[3] TRIANTAFYLLOU M S, TRIANTAFYLLOU G S. An efficient swimming machine[J]. Scientific American, 272, 64-70(1995).

[4] BREDER C M, Jr. The locomotion of fishes[J]. Zoologica, 4, 159-297(1926).

[5] WEBB P W. Form and function in fish swimming[J]. Scientific American, 251, 72-83(1984).

[6] SFAKIOTAKIS M, LANE D M, DAVIES J B C. Review of fish swimming modes for aquatic locomotion[J]. IEEE Journal of Oceanic Engineering, 24, 237-252(1999).

[7] NGUYEN D Q, HO V A. Anguilliform swimming performance of an eel-inspired soft robot[J]. Soft Robotics, 9, 425-439(2022).

[8] MURALIDHARAN M, PALANI I A. Development of Subcarangiform bionic robotic fish propelled by shape memory alloy actuators[J]. Defence Science Journal, 71, 94-101(2021).

[9] [9] DU S, WU Z X, WANG J, et al. Design control of a twomotactuated tunainspired robot system[J]. IEEE Transactions on Systems, Man, Cyberics: Systems, 2021, 51(8): 46704680.

[10] MATTA A, PENDAR H, BATTAGLIA F et al. Impact of caudal fin shape on thrust production of a Thunniform swimmer[J]. Journal of Bionic Engineering, 17, 254-269(2020).

[11] JI D X, REHMAN F U, AJWAD S A et al. Design and development of autonomous robotic fish for object detection and tracking[J]. International Journal of Advanced Robotic Systems, 17, 1-11(2020).

[12] LIU Q M, CHEN H, WANG Z H et al. A manta ray robot with soft material based flapping wing[J]. Journal of Marine Science and Engineering, 10, 962(2022).

[13] ZHOU C L, LOW K H. Better endurance and load capacity: an improved design of manta ray robot (RoMan-II)[J]. Journal of Bionic Engineering, 7, S137-S144(2010).

[14] LIU H L, CURET O. Swimming performance of a bio-inspired robotic vessel with undulating fin propulsion[J]. Bioinspiration & Biomimetics, 13, 056006(2018).

[15] ZHONG Y, LI Z, DU R X. Robot fish with two-DOF pectoral fins and a wire-driven caudal fin[J]. Advanced Robotics, 32, 25-36(2018).

[16] SHADWICK R E, GEMBALLA S. Structure, kinematics, and muscle dynamics in undulatory swimming[J]. Fish Physiology, 23, 241-280(2005).

[17] FLAMMANG B E, LAUDER G V. Functional morphology and hydrodynamics of backward swimming in bluegill sunfish, Lepomis macrochirus[J]. Zoology, 119, 414-420(2016).

[18] CHEN Z, SHATARA S, TAN X B. Modeling of biomimetic robotic fish propelled by an ionic polymer–metal composite caudal fin[J]. IEEE/ASME Transactions on Mechatronics, 15, 448-459(2010).

[19] WANG Z L, HANG G R, LI J et al. A micro-robot fish with embedded SMA wire actuated flexible biomimetic fin[J]. Sensors and Actuators A: Physical, 144, 354-360(2008).

[20] LI Y, XU Y T, WU Z G et al. A comprehensive review on fish-inspired robots[J]. International Journal of Advanced Robotic Systems, 19, 1-20(2022).

[21] DRUCKER E G, LAUDER G V. Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish[J]. Journal of Experimental Biology, 204, 2943-2958(2001).

[22] MENG H F, LOU J Q, CHEN T H et al. Cantilever-based micro thrust measurement and pressure field distribution of biomimetic robot fish actuated by macro fiber composites (MFCs) actuators[J]. Smart Materials and Structures, 30, 035001(2021).

[23] HAWKINS O H, ORTEGA-JIMÉNEZ V M, SANFORD C P. Knifefish turning control and hydrodynamics during forward swimming[J]. Journal of Experimental Biology, 225, jeb243498(2022).

[24] SUN W G, LIU Z M, REN Z Y et al. Linear acceleration of an undulatory robotic fish with dynamic morphing median fin under the instantaneous self-propelled condition[J]. Journal of Bionic Engineering, 17, 241-253(2020).

[25] REN Z Y, YANG X B, WANG T M et al. Hydrodynamics of a robotic fish tail: effects of the caudal peduncle, fin ray motions and the flow speed[J]. Bioinspiration & Biomimetics, 11, 016008(2016).

[26] ZHAO Z J, DOU L. Computational research on a combined undulating-motion pattern considering undulations of both the ribbon fin and fish body[J]. Ocean Enginee-ring, 183, 1-10(2019).

[27] SHIRGAONKAR A A, CURET O M, PATANKAR N A et al. The hydrodynamics of ribbon-fin propulsion during impulsive motion[J]. Journal of Experimental Biology, 211, 3490-3503(2008).

[28] TIAN R Y, LI L, WANG W et al. CFD based parameter tuning for motion control of robotic fish[J]. Bioinspiration & Biomimetics, 15, 026008(2020).

[29] [29] TAYL G I. Analysis of the swimming of long narrow animals[J]. Proceedings of the Royal Society A: Mathematical, Physical Engineering Sciences, 1952, 214(1117): 158–183.

[30] LIGHTHILL M J. Aquatic animal propulsion of high hydromechanical efficiency[J]. Journal of Fluid Mechanics, 44, 265-301(1970).

[31] LIGHTHILL M J. Large-amplitude elongated-body theory of fish locomotion[J]. Proceedings of the Royal Society B: Biological Sciences, 179, 125-138(1971).

[32] WU T Y T. Swimming of a waving plate[J]. Journal of Fluid Mechanics, 10, 321-344(1961).

[33] CHENG J Y, ZHUANG L X, TONG B G. Analysis of swimming three-dimensional waving plates[J]. Journal of Fluid Mechanics, 232, 341-355(1991).

[34] [34] HLOCK J H. Actuat disk they: discontinuities in thermofluid dynamics[M]. New Yk: McGrawHill International Book Co. , 1978.

[35] AURELI M, KOPMAN V, PORFIRI M. Free-locomotion of underwater vehicles actuated by ionic polymer metal composites[J]. IEEE/ASME Transactions on Mechatronics, 15, 603-614(2010).

[36] HU D Y, LOU J Q, CHEN T H et al. Micro thrust measurement experiment and pressure field evolution of bionic robotic fish with harmonic actuation of macro fiber composites[J]. Mechanical Systems and Signal Processing, 153, 107538(2021).

[37] BLAKE R W. Undulatory median fin propulsion of two teleosts with different modes of life[J]. Canadian Journal of Zoology, 58, 2116-2119(1980).

[38] JIANG H Z, LIU Y W. Nonlinear analysis of compliant robotic fish locomotion[J]. Journal of Vibration and Control, 28, 1673-1685(2022).

[39] YU J Z, YUAN J, WU Z X et al. Data-driven dynamic modeling for a swimming robotic fish[J]. IEEE Transactions on Industrial Electronics, 63, 5632-5640(2016).

[40] VERMA S, XU J X. Data-assisted modeling and speed control of a robotic fish[J]. IEEE Transactions on Industrial Electronics, 64, 4150-4157(2017).

[41] WANG J X, TAN X B. Averaging tail-actuated robotic fish dynamics through force and moment scaling[J]. IEEE Transactions on Robotics, 31, 906-917(2015).

[42] LIGHTHILL M J. Note on the swimming of slender fish[J]. Journal of fluid Mechanics, 9, 305-317(1960).

[43] YU J Z, SUN F H, XU D et al. Embedded vision-guided 3-D tracking control for robotic fish[J]. IEEE Transactions on Industrial Electronics, 63, 355-363(2016).

[44] JAN IJSPEERT A. Central pattern generators for locomotion control in animals and robots: a review[J]. Neural Networks, 21, 642-653(2008).

[45] AMARI S I. Characteristics of random nets of analog neuron-like elements[J]. IEEE Transactions on Systems, Man, and Cybernetics, SMC-2, 643-657(1972).

[46] YU J Z, WANG M, TAN M et al. Three-dimensional swimming[J]. IEEE Robotics & Automation Magazine, 18, 47-58(2011).

[47] [47] BUCHLI J, JAN IJSPEERT A. Distributed central pattern generat model f robotics application based on phase sensitivity analysis[C]Proceedings of the First International Wkshop on Biologically Inspired Approaches to Advanced Infmation Technology. Lausanne, Switzerl: Springer, 2004, 3141: 333−349.

[48] WU Z X, YU J Z, TAN M et al. Kinematic comparison of forward and backward swimming and maneuvering in a self-propelled sub-carangiform robotic fish[J]. Journal of Bionic Engineering, 11, 199-212(2014).

[50] YAN Z P, YANG H Y, ZHANG W et al. Research on motion mode switching method based on CPG network reconstruction[J]. IEEE Access, 8, 224871-224883(2020).

[51] NGUYEN V D, TRAN Q D, VU Q T et al. Force optimization of elongated undulating fin robot using improved PSO-based CPG[J]. Computational Intelligence and Neuroscience, 2022, 2763865(2022).

[52] [52] JAN IJSPEERT A, ARBIB M A. Locomotion visually guided behavi in salamer: a neuromechanical study[C]Proceedings of SPIE 4196, Sens Fusion Decentralized Control in Robotic Systems III. Boston, MA, USA: SPIE, 2000, 4196: 62–71.

[53] [53] COHEN A H, ROSSIGNOL S, GRILLNER S. Neural control of rhythmic movements in vertebrates[M]. New Yk: Wiley, 1988.

[56] BAL C, KOCA G O, KORKMAZ D et al. CPG-based autonomous swimming control for multi-tasks of a biomimetic robotic fish[J]. Ocean Engineering, 189, 106334(2019).

[57] CAO Y H, MA S M, CAO Y Z et al. Similarity evaluation rule and motion posture optimization for a manta ray robot[J]. Journal of Marine Science and Engineering, 10, 908(2022).

[58] MATSUOKA K. Sustained oscillations generated by mutually inhibiting neurons with adaptation[J]. Biological Cybernetics, 52, 367-376(1985).

[59] MATSUOKA K. Mechanisms of frequency and pattern control in the neural rhythm generators[J]. Biological Cybernetics, 56, 345-353(1987).

[60] [60] KIMURA H, FUKUOKA Y, NAKAMURA H. Biologically inspired adaptive dynamic walking of the quadruped on irregular terrain[M]HOLLERBACH J M, KODITSCHEK D E. The Ninth International Symposium on Robotics Research. London: Springer, 2000: 329–336.

[61] [61] CHOWDHURY A R, PA S K. Finding answers to biological control methods using modulated patterns: an application to bioinspired robotic fish[C]2015 IEEE International Conference on Robotics Automation (ICRA). Seattle, WA, USA: IEEE, 2015: 3146–3153.

[62] [62] WANG L, WANG S, CAO Z Q, et al. Motion control of a robot fish based on CPG[C]2005 IEEE International Conference on Industrial Technology. Hong Kong, China: IEEE, 2005: 1263–1268.

[65] WANG W, XIE G M. CPG-based locomotion controller design for a boxfish-like robot[J]. International Journal of Advanced Robotic Systems, 11, 87(2014).

[66] PHAMDUY P, CHEONG J, PORFIRI M. An autonomous charging system for a robotic fish[J]. IEEE/ASME Transactions on Mechatronics, 21, 2953-2963(2016).

[67] ZHANG P F, WU Z X, MENG Y et al. Nonlinear model predictive position control for a tail-actuated robotic fish[J]. Nonlinear Dynamics, 101, 2235-2247(2020).

[68] CASTAÑO M L, TAN X B. Model predictive control-based path-following for tail-actuated robotic fish[J]. Journal of Dynamic Systems, Measurement, and Control, 141, 071012(2019).

[69] [69] WANG J, WU Z X, TAN M, et al. Model predictive controlbased depth control in gliding motion of a gliding robotic dolphin[J]. IEEE Transactions on Systems, Man, Cyberics: Systems, 2021, 51(9): 5466–5477.

[70] YE M, WANG H, YAZDANI A et al. Discrete-time integral terminal sliding mode-based speed tracking control for a robotic fish[J]. Nonlinear Dynamics, 105, 359-370(2021).

[72] LI X F, REN Q Y, XU J X. Precise speed tracking control of a robotic fish via iterative learning control[J]. IEEE Transactions on Industrial Electronics, 63, 2221-2228(2016).

[73] WANG M, ZHANG Y L, DONG H F et al. Trajectory tracking control of a bionic robotic fish based on iterative learning[J]. Science China Information Sciences, 63, 170202(2020).

[74] REN Q Y, XU J X, FAN L P et al. A GIM-based biomimetic learning approach for motion generation of a multi-joint robotic fish[J]. Journal of Bionic Engineering, 10, 423-433(2013).

[75] [75] LI G D, SHINTAKE J, HAYASHIBE M. Deep reinfcement learning framewk f underwater locomotion of soft robot[C]2021 IEEE International Conference on Robotics Automation (ICRA). Xi''an,China: IEEE, 2021: 1203312039.

[76] YU J Z, WU Z X, WANG M et al. CPG network optimization for a biomimetic robotic fish via PSO[J]. IEEE Transactions on Neural Networks and Learning Systems, 27, 1962-1968(2016).

[77] ZHOU C L, LOW K H. On-line optimization of biomimetic undulatory swimming by an experiment-based approach[J]. Journal of Bionic Engineering, 11, 213-225(2014).

[79] YU J Z, LIU J C, WU Z X et al. Depth control of a bioinspired robotic dolphin based on sliding-mode fuzzy control method[J]. IEEE Transactions on Industrial Electronics, 65, 2429-2438(2018).

[80] WANG S, WANG Y, WEI Q P et al. A bio-inspired robot with undulatory fins and its control methods[J]. IEEE/ASME Transactions on Mechatronics, 22, 206-216(2017).