Tendon friction compensation and slack avoidance for trajectory tracking control of the tendon-driven medical continuum manipulator

Abstract

Tendon-driven continuum manipulators can perform tasks in confined environments due to their flexibility and curvilinearity, especially in minimally invasive surgeries. However, the friction along tendons and tendon slack present challenges to their motion control. This work proposes a trajectory tracking controller based on adaptive fuzzy sliding mode control (AFSMC) for the tendon-driven continuum manipulators. It consists of a sliding mode control (SMC) law with two groups of adaptive fuzzy subcontrollers. The first one is utilized to estimate and compensate for friction forces along tendons. The second one adapts the switching terms of SMC to alleviate the chattering phenomenon and enhance control robustness. To prevent tendon slack, an antagonistic strategy along with the AFSMC controller is adopted to allocate driving forces. Simulation and experiment studies have been conducted to investigate the efficacy of the proposed controller. In free space experiments, the AFSMC controller generates an average root-mean-square error (RMSE) of 0.42% compared with 0.90% of the SMC controller. In the case of a 50 g load, the proposed controller reduces the average RMSE to 1.47% compared with 4.29% of the SMC controller. These experimental results demonstrate that the proposed AFSMC controller has high control accuracy, robustness, and reduced chattering.

Keywords

Continuum manipulator / Minimally invasive surgeries / Trajectory tracking / Adaptive fuzzy control

CRediT authorship contribution statement

Pengyu Du: Writing - original draft, Validation, Methodology. Jianxiong Hao: Writing - original draft, Methodology, Data curation. Kun Qian: Writing - original draft, Supervision, Methodology. Yue Zhang: Writing - review & editing, Visualization, Validation, Data curation. Zhiqiang Zhang: Writing - review & editing, Supervision, Project administration, Methodology, Investigation, Funding acquisition. Chaoyang Shi: Writing - review & editing, Methodology, Investigation, Funding acquisition, Conceptualization.

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

This work is partly supported by the National Natural Science Foundation of China (92148201, 52475029). This work is also supported by International Institute for Innovative Design and Intelligent Manufacturing of Tianjin University in Zhejiang, Shaoxing 312000, China.

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.

References

[1] P.E. Dupont, B.J. Nelson, M. Goldfarb, B. Hannaford, A. Menciassi, M.K. O’Malley, N. Simaan, P. Valdastri, G.-Z. Yang, A decade retrospective of medical robotics research from 2010 to 2020, Sci. Robot. 6 (2021) eabi8017, http://dx.doi.org/10.1126/scirobotics.abi8017.

[2] B. Lin, S. Song, J. Wang, Variable stiffness methods of flexible robots for minimally invasive surgery: A review, Biomim. Intell. Robot. 4 (2024) 100168, http://dx.doi.org/10.1016/j.birob.2024.100168.

[3] Z. Lin, Z. Xu, H. Liu, X. Wang, X. Ai, C. Zhou, B. Huang, W. Chen, G.-Z. Yang, A. Gao, Robotic manipulator-assisted omnidirectional augmented reality for endoluminal intervention telepresence, Adv. Intell. Syst. 6 (2024) 2300373, http://dx.doi.org/10.1002/aisy.202300373.

[4] P.E. Dupont, N. Simaan, H. Choset, C. Rucker, Continuum robots for medical interventions, Proc. IEEE 110 (2022) 847-870, http://dx.doi.org/10.1109/JPROC.2022.3141338.

[5] Chaoyang Shi, Xiongbiao Luo, Peng Qi, Tianliang Li, Shuang Song, Z. Najdovski T. Fukuda H. Ren, Shape sensing techniques for continuum robots in minimally invasive surgery: A survey, IEEE Trans. Biomed. Eng. 64 (2017) 1665-1678, http://dx.doi.org/10.1109/TBME.2016.2622361.

[6] D.A. Troncoso, J.A. Robles-Linares, M. Russo, M.A. Elbanna, S. Wild, X. Dong, A. Mohammad, J. Kell, A.D. Norton, D. Axinte, A continuum robot for remote applications: From industrial to medical surgery with slender continuum robots, IEEE Robot. Autom. Mag. 30 (2023) 94-105, http://dx.doi.org/10.1109/MRA.2022.3223220.

[7] Y. Lei, F. Du, H. Song, L. Zhang, Design and kinematics analysis of a cable-stayed notch manipulator for transluminal endoscopic surgery, Biomim. Intell. Robot. 4 (2024) 100191, http://dx.doi.org/10.1016/j.birob.2024.100191.

[8] D. Song, S. Wang, Z. Zhang, X. Yu, C. Shi, A novel continuum overtube with improved triangulation for flexible robotic endoscopy, IEEE Trans. Med. Robot. Bionics 5 (2023) 657-668, http://dx.doi.org/10.1109/TMRB.2023.3294527.

[9] M. Russo, S.M.H. Sadati, X. Dong, A. Mohammad, I.D. Walker, C. Bergeles, K. Xu, D.A. Axinte, Continuum robots: An overview, Adv. Intell. Syst. 5 (2023) 2200367, http://dx.doi.org/10.1002/aisy.202200367.

[10] R.J. Webster, B.A. Jones, Design and kinematic modeling of constant curva-ture continuum robots: A review, Int. J. Robot. Res. 29 (2010) 1661-1683, http://dx.doi.org/10.1177/0278364910368147.

[11] X. Zhang, Y. Liu, D.T. Branson, C. Yang, J.S. Dai, R. Kang, Variable-gain control for continuum robots based on velocity sensitivity, Mech. Mach. Theory 168 (2022) 104618, http://dx.doi.org/10.1016/j.mechmachtheory.2021.104618.

[12] J. Hao, K. Zhang, Z. Zhang, S. Wang, C. Shi, An online model-free adaptive tracking controller for cable-driven medical continuum manipulators, IEEE Trans. Med. Robot. Bionics 5 (2023) 623-635, http://dx.doi.org/10.1109/TMRB.2023.3291024.

[13] T. Mahl, A. Hildebrandt, O. Sawodny, A variable curvature continuum kine-matics for kinematic control of the bionic handling assistant, IEEE Trans. Robot. 30 (2014) 935-949, http://dx.doi.org/10.1109/TRO.2014.2314777.

[14] S. Neppalli, M.A. Csencsits, B.A. Jones, I. Walker, A geometrical approach to inverse kinematics for continuum manipulators, in: 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, Nice, 2008, pp. 3565-3570, http://dx.doi.org/10.1109/IROS.2008.4651125.

[15] K. Qiu, J. Zhang, D. Sun, R. Xiong, H. Lu, Y. Wang, An efficient multi-solution solver for the inverse kinematics of 3-section constant-curvature robots, in: Robotics: Science and Systems XIX, Robotics: Science and Systems Foundation, 2023, http://dx.doi.org/10.15607/RSS.2023.XIX.091.

[16] H. Li, L. Xun, G. Zheng, F. Renda, Discrete cosserat static model-based control of soft manipulator, IEEE Robot. Autom. Lett. 8 (2023) 1739-1746, http://dx.doi.org/10.1109/LRA.2023.3243799.

[17] X. Huang, J. Zou, G. Gu, Kinematic modeling and control of variable curvature soft continuum robots, IEEE/ASME Trans. Mechatron. 26 (2021) 3175-3185, http://dx.doi.org/10.1109/TMECH.2021.3055339.

[18] V. Falkenhahn, A. Hildebrandt, R. Neumann, O. Sawodny, Dynamic control of the bionic handling assistant, IEEE/ASME Trans. Mechatron. 22 (2017) 6-17, http://dx.doi.org/10.1109/TMECH.2016.2605820.

[19] R.K. Katzschmann, C.D. Santina, Y. Toshimitsu, A. Bicchi, D. Rus, Dynamic motion control of multi-segment soft robots using piecewise constant curvature matched with an augmented rigid body model, in: 2019 2nd IEEE International Conference on Soft Robotics, RoboSoft, IEEE, Seoul, Korea (South), 2019, pp. 454-461, http://dx.doi.org/10.1109/ROBOSOFT.2019.8722799.

[20] C. Della Santina, R.K. Katzschmann, A. Bicchi, D. Rus, Model-based dynamic feedback control of a planar soft robot: trajectory tracking and interaction with the environment, Int. J. Robot. Res. 39 (2020) 490-513, http://dx.doi.org/10.1177/0278364919897292.

[21] Y. Ma, Q. Wu, Z. Qiu, Y. Fang, N. Sun, Modeling and precise tracking control of spatial bending pneumatic soft actuators, Biomim. Intell. Robot. 4 (2024) 100192, http://dx.doi.org/10.1016/j.birob.2024.100192.

[22] A.D. Kapadia, K.E. Fry, I.D. Walker, Empirical investigation of closed-loop control of extensible continuum manipulators, in: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, Chicago, IL, USA, 2014, pp. 329-335, http://dx.doi.org/10.1109/IROS.2014.6942580.

[23] A. Kazemipour, O. Fischer, Y. Toshimitsu, K.W. Wong, R.K. Katzschmann, Adaptive dynamic sliding mode control of soft continuum manipulators, in: 2022 International Conference on Robotics and Automation, ICRA, IEEE, Philadelphia, PA, USA, 2022, pp. 3259-3265, http://dx.doi.org/10.1109/ICRA46639.2022.9811715.

[24] X. Shao, P. Pustina, M. Stölzle, G. Sun, A. De Luca, L. Wu, C.D. Santina, Model-based control for soft robots with system uncertainties and input saturation, IEEE Trans. Ind. Electron. (2023) 1-10, http://dx.doi.org/10.1109/TIE.2023.3303636.

[25] R. Kang, Y. Guo, L. Chen, D.T. Branson, J.S. Dai, Design of a pneu-matic muscle based continuum robot with embedded tendons, IEEE/ASME Trans. Mechatron. 22 (2017) 751-761, http://dx.doi.org/10.1109/TMECH.2016.2636199.

[26] J. Hao, Z. Zhang, S. Wang, C. Shi, 2D shape estimation of a pneumatic-driven soft finger with a large bending angle based on learning from two sensing modalities, Adv. Intell. Syst. 5 (2023) 2200324, http://dx.doi.org/10.1002/aisy.202200324.

[27] H. Yuan, L. Zhou, W. Xu, A comprehensive static model of cable-driven multi-section continuum robots considering friction effect, Mech. Mach. Theory 135 (2019) 130-149, http://dx.doi.org/10.1016/j.mechmachtheory.2019.02.005.

[28] J. Jung, R.S. Penning, M.R. Zinn, A modeling approach for robotic catheters: effects of nonlinear internal device friction, Adv. Robot. 28 (2014) 557-572, http://dx.doi.org/10.1080/01691864.2013.879371.

[29] G. Subramani, M.R. Zinn, Tackling friction - an analytical modeling approach to understanding friction in single tendon driven continuum manipulators, in: 2015 IEEE International Conference on Robotics and Automation, ICRA, IEEE, Seattle, WA, USA, 2015, pp. 610-617, http://dx.doi.org/10.1109/ICRA.2015.7139242.

[30] R. Roy, L. Wang, N. Simaan, Modeling and estimation of friction, exten-sion, and coupling effects in multisegment continuum robots, IEEE/ASME Trans. Mechatron. 22 (2017) 909-920, http://dx.doi.org/10.1109/TMECH.2016.2643640.

[31] Y. Liu, F. Alambeigi, Effect of external and internal loads on tension loss of tendon-driven continuum manipulators, IEEE Robot. Autom. Lett. 6 (2021) 1606-1613, http://dx.doi.org/10.1109/LRA.2021.3058913.

[32] R.E. Goldman, A. Bajo, N. Simaan, Compliant motion control for multiseg-ment continuum robots with actuation force sensing, IEEE Trans. Robot. 30 (2014) 890-902, http://dx.doi.org/10.1109/TRO.2014.2309835.

[33] D.B. Camarillo, C.F. Milne, C.R. Carlson, M.R. Zinn, J.K. Salisbury, Mechanics modeling of tendon-driven continuum manipulators, IEEE Trans. Robot. 24 (2008) 1262-1273, http://dx.doi.org/10.1109/TRO.2008.2002311.

[34] M.M. Dalvand, S. Nahavandi, R.D. Howe, An analytical loading model for$n$ -Tendon continuum robots, IEEE Trans. Robot. 34 (2018) 1215-1225, http://dx.doi.org/10.1109/TRO.2018.2838548.

[35] B. Kim, J. Ryu, K.-J. Cho, Joint angle estimation of a tendon-driven soft wearable robot through a tension and stroke measurement, Sensors 20 (2020) 2852, http://dx.doi.org/10.3390/s20102852.

[36] C. Della Santina, C. Duriez, D. Rus, Model-based control of soft robots: A survey of the state of the art and open challenges, IEEE Control. Syst. 43 (2023) 30-65, http://dx.doi.org/10.1109/MCS.2023.3253419.

[37] J. Duan, K. Zhang, K. Qian, J. Hao, Z. Zhang, C. Shi, An operating stiffness controller for the medical continuum robot based on impedance control, Cyborg. Bionic Syst. 5 (2024) 0110, http://dx.doi.org/10.34133/cbsystems.0110.

[38] V. Falkenhahn, T. Mahl, A. Hildebrandt, R. Neumann, O. Sawodny, Dynamic modeling of bellows-actuated continuum robots using the Euler-Lagrange formalism, IEEE Trans. Robot. 31 (2015) 1483-1496, http://dx.doi.org/10.1109/TRO.2015.2496826.

[39] J.-J.E. Slotine, Weiping Li, On the adaptive control of robot manip-ulators, Int. J. Robot. Res. 6 (1987) 49-59, http://dx.doi.org/10.1177/027836498700600303.

[40] Z. Li, C.-Y. Su, G. Li, H. Su, Fuzzy approximation-based adaptive backstep-ping control of an exoskeleton for human upper limbs, IEEE Trans. Fuzzy Syst. 23 (2015) 555-566, http://dx.doi.org/10.1109/TFUZZ.2014.2317511.

[41] L.-X. Wang, J.M. Mendel, Fuzzy basis functions, universal approximation, and orthogonal least-squares learning, IEEE Trans. Neural Netw. 3 (1992) 807-814, http://dx.doi.org/10.1109/72.159070.

[42] J. Li, S. Wang, Z. Zhang, C. Shi, A robotic system for transanal endoscopic microsurgery: Design, dexterity optimization, and prototyping, IEEE Robot. Autom. Mag. (2023) 2-16, http://dx.doi.org/10.1109/MRA.2023.3323849.

[43] Y. Xu, D. Song, Z. Zhang, S. Wang, C. Shi, A novel extensible continuum robot with growing motion capability inspired by plant growth for path-following in transoral laryngeal surgery, Soft Robot. (2023) http://dx.doi.org/10.1089/soro.2023.0014, soro.2023.0014.

[44] L. Wang, C. Zhou, Y. Cao, R. Zhao, K. Xu, Vision-based markerless tracking for continuum surgical instruments in robot-assisted minimally invasive surgery, IEEE Robot. Autom. Lett. 8 (2023) 7202-7209, http://dx.doi.org/10.1109/LRA.2023.3315229.

[45] X. Ma, P.W.-Y. Chiu, Z. Li, Shape sensing of flexible manipulators with vi-sual occlusion based on bezier curve, IEEE Sensors J. 18 (2018) 8133-8142, http://dx.doi.org/10.1109/JSEN.2018.2862925.

[46] A.A. Nazari, K. Zareinia, F. Janabi-Sharifi, Visual servoing of continuum robots: Methods, challenges, and prospects, Robot. Comput. Surg. 18 (2022) e2384, http://dx.doi.org/10.1002/rcs.2384.

[47] W. Ba, X. Dong, A. Mohammad, M. Wang, D. Axinte, A. Norton, Design and validation of a novel fuzzy-logic-based static feedback controller for tendon-driven continuum robots, IEEE/ASME Trans. Mechatron. 26 (2021) 3010-3021, http://dx.doi.org/10.1109/TMECH.2021.3050263.

[48] F. Ma, G. Chen, Modeling large planar deflections of flexible beams in compliant mechanisms using chained beam-constraint-Model1, J. Mech. Robot. 8 (2016) 021018, http://dx.doi.org/10.1115/1.4031028.

[49] Y. Chen, S. Yao, M.Q.-H. Meng, L. Liu, Chained spatial beam constraint model: A general kinetostatic model for tendon-driven continuum robots, IEEE/ASME Trans. Mechatron. 29 (2024) 3534-3545, http://dx.doi.org/10.1109/TMECH.2023.3348510.

[50] C. Shi, Z. Tang, S. Wang, Design and experimental validation of a fiber bragg grating-enabled force sensor with an ortho-planar spring-based flexure for surgical needle insertion, IEEE Trans. Med. Robot. Bionics 3 (2021) 362-371, http://dx.doi.org/10.1109/TMRB.2021.3073198.

[51] Y. Hao, H. Zhang, Z. Zhang, C. Hu, C. Shi,Development of force sensing techniques for robot-assisted laparoscopic surgery: A review, IEEE Trans. Med. Robot. Bionics 6 (2024) 868-887, http://dx.doi.org/10.1109/TMRB.2024.3407238.