A feedforward tendon-elongation compensator for tendon-sheath mechanisms with arbitrary and time-varying transmission routes in three-dimensional space

Abstract

Tendon-sheath mechanisms (TSMs) are widely used for position transmission in robotic systems that require compactness and adaptability to complex environments. However, friction-induced tendon-elongation disrupts the alignment between input and output positions, preventing the robotic end-effector from accurately following motion commands. Since tendon-elongation depends on the configuration of the transmission route, resolving position transmission misalignment in TSMs becomes even more challenging. Building upon the tendon-elongation compensator developed in the author’s recent work, this study presents a technical note aiming to align the actual output position with the desired position. The improved compensator operates without relying on any distal sensory feedback, thereby preserving the compactness of the system. Notably, it is applicable to TSMs with arbitrary and time-varying transmission routes in three-dimensional (3-D) space, fulfilling the adaptability requirement. Preliminary experimental results demonstrate the potential of the presented technique, achieving 96.44%–97.56% accuracy in distal position tracking. By tackling a long-standing challenge in TSM research, this study lays a technical foundation for future advancements in the field.

Keywords

Tendon-sheath mechanism / Tendon-elongation compensation / Feedforward control / Flexible position transmission

CRediT authorship contribution statement

Qian Gao: Writing – review & editing, Supervision, Resources, Project administration, Methodology, Investigation, Conceptualization. Jiaqi Li: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Formal analysis, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors would like to express sincere gratitude to Mr. Guanglin Ji from the Chinese University of Hong Kong (Shenzhen) and the Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, China, for his invaluable guidance and generous assistance in programming-related aspects. Special thanks are also extended to Ms. Minyi Sun from Vanderbilt University, Nashville, United States; Mr. Yin Xiao and Mr. Sihan Shang from the Chinese University of Hong Kong (Shenzhen), Shenzhen, China; and Mr. Huaiyuan Rao from the Georgia Institute of Technology, Atlanta, United States, for their helpful contributions to code implementation and debugging.

The authors are deeply grateful to Prof. Zhenglong Sun from the Chinese University of Hong Kong (Shenzhen) and the Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, China, for his insightful guidance on the research direction. In addition, heartfelt thanks go to Prof. Qinghua Zeng from Nanjing University of Aeronautics and Astronautics, Nanjing, China, for kindly providing partial experimental equipment and assigning a student to assist with the execution of this research.

Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.birob.2026.100278.

References

[1] Z. Zhang, G. Zhang, S. Wang, C. Shi, Hysteresis modeling and compensation for tendon-sheath mechanisms in robot-assisted endoscopic surgery based on the modified Bouc-Wen model with decoupled model parameters, IEEE Trans. Med. Robot. Bionics 5 (2) (2023) 218-229.

[2] T. Do, T. Tjahjowidodo, M. Lau, S. Phee, Adaptive control for enhancing tracking performances of flexible tendon–sheath mechanism in natural orifice transluminal endoscopic surgery, Mechatronics 28 (2015) 67-78.

[3] M. Yin, D. Shang, T. Xu, X. Wu, Joint modeling and closed-loop control of a robotic hand driven by the tendon-sheath, IEEE Robot. Autom. Lett. 6 (4) (2021) 7333-7340.

[4] J. Sanjuan, A.D. Castillo, M.A. Padilla, M.C. Quintero, E. Gutierrez, I.P. Sampayo, J.R. Hernandez, M.H. Rahman, Cable driven exoskeleton for upper-limb rehabilitation: A design review, Robot. Auton. Syst. 126 (2020) 103445.

[5] X. Wang, Q. Zhang, X. Shen, J. Li, Noncollocated position control of tendon-sheath actuated slender manipulator, IEEE Trans. Control Syst. Technol. 28 (2) (2018) 688-696.

[6] P. Daemi, Y. Zhou, M.D. Naish, A.D. Price, A.L. Trejos, Comprehensive kinematic model of a tendon-driven wearable tremor suppression device, IEEE Trans. Robot. 40 (2023) 421-437.

[7] M. Yin, H. Wu, Z. Xu, W. Han, Z. Zhao, Compliant control of single tendon-sheath actuators applied to a robotic manipulator, IEEE Access 8 (2020) 37361-37371.

[8] X. Li, L. Cao, A.M.H. Tiong, P.T. Phan, S.J. Phee, Distal-end force prediction of tendon-sheath mechanisms for flexible endoscopic surgical robots using deep learning, Mech. Mach. Theory 134 (2019) 323-337.

[9] Z. Sun, Z. Wang, S.J. Phee, Modeling and motion compensation of a bidirectional tendon-sheath actuated system for robotic endoscopic surgery, Comput. Methods Programs Biomed. 119 (2) (2015) 77-87.

[10] X. Shen, X. Wang, M. Tian, Q. Zhang, Modeling and sensorless force control of novel tendon-sheath artificial muscle based on hill muscle model, Mechatronics 62 (2019) 102243.

[11] Y. Jung, J. Bae, Torque control of a series elastic tendon-sheath actuation mechanism, IEEE/ASME Trans. Mechatronics 25 (6) (2020) 2915-2926.

[12] T. Do, T. Tjahjowidodo, M.W.S. Lau, S.J. Phee, An investigation of friction-based tendon sheath model appropriate for control purposes, Mech. Syst. Signal Process. 42 (1–2) (2014) 97-114.

[13] Q. Wu, X. Wang, L. Chen, F. Du, Transmission model and compensation control of double-tendon-sheath actuation system, IEEE Trans. Ind. Electron. 62 (3) (2014) 1599-1609.

[14] W. Lai, L. Cao, Z. Xu, P.T. Phan, P. Shum, S.J. Phee, Distal end force sensing with optical fiber bragg gratings for tendon-sheath mechanisms in flexible endoscopic robots, 2018 IEEE International Conference on Robotics and Automation, ICRA, IEEE, 2018, pp. 5255-5349.

[15] Y. Li, W. Lu, Y. Liu, D. Meng, X. Wang, B. Liang, Optimization design method of tendon-sheath transmission path under curvature constraint, IEEE Trans. Robot. 39 (4) (2023) 2933-2953.

[16] H. Gao, R. Hao, X. Yang, C. Li, Z. Zhang, X. Zuo, Y. Li, H. Ren, Modeling and compensation of stiffness-dependent hysteresis for stiffness-tunable tendon-sheath mechanism in flexible endoscopic robots, IEEE Trans. Ind. Electron. 71 (8) (2023) 9328-9338.

[17] Z. Sun, Z. Wang, S.J. Phee, Elongation modeling and compensation for the flexible tendon–sheath system, IEEE/ASME Trans. Mechatronics 19 (4) (2013) 1243-1250.

[18] X. Wang, Y. Fang, N. Yu, J. Han, Barrier function-based adaptive control of twisted tendon-sheath actuated system with unknown rigid–flexible coupling for robotic ureteroscopy, IEEE/ASME Trans. Mechatronics 29 (3) (2023) 2362-2372.

[19] Q. Zhang, M. Yang, X. Shen, M. Tian, X. Wang, Muscle-like contraction control of tendon-sheath artificial muscle, Mechatronics 77 (2021) 102584.

[20] Z. Wang, Z. Sun, S.J. Phee, Modeling tendon-sheath mechanism with flexible configurations for robot control, Robotica 31 (7) (2013) 1131-1142.

[21] D. Kim, H. Kim, S. Jin, Recurrent neural network with preisach model for configuration-specific hysteresis modeling of tendon-sheath mechanism, IEEE Robot. Autom. Lett. 7 (2) (2022) 2763-2770.

[22] T. Do, T. Tjahjowidodo, M.W.S. Lau, S.J. Phee, A new approach of friction model for tendon-sheath actuated surgical systems: Nonlinear modelling and parameter identification, Mech. Mach. Theory 85 (2015) 14-24.

[23] Q. Wu, X. Wang, B. Chen, H. Wu, Modeling, online identification, and compensation control of single tendon sheath system with time-varying configuration, Mech. Syst. Signal Process. 130 (2019) 56-73.

[24] W. Lai, L. Cao, J. Liu, S.C. Tjin, S.J. Phee, A three-axial force sensor based on fiber Bragg gratings for surgical robots, IEEE/ASME Trans. Mechatronics 27 (2) (2021) 777-789.

[25] Y. Lu, H. Li, K. Shi, J. Lai, Y. Li, M. Zhang, A. Song, A comprehensive control method for tendon–sheath system using friction model-based angle estimation and feedforward-feedback control in time-varying configurations, IEEE Trans. Ind. Electron. 71 (5) (2023) 5166-5175.

[26] Z. Shao, Q. Wu, B. Chen, H. Wu, Y. Zhang, Modeling and inverse control of a compliant single-tendon-sheath artificial tendon actuator with bending angle compensation, Mechatronics 63 (2019) 102262.

[27] W. Lai, L. Cao, R.X. Tan, P.T. Phan, J. Hao, S.C. Tjin, S.J. Phee, Force sensing with 1 mm fiber Bragg gratings for flexible endoscopic surgical robots, IEEE/ASME Trans. Mechatronics 25 (1) (2019) 371-382.

[28] X. Wang, N. Yu, J. Han, Y. Fang, Modeling and robust control for tendon–sheath artificial muscle system twist with time-varying parameters and input constraints: An exploratory research, IEEE Trans. Ind. Electron. 70 (1) (2021) 878-887.

[29] T. Do, T. Tjahjowidodo, M. Lau, S. Phee, Nonlinear friction modelling and compensation control of hysteresis phenomena for a pair of tendon-sheath actuated surgical robots, Mech. Syst. Signal Process. 60 (2015) 770-784.

[30] L. Chen, X. Wang, W. Xu, Inverse transmission model and compensation control of a single-tendon–sheath actuator, IEEE Trans. Ind. Electron. 61 (3) (2013) 1424-1433.

[31] D.-H. Lee, Y.-H. Kim, J. Collins, A. Kapoor, D.-S. Kwon, T. Mansi, Non-linear hysteresis compensation of a tendon-sheath-driven robotic manipulator using motor current, IEEE Robot. Autom. Lett. 6 (2) (2021) 1224-1231.

[32] G. Zhang, X. Wang, Design and 3D reconstruction of a tendon-sheath-driven searching and rescuing robot, 2013 IEEE International Symposium on Safety, Security, and Rescue Robotics, SSRR, IEEE, 2013, pp. 1-6.

[33] A. Wang, J. Ramos, J. Mayo, W. Ubellacker, J. Cheung, S. Kim, The HERMES humanoid system: A platform for full-body teleoperation with balance feedback, 2015 IEEE-RAS 15th International Conference on Humanoid Robots, Humanoids, IEEE, 2015, pp. 730-737.

[34] J. Kim, J. Moon, S. Park, G. Lee, Characterizing force capability and stiffness of hip exosuits under different anchor points, Plos One 17 (8) (2022) e0271764.

[35] B.B. Kang, H. Choi, H. Lee, K.-J. Cho, Exo-glove poly II: A polymer-based soft wearable robot for the hand with a tendon-driven actuation system, Soft Robot. 6 (2) (2019) 214-227.

[36] U. Jeong, K.-J. Cho, A novel low-cost, large curvature bend sensor based on a Bowden-cable, Sensors 16 (7) (2016) 961.

[37] X. Li, A.M.H. Tiong, L. Cao, W. Lai, P.T. Phan, S.J. Phee, Deep learning for haptic feedback of flexible endoscopic robot without prior knowledge on sheath configuration, Int. J. Mech. Sci. 163 (2019) 105-129.

[38] Q. Gao, G. Ji, M. Sun, Y. Xiao, H. Rao, Z. Sun, Dynamic hysteresis compensation for tendon-sheath mechanism in flexible surgical robots without distal perception, IEEE Trans. Robot. 41 (2025) 3703-3721.

[39] S. Atallah, B. Martin-Perez, D. Keller, J. Burke, L. Hunter, Natural-orifice transluminal endoscopic surgery, J. Br. Surg. 102 (2) (2015) e73-e92.

[40] E.D. Auyang, B.F. Santos, D.H. Enter, E.S. Hungness, N.J. Soper, Natural orifice translumenal endoscopic surgery (notes®): a technical review, Surg. Endosc. 25 (10) (2011) 3135-3148.

[41] Q. Gao, Z. Sun, A novel design of water-activated variable stiffness endoscopic manipulator with safe thermal insulation, Actuators, vol. 10, MDPI (2021), p. 130.

[42] H. Kim, D. Kim, S.H. Park, S. Jin, Hysteresis compensation of tendon-sheath mechanism using nonlinear programming based on Preisach model, IEEE Robot. Autom. Lett. 9 (6) (2024) 5246-5253.

[43] B.K. Dinh, M. Xiloyannis, L. Cappello, C.W. Antuvan, S.-C. Yen, L. Masia, Adaptive backlash compensation in upper limb soft wearable exoskeletons, Robot. Auton. Syst. 92 (2017) 173-186.

[44] T. Zhang, M. Liu, Y. Lei, F. Du, R. Song, Y. Li, Analysis of dynamic friction and elongation characteristics of the tendon sheath system, International Conference on Intelligent Robotics and Applications, Springer, 2021, pp. 145-154.

[45] X. Wang, D. Bie, J. Han, Y. Fang, Active modeling and compensation for the hysteresis of a robotic flexible ureteroscopy, IEEE Access 8 (2020) 100620-100630.

[46] T. Do, T. Tjahjowidodo, M. Lau, S. Phee, Real-time enhancement of tracking performances for cable-conduit mechanisms-driven flexible robots, Robot. Comput.-Integr. Manuf. 37 (2016) 197-207.

[47] W. Jiang, T. Yu, X. He, Y. Yang, Z. Wang, H. Liu, Data-driven modeling the nonlinear backlash of steerable endoscope under a large deflection cannulation in ERCP surgery, 2021 IEEE International Conference on Real-Time Computing and Robotics, RCAR, IEEE, 2021, pp. 39-44.

[48] Q. Gao, N. Tan, Z. Sun, A hybrid learning-based hysteresis compensation strategy for surgical robots, Int. J. Med. Robot. Comput. Assist. Surg. 17 (4) (2021) e2275.

[49] Y. Lu, B. Lu, B. Li, H. Guo, Y.-h. Liu, Robust three-dimensional shape sensing for flexible endoscopic surgery using multi-core FBG sensors, IEEE Robot. Autom. Lett. 6 (3) (2021) 4835-4842.

[50] C.-H. Yeh, Y.-H. Zhuang, N. Tsai, C.-W. Chow, Capacity and capability enhancements of FBG sensor system by utilizing intensity and WDM detection technique, Smart Mater. Struct. 26 (3) (2017) 026-035.

[51] H. Lin, Q. Gao, X. Chu, Q. Dou, A. Deguet, P. Kazanzides, K.S. Au, Learning deep nets for gravitational dynamics with unknown disturbance through physical knowledge distillation: initial feasibility study, IEEE Robot. Autom. Lett. 6 (2) (2021) 2658-2665.

[52] W. Luo, B. Qiao, Z. Shen, Z. Yang, H. Cao, X. Chen, Investigation on the influence of spalling defects on the dynamic performance of planetary gear sets with sliding friction, Tribol. Int. 154 (2021) 106639.

[53] Y. Tang, M. Pan, Y. Lin, K. Liang, Research on force and position control performance of the tendon sheath system with time-varying parameters and flexible robotic arms, Int. J. Med. Robot. Comput. Assist. Surg. 19 (4) (2023) e2517.

[54] Y. Lu, W. Chen, B. Li, B. Lu, J. Zhou, Z. Chen, Y.-H. Liu, A robust graph-based framework for 3-d shape reconstruction of flexible medical instruments using multi-core fbgs, IEEE Trans. Med. Robot. Bionics 5 (3) (2023) 472-485.

[55] O. Al-Ahmad, M. Ourak, J. Van Roosbroeck, J. Vlekken, E. Vander Poorten, Improved FBG-based shape sensing methods for vascular catheterization treatment, IEEE Robot. Autom. Lett. 5 (3) (2020) 4687-4694.

[56] Q. Gao, G. Ji, Z. Sun, Robust shape-distortion prediction for a wire-driven hyper-redundant manipulator with engaging rolling joints, IEEE Trans. Med. Robot. Bionics 5 (2) (2023) 265-277.

[57] T. Hogervorst, R. Nane, G. Marchiori, T.D. Qiu, M. Blatt, A.B. Rustad, Hardware acceleration of high-performance computational flow dynamics using high-bandwidth memory-enabled field-programmable gate arrays, ACM Trans. Reconfigurable Technol. Syst. (TRETS) 15 (2) (2021) 1-35.