 × 103 over the Levenberg–Marquardt (LM) method. In addition, experimental results demonstrate that the coupled-motion system achieves high levels of accuracy. Specifically, the repetitive positioning accuracy is measured to be 0.9 mm, and the tracking accuracy is 1.5 mm. This paper is significant for dealing with the coupling of the compound continuum robot.

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46

Ha, Junhyoung, Georgios Fagogenis, and Pierre E. Dupont. "Modeling Tube Clearance and Bounding the Effect of Friction in Concentric Tube Robot Kinematics." IEEE Transactions on Robotics 35, no. 2 (April 2019): 353–70. http://dx.doi.org/10.1109/tro.2018.2878906.

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Li, Zihao, Xing Yang, Shuang Song, Li Liu, and Max Q. H. Meng. "Tip estimation approach for concentric tube robots using 2D ultrasound images and kinematic model." Medical & Biological Engineering & Computing 59, no. 7-8 (June 22, 2021): 1461–73. http://dx.doi.org/10.1007/s11517-021-02369-z.

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Yang, Xing, Jiaole Wang, Shuang Song, and Max Q. H. Meng. "Model-Free and Uncalibrated Eye-in-Hand Visual Servoing Approach for Concentric-Tube Robots." IEEE Transactions on Instrumentation and Measurement 71 (2022): 1–11. http://dx.doi.org/10.1109/tim.2022.3147867.

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Chikhaoui, Mohamed Taha, Josephine Granna, Julia Starke, and Jessica Burgner-Kahrs. "Toward Motion Coordination Control and Design Optimization for Dual-Arm Concentric Tube Continuum Robots." IEEE Robotics and Automation Letters 3, no. 3 (July 2018): 1793–800. http://dx.doi.org/10.1109/lra.2018.2800037.

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Girerd, Cedric, Andrey V. Kudryavtsev, Patrick Rougeot, Pierre Renaud, Kanty Rabenorosoa, and Brahim Tamadazte. "Automatic Tip-Steering of Concentric Tube Robots in the Trachea Based on Visual SLAM." IEEE Transactions on Medical Robotics and Bionics 2, no. 4 (November 2020): 582–85. http://dx.doi.org/10.1109/tmrb.2020.3034720.

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