Abstract：Various controllers developed for tendon-driven continuum robot are analyzed in-depth, which can be used as a reference for future applications in the field of tendon-driven continuum robot. The control strategy is divided into model-based control and model-free control. Among them, model-based control can be divided into static control, dynamic control and geometric kinematics model control. Model-free control is a relatively unknown field. Comprehensive analysis is carried out from model-free static control, model-free dynamic control and model-free shape perception control. Finally, the various model-based and mode-free control strategies are evaluated, and the future research direction in this field is prospected.
[1] Anderson V C, Horn R C. Tensor arm manipulator design[J]. ASME Transactions, 1967, 67(1):1-12. [2] Klein C A, Huang C H. Review of pseudoinverse control for use with kinematically redundant manipulators[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1983, 13(2):245-250. [3] Kirćanski M, Vukobratović M. Contribution to control of redundant robotic manipulators in an environment with obstacles[J]. International Journal of Robotics Research, 1986, 5(4):112-119. [4] Gu Y L. Dynamics and control for redundant robots[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 1988:194-199. [5] Robinson G, Davies J B C. Continuum robots-A state of the art[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 1999:2849-2854. [6] Rus D, Tolley M T. Design, fabrication and control of soft robots[J]. Nature, 2015, 521(5):467-475. [7] Davies J B C, Lane D M, Robinson G C, et al. Subsea applications of continuum robots[C]//International Symposium on Underwater Technology. Piscataway, USA:IEEE, 1998:363-369. [8] Pfeifer R. Morphological computation-connecting brain, body, and environment[C]//Australian Joint Conference on Artificial Intelligence:Advances in Artificial Intelligence. Berlin, Germany:Springer-Verlag, 2006:66-83. [9] Burgner-Kahrs J, Rucker D C, Choset H. Continuum robots for medical applications:A survey[J]. IEEE Transactions on Robotics, 2015, 31(6):1261-1280. [10] Manti M, Cacucciolo V, Cianchetti M. Stiffening in soft robotics:A review of the state of the art[J]. IEEE Robotics and Automation Magazine, 2016, 23(3):93-106. [11] Chen Y F, Zhao H C, Mao J, et al. Controlled flight of a microrobot powered by soft artificial muscles[J]. Nature, 2019, 575(11):324-329. [12] Thuruthel T G, Ansari Y, Falotico E. et al. Control strategies for soft robotic manipulators:A survey[J]. Soft Robotics, 2018, 5(2):149-163. [13] Chikhaoui M T, Burgner-Kahrs J. Control of continuum robots for medical applications:State of the art[C]//16th International Conference on New Actuators. Berlin, Germany:VDE, 2018. [14] Mahon S T, Roberts J O, Sayed M E, et al. Capability by stacking:The current design heuristic for soft robots[J]. Biomimetics, 2018, 3(3):1-16. [15] Walker I. Continuous backbone "continuum" robot manipulators[J]. International Scholarly Research Notices, 2013(7):1-19. [16] Laschi C, Mazzolai B, Cianchetti M. Soft robotics:Technologies and systems pushing the boundaries of robot abilities[J]. Science Robotics, 2016, 1(1):1-11. [17] Singh P, Krishna C. Continuum arm robotic manipulator:A review[J]. Universal Journal of Mechanical Engineering, 2014, 2(6):193-198. [18] Oladipupo G G. A review of soft robots[J]. Robotics, 2019, 19(10):1-14. [19] Amouri A, Zaatri A, Mahfoudi C. Dynamic modeling of a class of continuum manipulators in fixed orientation[J]. Journal of Intelligent and Robotic Systems, 2018, 91(3):413-424. [20] Huang S P, Meng D S, She Y, et al. Statics of continuum space manipulators with nonconstant curvature via pseudorigid-body 3R model[J]. IEEE Access, 2018, 6(1):70854-70865. [21] Wang H S, Wang C, Chen W D, et al. Three-dimensional dynamics for cable-driven soft manipulator[J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(1):18-28. [22] Yuan H, Zhou L L, Xu W F. A comprehensive static model of cable-driven multi-section continuum robots considering friction effect[J]. Mechanism and Machine Theory, 2019, 135(2):130-149. [23] Roy R, Wang L, Simaan N. Modeling and estimation of friction, extension, and coupling effects in multisegment continuum robots[J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(2):909-920. [24] Gao A Z, Murphy R J, Liu H, et al. Mechanical model of dexterous continuum manipulators with compliant joints and tendon/external force interactions[J]. IEEE/ASME Transactions on Mechatronics, 2016, 22(1):465-475. [25] Subramani G, Zinn M R. Tackling friction-An analytical modeling approach to understanding friction in single tendon driven continuum manipulators[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2015:610-617. [26] Moses M S, Murphy R J, Kutzer M D, et al. Modeling cable and guide channel interaction in a high-strength cable-driven continuum manipulator[J]. IEEE/ASME Transactions on Mechatronics, 2015, 20(6):2876-2889. [27] Chirikjian G S, Burdick J W. Hyper-redundant robot mechanisms and their applications[C]//IEEE/RSJ International Workshop on Intelligent Robots and Systems. Piscataway, USA:IEEE, 1991:185-190. [28] Gravagne I A, Walker I D. Manipulability, force, and compliance analysis for planar continuum manipulators[J]. IEEE Transactions on Robotics and Automation, 2002, 18(3):263-273. [29] Jones B A, Walker I D. Kinematics for multisection continuum robots[J]. IEEE Transactions on Robotics, 2006, 22(1):43-55. [30] Huang S, Zhang Q Y, Liu Z Y, et al. Control of a piecewise constant curvature continuum manipulator via policy search method[C]//IEEE International Conference on Robotics and Biomimetics. Piscataway, USA:IEEE, 2018:1777-1782. [31] Gravagne I A, Rahn C D, Walker I D. Large deflection dynamics and control for planar continuum robots[J]. IEEE/ASME Transactions on Mechatronics, 2003, 8(2):299-307. [32] Cosserat E, Cosserat F. Théorie des corps déformables[J]. Nature, 1909, 81(1909):67. [33] Cosserat E, Cosserat F. Theory of deformable bodies[M]. Paris, France:Scientific Library A. Hermann and Sons, 1970:1-254. [34] Trivedi D, Lotfi A, Rahn C D. Geometrically exact models for soft robotic manipulators[J]. IEEE Transactions on Robotics, 2008, 24(4):773-780. [35] Chikhaoui M T, Lilge S, Kleinschmidt S, et al. Comparison of modeling approaches for a tendon actuated continuum robot with three extensible segments[J]. IEEE Robotics and Automation Letters, 2019, 4(2):989-996. [36] Mous A, Khoo S, Norton M. Robust control of tendon driven continuum robots[C]//15th International Workshop on Variable Structure Systems. Piscataway, USA:IEEE, 2018:49-54. [37] Alqumsan A A, Khoo S, Norton M. Robust control of continuum robots using Cosserat rod theory[J]. Mechanism and Machine Theory, 2019, 131(1):48-61. [38] Alqumsan A A, Khoo S, Norton M. Multi-surface sliding mode control of continuum robots with mismatched uncertainties[J]. Meccanica, 2019, 54(14):2307-2316. [39] Bailly Y, Amirat Y. Modeling and control of a hybrid continuum active catheter for aortic aneurysm treatment[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2005:924-929. [40] Camarillo D B, Carlson C R, Salisbury J K. Configuration tracking for continuum manipulators with coupled tendon drive[J]. IEEE Transactions on Robotics, 2009, 25(4):798-808. [41] Camarillo D B, Carlson C R, Salisbury J K. Task-space control of continuum manipulators with coupled tendon drive[C]//11th International Symposium on Experimental Robotics. Berlin, Germany:Springer, 2009:271-280. [42] Xu K, Simaan N. Actuation compensation for flexible surgical snake-like robots with redundant remote actuation[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2006:4148-4154. [43] Prisco G, Bergamasco M. Dynamic modelling of a class of tendon driven manipulators[C]//8th International Conference on Advanced Robotics. Piscataway, USA:IEEE, 1997:893-899. [44] Bajo A, Goldman R E, Simaan N. Configuration and joint feedback for enhanced performance of multi-segment continuum robots[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2011:2905-2912. [45] Penning R S, Jung J, Ferrier N J, et al. An evaluation of closed-loop control options for continuum manipulators[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2012:5392-5397. [46] Goldman R E, Bajo A, Simaan N. Compliant motion control for continuum robots with intrinsic actuation sensing[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2011:1126-1132. [47] Yasin R, Wang L, Abah C, et al. Using continuum robots for force-controlled semi autonomous organ exploration and registration[C]//International Symposium on Medical Robotics. Piscataway, USA:IEEE, 2018. [48] Bajo A, Simaan N. Hybrid motion/force control of multi-backbone continuum robots[J]. International Journal of Robo-tics Research, 2016, 35(4):422-434. [49] Wang L, Chen Z H, Chalasani P, et al. Force-controlled exploration for updating virtual fixture geometry in model-mediated telemanipulation[J]. Journal of Mechanisms and Robotics, 2017, 9(2):10-21. [50] Mahvash M, Dupont P E. Stiffness control of surgical continuum manipulators[J]. IEEE Transactions on Robotics, 2011, 27(2):334-345. [51] Wang H S, Chen W D, Yu X J, et al. Visual servo control of cable-driven soft robotic manipulator[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2013:57-62. [52] Mahl T, Mayer A E, Hildebrandt A, et al. A variable curvature modeling approach for kinematic control of continuum manipulators[C]//American Control Conference. Piscataway, USA:IEEE, 2013:4945-4950. [53] Mahl T, Hildebrandt A, Sawodny O. A variable curvature continuum kinematics for kinematic control of the bionic handling assistant[J]. IEEE Transactions on Robotics, 2014, 30(4):935-949. [54] Till J, Bryson C E, Chung S, et al. Efficient computation of multiple coupled Cosserat rod models for real-time simulation and control of parallel continuum manipulators[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2015:5067-5074. [55] Boushaki M N, Liu C, Poignet P. Task-space position control of concentric-tube robot with inaccurate kinematics using approximate Jacobian[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2014:5877-5882. [56] Largilliere F, Verona V, Coevoet E, et al. Real-time control of soft-robots using asynchronous finite element modeling[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2015:2550-2555. [57] Zhang Z K, Dequidt J, Back J, et al. Motion control of cable-driven continuum catheter robot through contacts[J]. IEEE Robotics and Automation Letters, 2019, 4(2):1852-1859. [58] Xu S, He B, Zhou Y, et al. A hybrid position/force control method for a continuum robot with robotic and environmental compliance[J]. IEEE Access, 2019, 7(1):467-497. [59] Conrad B, Zinn M. Closed loop task space control of an interleaved continuum-rigid manipulator[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2015:1743-1750. [60] Yeshmukhametov A, Koganezawa K, Yamamoto Y. Design and kinematics of cable-driven continuum robot arm with universal joint backbone[C]//IEEE International Conference on Robotics and Biomimetics. Piscataway, USA:IEEE, 2018:2444-2449. [61] Yeshmukhametov A, Koganezawa K, Yamamoto Y. A novel discrete wire-driven continuum robot arm with passive sliding disc:Design, kinematics and passive tension control[J]. Robotics, 2019, 8(3). [62] Gravagne I A, Walker I D. Uniform regulation of a multi-section continuum manipulator[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2002:1519-1524. [63] Kapadia A, Walker I D. Task-space control of extensible continuum manipulators[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2011:1087-1092. [64] Trivedi D, Lotfi A, Rahn C D. Geometrically exact dynamic models for soft robotic manipulators[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2007:1497-1502. [65] Kapadia A D, Walker I D, Dawson D M, et al. A model-based sliding mode controller for extensible continuum robots[M]//Recent Advances in Signal Processing, Robotics and Automation. Cambridge, UK:University of Cambridge, 2011:113-120. [66] Amouri A, Mahfoudi C, Djeffal S. Computational methods and experimental testing in mechanical engineering[M]//Lecture Notes in Mechanical Engineering. Berlin, Germany:Springer, 2017:27-37. [67] Xu W F, Liu T L, Li Y M. Kinematics, dynamics, and control of a cable-driven hyper-redundant manipulator[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(4):1693-1704. [68] Xu F, Wang H S, Au K W S, et al. Underwater dynamic model-ing for a cable-driven soft robot arm[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(6):2726-2738. [69] Qi F, Ju F, Bai D, et al. Motion modelling and error compensation of a cable-driven continuum robot for applications to minimally invasive surgery[J]. International Journal of Medical Robotics and Computer Assisted Surgery, 2018, 14(6). [70] Till J, Aloi V, Rucker C. Real-time dynamics of soft and continuum robots based on Cosserat rod models[J]. International Journal of Robotics Research, 2019, 38(6):723-746. [71] Xu F, Wang H S, Wang J C, et al. Underwater dynamic visual servoing for a soft robot arm with online distortion correction[J]. IEEE/ASME Transactions on Mechatronics, 2019, 24(3):979-989. [72] Kapadia A D, Fry K E, Walker I D. Empirical investigation of closed-loop control of extensible continuum manipulators[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2014:329-335. [73] Falkenhahn V, Hildebrandt A, Neumann R, et al. Dynamic control of the bionic handling assistant[J]. IEEE/ASME Transactions on Mechatronics, 2016, 22(1):6-17. [74] Falkenhahn V, Hildebrandt A, Neumann R, et al. Model based feedforward position control of constant curvature continuum robots using feedback linearization[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2015:762-767. [75] Best C M, Gillespie M T, Hyatt P, et al. A new soft robot control method:Using model predictive control for a pneumatically actuated humanoid[J]. IEEE Robotics and Automation Magazine, 2016, 23(3):75-84. [76] Ivanescu M, Nitulescu M, Vladu C. Fractional order control of a continuum robot arm[C]//International Conference on System Theory, Control and Computing. Piscataway, USA:IEEE, 2019:525-530. [77] Chirikjian G S, Burdick J W. A modal approach to hyper-redundant manipulator kinematics[J]. IEEE Transactions on Robotics and Automation, 1994, 10(3):343-354. [78] Chirikjian G S, Burdick J W. The kinematics of hyper-redundant robot locomotion[J]. IEEE Transactions on Robotics and Automation, 1995, 11(6):781-793. [79] Hannan M W, Walker I D. Novel kinematics for continuum robots in advances in robot kinematics[M]. Berlin, Germany:Springer, 2000:227-238. [80] Hannan M W, Walker I D. Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots[J]. Journal of Robotic Systems, 2003, 20(2):45-63. [81] Chen G, Pham M T, Redarce T. Development and kinematic analysis of a silicone-rubber bending tip for colonoscopy[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2006:168-173. [82] Jones B A, Walker I D. Practical kinematics for real-time implementation of continuum robots[J]. IEEE Transactions on Robotics, 2006, 22(6):1087-1099. [83] Yahya S, Mohamed H A, Moghavvemi M, et al. A geometrical inverse kinematics method for hyper-redundant manipulators[C]//International Conference on Control, Automation, Robotics and Vision. Piscataway, USA:IEEE, 2008:1954-1958. [84] 胡海燕,王鹏飞,孙立宁,等. 线驱动连续型机器人的运动学分析与仿真[J],机械工程学报,2010,46(19):1-8. Hu H Y, Wang P F, Sun L N, et al. Kinematic analysis and simulation for cable-driven continuum robot[J]. Journal of Mechanical Engineering, 2010, 46(19):1-8. [85] Webster R J, Jones B A. Design and kinematic modeling of constant curvature continuum robots:A review[J]. International Journal of Robotics Research, 2010, 29(13):1661-1683. [86] Pisla D, Szilaghyi A, Vaida C, et al. Kinematics and workspace modeling of a new hybrid robot used in minimally invasive surgery[J]. Robotics and Computer Integrated Manufacturing, 2013, 29(2):463-474. [87] Meng G Z, Yuan G M, Liu Z, et al. Forward and inverse kinematic of continuum robot for search and rescue[J]. Advanced Materials Research, 2013, 712-715(1):2290-2295. [88] Xu K, Zhao J R, Qiu D, et al. A pilot study of a continuum shoulder exoskeleton for anatomy adaptive assistances[J]. Journal of Mechanisms and Robotics, 2014, 6(4). [89] Du Z J, Yang W L, Dong W. Kinematics modeling of a notched continuum manipulator[J]. Journal of Mechanisms and Robo-tics, 2015, 7(4). [90] Tian Y Z, Yang S C, Geng H, et al. Kinematic modeling of the constant curvature continuum line drive robot[C]//IEEE International Conference on Robotics and Biomimetics. Piscataway, USA:IEEE, 2016:289-294. [91] Tian Y Z, Luan M X, Gao X, et al. Kinematic analysis of continuum robot consisted of driven flexible rods[J]. Mathematical Problems in Engineering, 2016, 31(10):196-204. [92] Oliver-Butler K, Till J, Rucker C. Continuum robot stiffness under external loads and prescribed tendon displacements[J]. IEEE Transactions on Robotics, 2019, 35(2):403-419. [93] Nguyen-Tuong D, Peters J. Model learning for robot control:A survey[J]. Cognitive Processing, 2011, 12(4):319-340. [94] Yip M, Sganga J, Camarillo D. Autonomous control of continuum robot manipulators for complex cardiac ablation tasks[J]. Journal of Medical Robotics Research, 2017, 2(1). [95] Melingui A, Ahanda J J B M, Lakhal O, et al. Adaptive algorithms for performance improvement of a class of continuum manipulators[J]. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2018, 48(9):1531-1541. [96] Verghese M, Richter F, Gunn A, et al. Model-free visual control for continuum robot manipulators via orientation adaptation[J/OL]. (2019-09-01)[2019-10-08]. https://arxiv.org/abs/1909.00450. [97] Giorelli M, Renda F, Calisti M, et al. Learning the inverse kinetics of an octopus-like manipulator in three-dimensional space[J]. Bioinspiration and Biomimetics, 2015, 10(3). [98] Thuruthel T G, Falotico E, Renda F, et al. Laschi, learning dynamic models for open loop predictive control of soft robotic manipulators[J]. Bioinspiration and Biomimetics, 2017, 12(6). [99] Giorelli M, Renda F, Ferri G, et al. A feed-forward neural network learning the inverse kinetics of a soft cable-driven manipulator moving in three-dimensional space[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2013:5033-5039. [100] Giorelli M, Renda F, Calisti M, et al. Neural network and Jacobian method for solving the inverse statics of a cable-driven soft arm with nonconstant curvature[J]. IEEE Transactions on Robotics, 2015, 31(4):823-834. [101] Rolf M, Steil J J. Efficient exploratory learning of inverse kinematics on a bionic elephant trunk[J]. IEEE Transactions on Neural Networks and Learning Systems, 2013, 25(6):1147-1160. [102] Yip M C, Camarillo D B. Model-less feedback control of continuum manipulators in constrained environments[J]. IEEE Transactions on Robotics, 2014, 30(4):880-889. [103] Yip M C, Camarillo D B. Model-less hybrid position/force control:A minimalist approach for continuum manipulators in unknown constrained environments[J]. IEEE Robotics and Automation Letters, 2016, 1(2):844-851. [104] Thuruthel T G, Falotico E, Manti M, et al. Learning closed loop kinematic controllers for continuum manipulators in unstructured environments[J]. Soft Robotics, 2017, 4(3):285-296. [105] Chattopadhyay S, Bhattacherjee S, Bandyopadhyay S, et al. Control of single-segment continuum robots:Reinforcement learning vs. neural network based PID[C]//International Conference on Control, Power, Communication and Computing Technologies. Piscataway, USA:IEEE, 2018:222-226. [106] Malekzadeh M S, Calinon S, Bruno D, et al. Learning by imitation with the STIFF-FLOP surgical robot:A biomimetic approach inspired by octopus movements[J]. Robotics and Biomimetics, 2014, 1(1). [107] Ansari Y, Manti M, Falotico E, et al. Multiobjective optimization for stiffness and position control in a soft robot arm module[J]. IEEE Robotics and Automation Letters, 2017, 3(1):108-115. [108] Qi P, Liu C, Ataka A, et al. Kinematic control of continuum manipulators using a fuzzy-model-based approach[J]. IEEE Transactions on Industrial Electronics, 2016, 63(8):5022-5035. [109] Lakhal O, Melingui A, Merzouki R. Hybrid approach for modeling and solving of kinematics of a compact bionic handling assistant manipulator[J]. IEEE/ASME Transactions on Mechatronics, 2016, 21(3):1326-1335. [110] Reinhart R F, Shareef Z, Steil J J. Hybrid analytical and data-driven modeling for feed-forward robot control[J]. Sensors, 2017, 17(2). [111] Jiang H, Wang Z C, Liu X H, et al. A two-level approach for solving the inverse kinematics of an extensible soft arm considering viscoelastic behavior[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2017:6127-6133. [112] Braganza D, Dawson D M, Walker I D, et al. A neural network controller for continuum robots[J]. IEEE Transactions on Robotics, 2007, 23(6):1270-1277. [113] Xian B, Dawson D M, Queiroz M S, et al. A continuous asymptotic tracking control strategy for uncertain nonlinear systems[J]. IEEE Transactions on Automatic Control, 2004, 49(7):1206-1211. [114] Engel Y, Szabó P, Volkinshtein D. Learning to control an octopus arm with Gaussian process temporal difference methods[J]. Computer Science, 2005:1-16. [115] Silver D, Lever G, Heess N, et al. Deterministic policy gradient algorithms[C]//31st International Conference on Machine Learning. Lille, France:W&CP, 2014:387-395. [116] Jakes D, Ge Z, Wu L. Model-less active compliance for continuum robots using recurrent neural networks[DB/OL]. (2019-11-12)[2019-10-08]. https://arxiv.org/abs/1902.08943. [117] Mayer H, Gomez F, Wierstra D, et al. A system for robotic heart surgery that learns to tie knots using recurrent neural networks[J]. Advanced Robotics, 2008, 22(13/14):1521-1537. [118] Jiang S, Wang Y, Ju F, et al. A new fuzzy time-delay control for cable-driven robot[J]. International Journal of Advanced Robotic Systems, 2019, 16(2). [119] Wang Y Y, Zhu K W, Yan F, et al. Adaptive super-twisting nonsingular fast terminal sliding mode control for cable-driven manipulators using time-delay estimation[J]. Advances in Engineering Software, 2019, 128:113-124. [120] Shi C, Luo X B, Qi P, et al. Shape sensing techniques for continuum robots in minimally invasive surgery:A survey[J]. IEEE Transactions on Biomedical Engineering, 2016, 64(8):1665-1678. [121] Kim B, Ha J, Park F C, et al. Optimizing curvature sensor placement for fast, accurate shape sensing of continuum robots[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2014:5374-5379. [122] Wang H S, Zhang R, Chen W, et al. Shape detection algorithm for soft manipulator based on fiber Bragg gratings[J]. IEEE/ASME Transactions on Mechatronics, 2016, 21(6):2977-2982. [123] Xu R, Yurkewich A, Patel R V. Curvature, torsion, and force sensing in continuum robots using helically wrapped FBG sensors[J]. IEEE Robotics and Automation Letters, 2016, 1(2):1052-1059. [124] Al Jaber F, Althoefer K. Towards creating a flexible shape senor for soft robots[C]//IEEE International Conference on Soft Robotics. Piscataway, USA:IEEE, 2018:114-119. [125] Khan F, Denasi A, Barrera D, et al. Multi-core optical fibers with Bragg gratings as shape sensor for flexible medical instruments[J]. IEEE Sensors Journal, 2019, 19(14):5878-5884. [126] Liu H, Farvardin A, Pedram S A, et al. Large deflection shape sensing of a continuum manipulator for minimally-invasive surgery[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2015:201-206. [127] Liu H, Farvardin A, Grupp R, et al. Shape tracking of a dexterous continuum manipulator utilizing two large deflection shape sensors[J]. IEEE Sensors Journal, 2015, 15(10):5494-5503. [128] Sefati S, Alambeigi F, Iordachita I, et al. FBG-based large deflection shape sensing of a continuum manipulator:Manufacturing optimization[C]//IEEE Sensors. Piscataway, USA:IEEE, 2016. [129] Lai W J, Cao L, Tan R X, et al. Force sensing with 1mm fiber Bragg gratings for flexible endoscopic surgical robots[J]. IEEE/ASME Transactions on Mechatronics, 2020, 25(1):371-382. [130] Khan F, Roesthuis R, Misra S. Force sensing in continuum manipulators using fiber Bragg grating sensors[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2017:2531-2536. [131] Ren H L, Sun J J. Electromagnetic actuation and sensing in medical robotics[M]. Berlin, Germany:Springer, 2018:141-162. [132] Song S, Li Z, Meng M Q H, et al. Real-time shape estimation for wire-driven flexible robots with multiple bending sections based on quadratic Bézier curves[J]. IEEE Sensors Journal, 2015, 15(11):6326-6334. [133] Song S, Li Z, Yu H Y, et al. Electromagnetic positioning for tip tracking and shape sensing of flexible robots[J]. IEEE Sensors Journal, 2015, 15(8):4565-4575. [134] Song S, Li Z, Yu H Y, et al. Shape reconstruction for wiredriven flexible robots based on Bézier curve and electromagnetic positioning[J]. Mechatronics, 2015, 29:28-35. [135] Zhang C C, Lu Y, Qiu X X, et al. Preliminary study on magnetic tracking based navigation for wire-driven flexible robot[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2017:2517-2523. [136] Kwartowitz D M, Herrell S D, Galloway R L. Toward imageguided robotic surgery:Determining intrinsic accuracy of the da Vinci robot[J]. International Journal of Computer Assisted Radiology and Surgery, 2006, 1(3):157-165. [137] Guo H, Ju F, Cao Y F, et al. Continuum robot shape estimation using permanent magnets and magnetic sensors[J]. Sensors and Actuators A:Physical, 2019, 285(1):519-530. [138] Aloi V A, Rucker D C. Estimating loads along elastic rods[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2019:2867-2873. [139] Vrooijink G J. Control of continuum robots for minimally invasive interventions[D]. Enschede, Netherlands:University of Twente, 2019. [140] Sadati S H, Naghibi S E, Shiva A, et al. Mechanics of continuum manipulators, a comparative study of five methods with experiments[C]//Annual Conference towards Autonomous Robotic Systems. Berlin, Germany:Springer, 2017:686-702. [141] Godage I S, Wirz R, Walker I D, et al. Accurate and efficient dynamics for variable-length continuum arms:A center of gravity approach[J]. Soft Robotics, 2015, 2(3):96-106. [142] Falkenhahn V, Mahl T, Hildebrandt A, et al. Dynamic modeling of bellows-actuated continuum robots using the Euler-Lagrange formalism[J]. IEEE Transactions on Robotics, 2015, 31(6):1483-1496. [143] Fraś J, Czarnowski J, Maciá s M, et al. Recent advances in automation, robotics and measuring techniques[M]. Berlin, Germany:Springer, 2014:365-375. [144] Mahvash M, Dupont P E. Stiffness control of a continuum manipulator in contact with a soft environment[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2010:863-870. [145] Godage I S, Branson D T, Guglielmino E, et al. Shape function-based kinematics and dynamics for variable length continuum robotic arms[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2011:452-457. [146] Marchese A D, Tedrake R, Rus D. Dynamics and trajectory optimization for a soft spatial fluidic elastomer manipulator[J]. International Journal of Robotics Research, 2016, 35(8):1000-1019. [147] Venkatraman A, Hebert M, Bagnell J A. Improving multi-step prediction of learned time series models[C]//29th AAAI Conference on Artificial Intelligence. Palo Alto, USA:AAAI, 2015. [148] Bengio S, Vinyals O, Jaitly N, et al. Scheduled sampling for sequence prediction with recurrent neural networks[C]//International Conference on Neural Information Processing Systems. La Jolla, USA:Neural Information Processing Systems Foundation, 2015:1171-1179. [149] Bajo A, Simaan N. Kinematics-based detection and localization of contacts along multisegment continuum robots[J]. IEEE Transactions on Robotics, 2011, 28(2):291-302. [150] Wang L, Simaan N. Geometric calibration of continuum robots:Joint space and equilibrium shape deviations[J]. IEEE Transactions on Robotics, 2019, 35(2):387-402. [151] Lugez E, Sadjadi H, Pichora D R, et al. Electromagnetic tracking in surgical and interventional environments:Usability study[J]. International Journal of Computer Assisted Radiology and Surgery, 2015, 10(3):253-262.
