“Review on Modeling and Control of Flexible Link Manipulators”

Authors: Dipendra Subedi, Ilya Tyapin and Geir Hovland,
Affiliation: University of Agder
Reference: 2020, Vol 41, No 3, pp. 141-163.

Keywords: Flexible link manipulator, dynamic modeling, vibrations, control, elasticity, flexibility, deflection

Abstract: This paper presents a review of dynamic modeling techniques and various control schemes to control flexible link manipulators (FLMs) that were studied in recent literature. The advantages and complexities associated with the FLMs are discussed briefly. A survey of the reported studies is carried out based on the method used for modeling link flexibility and obtaining equations of motion of the FLMs. The control techniques are reviewed by classifying them into two main categories: model-based and model-free control schemes. The merits and limitations of different modeling and control methods are highlighted.

PDF PDF (549 Kb)        DOI: 10.4173/mic.2020.3.2

References:
[1] Aarts, R.G. and Jonker, J.B. (2002). Aarts, R, G. and Jonker, J.B. Dynamic simulation of planar flexible link manipulators using adaptive modal integration. Multibody System Dynamics. 7(1):31--50. doi:10.1023/A:1015271000518
[2] Abd Latip, S.F., Rashid Husain, A., Mohamed, Z., and Mohd Basri, M.A. (2019). Abd Latip, S, F., Rashid Husain, A., Mohamed, Z., and Mohd Basri, M.A. Adaptive PID actuator fault tolerant control of single-link flexible manipulator. Transactions of the Institute of Measurement and Control, 2019. 41(4):1019--1031. doi:10.1177/0142331218776720
[3] Abe, A. (2009). Abe, A, Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation. Mechanism and Machine Theory. 44(9):1627--1639. doi:10.1016/j.mechmachtheory.2009.01.009
[4] Agrawal, K., Negi, R., and Singh, N. (2020). Agrawal, K, , Negi, R., and Singh, N. Dynamically Tuned PIDD2 Controller for Single-Link Flexible Manipulator. In D.Dutta, H.Kar, C.Kumar, and V.Bhadauria, editors, Advances in VLSI, Communication, and Signal Processing. Springer Singapore, Singapore, pages 907--924. .
[5] Ahmad, M.A., Mohamed, Z., and Hambali, N. (2008). Ahmad, M, A., Mohamed, Z., and Hambali, N. Dynamic modelling of a two-link flexible manipulator system incorporating payload. 2008 3rd IEEE Conference on Industrial Electronics and Applications, ICIEA 2008. pages 96--101. doi:10.1109/ICIEA.2008.4582487
[6] Alandoli, E.A., Sulaiman, M., Rashid, M.Z., Shah, H.N., and Ismail, Z. (2016). Alandoli, E, A., Sulaiman, M., Rashid, M.Z., Shah, H.N., and Ismail, Z. A review study on flexible link manipulators. Journal of Telecommunication, Electronic and Computer Engineering. 8(2):93--97. .
[7] Amirouche, F. and Xie, M. (1993). Amirouche, F, and Xie, M. An explicit matrix formulation of the dynamical equations for flexible multibody systems: A recursive approach. Computers & Structures. 46(2):311--321. doi:10.1016/0045-7949(93)90195-J
[8] Ata, A.A., Fares, W.F., and Sa'Adeh, M.Y. (2012). Ata, A, A., Fares, W.F., and Sa'Adeh, M.Y. Dynamic analysis of a two-link flexible manipulator subject to different sets of conditions. Procedia Engineering. 41(Iris):1253--1260. doi:10.1016/j.proeng.2012.07.308
[9] Badfar, E. and Abdollahi, R. (2019). Badfar, E, and Abdollahi, R. Trajectory tracking of rigid-flexible manipulator based on LMI optimization approach. EEA - Electrotehnica, Electronica, Automatica. 67(2):62--67. .
[10] Barbieri, E. and Ozguner, U. (1988). Barbieri, E, and Ozguner, U. Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link. In 1988 American Control Conference. pages 83--88. doi:10.23919/ACC.1988.4789697
[11] Bascetta, L., Ferretti, G., and Scaglioni, B. (2017). Bascetta, L, , Ferretti, G., and Scaglioni, B. Closed form Newton-Euler dynamic model of flexible manipulators. Robotica. 35(5):1006--1030. doi:10.1017/S0263574715000934
[12] Bazaei, A. and Moallem, M. (2010). Bazaei, A, and Moallem, M. Improving force control bandwidth of flexible-link arms through output redefinition. IEEE/ASME Transactions on Mechatronics. 16(2):380--386. doi:10.1109/TMECH.2010.2046332
[13] Benosman, M. and Le Vey, G. (2004). Benosman, M, and Le Vey, G. Control of flexible manipulators: A survey. Robotica. 22(5):533--545. doi:10.1017/S0263574703005642
[14] Beres, W., Sasiadek, J.Z., and Vukovich, G. (1993). Beres, W, , Sasiadek, J.Z., and Vukovich, G. Control and dynamic analysis of multilink flexible manipulator. Proceedings - IEEE International Conference on Robotics and Automation. 3:478--483. doi:10.1109/robot.1993.292218
[15] Bian, Y. and Gao, Z. (2018). Bian, Y, and Gao, Z. Nonlinear vibration control for flexible manipulator using 1: 1 internal resonance absorber. Journal of Low Frequency Noise Vibration and Active Control, 2018. 37(4):1053--1066. doi:10.1177/1461348418765951
[16] Bian, Y., Gao, Z., Lv, X., and Fan, M. (2018). Bian, Y, , Gao, Z., Lv, X., and Fan, M. Theoretical and experimental study on vibration control of flexible manipulator based on internal resonance. JVC/Journal of Vibration and Control. 24(15):3321--3337. doi:10.1177/1077546317704792
[17] Book, W.J. (1990). Book, W, J. Modeling, design, and control of flexible manipulator arms: a tutorial review. In 29th IEEE Conference on Decision and Control. pages 500--506 vol.2. doi:10.1109/CDC.1990.203648
[18] Boucetta, R., Hamdi, S., and Bel Hadj Ali, S. (2020). Boucetta, R, , Hamdi, S., and Bel Hadj Ali, S. Flexible-Link Manipulators: Dynamic Analysis and Advanced Control Strategies, pages 19--46. Springer Singapore, Singapore. doi:10.1007/978-981-15-1819-5_2
[19] Boyer, F. and Glandais, N. (1999). Boyer, F, and Glandais, N. Simulation of flexible manipulators with elastic nonlinearities. In Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C), volume1. pages 759--766 vol.1. doi:10.1109/ROBOT.1999.770066
[20] Buffinton, K.W. (1992). Buffinton, K, W. Dynamics of Elastic Manipulators With Prismatic Joints. Journal of Dynamic Systems, Measurement, and Control. 114(1):41--49. doi:10.1115/1.2896506
[21] Cambera, J.C. and Feliu-Batlle, V. (2017). Cambera, J, C. and Feliu-Batlle, V. Input-state feedback linearization control of a single-link flexible robot arm moving under gravity and joint friction. Robotics and Autonomous Systems. 88:24--36. doi:10.1016/j.robot.2016.11.019
[22] Cambera, J.C. and Feliu-Batlle, V. (2018). Cambera, J, C. and Feliu-Batlle, V. Feedback Linearizing Controller for a Single Link Flexible Arm with a Passive Gravity Compensation Mechanism. IEEE International Conference on Intelligent Robots and Systems. pages 6404--6410. doi:10.1109/IROS.2018.8594409
[23] Cao, F. and Liu, J. (2017). Cao, F, and Liu, J. An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator. Journal of the Franklin Institute, 2017. 354(1):277--297. doi:10.1016/j.jfranklin.2016.10.013
[24] Cao, F. and Liu, J. (2017). Cao, F, and Liu, J. Vibration control for a rigid-flexible manipulator with full state constraints via Barrier Lyapunov Function. Journal of Sound and Vibration, 2017. 406:237--252. doi:10.1016/j.jsv.2017.05.050
[25] Cao, F. and Liu, J. (2018). Cao, F, and Liu, J. Adaptive actuator fault compensation control for a rigid-flexible manipulator with ODEs-PDEs model. International Journal of Systems Science, 2018. 49(8):1748--1759. doi:10.1080/00207721.2018.1479002
[26] Cao, F. and Liu, J. (2018). Cao, F, and Liu, J. Optimal trajectory control for a two-link rigid-flexible manipulator with ODE-PDE model. Optimal Control Applications and Methods, 2018. 39(4):1515--1529. doi:10.1002/oca.2423
[27] Cao, F. and Liu, J. (2019). Cao, F, and Liu, J. Boundary vibration control for a two-link rigid–flexible manipulator with quantized input. JVC/Journal of Vibration and Control. 25(23-24):2935--2945. doi:10.1177/1077546319873507
[28] Cao, F. and Liu, J. (2020). Cao, F, and Liu, J. Three-dimensional modeling and input saturation control for a two-link flexible manipulator based on infinite dimensional model. Journal of the Franklin Institute. 357(2):1026--1042. doi:10.1016/j.jfranklin.2019.10.018
[29] Celentano, L. (2016). Celentano, L, Modeling of Flexible Robots with Varying Cross Section and Large Link Deformations. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME. 138(2):1--12. doi:10.1115/1.4032133
[30] Celentano, L. and Coppola, A. (2011). Celentano, L, and Coppola, A. A computationally efficient method for modeling flexible robots based on the assumed modes method. Applied Mathematics and Computation. 218(8):4483--4493. doi:10.1016/j.amc.2011.10.029
[31] Chen, T., Li, M., and Shan, J. (2019). Chen, T, , Li, M., and Shan, J. Iterative learning control of a flexible manipulator considering uncertain parameters and unknown repetitive disturbance. In 2019 American Control Conference (ACC). pages 2209--2214, 2019. doi:10.23919/ACC.2019.8815014
[32] Comi, F., Miguel, A.O., Cavenago, F., Ferretti, G., Magnani, G., and Rusconi, A. (2019). Comi, F, , Miguel, A.O., Cavenago, F., Ferretti, G., Magnani, G., and Rusconi, A. Modelling, validation and control of DELIAN flexible manipulator. IFAC-PapersOnLine. 52(15):364--369. doi:10.1016/j.ifacol.2019.11.702
[33] De Luca, A. and Book, W.J. (2016). De Luca, A, and Book, W.J. Robots with Flexible Elements, pages 243--282. Springer International Publishing, Cham. doi:10.1007/978-3-319-32552-1_11
[34] Depraetere, B., Liu, M., Pinte, G., Grondman, I., and Babuska, R. (2014). Depraetere, B, , Liu, M., Pinte, G., Grondman, I., and Babuska, R. Comparison of model-free and model-based methods for time optimal hit control of a badminton robot. Mechatronics. 24(8):1021--1030. doi:10.1016/j.mechatronics.2014.08.001
[35] Ding, X., Tarn, T.J., and Bejczy, A.K. (1989). Ding, X, , Tarn, T.J., and Bejczy, A.K. A general dynamic model of flexible robot arms for control. In Proceedings, 1989 International Conference on Robotics and Automation. pages 1678--1683 vol.3. doi:10.1109/ROBOT.1989.100217
[36] Dogan, M. and Morgul, O. (2010). Dogan, M, and Morgul, O. On the control of two-link flexible robot arm with nonuniform cross section. JVC/Journal of Vibration and Control. 16(5):619--646. doi:10.1177/1077546309340994
[37] Dong, J., He, B., Ma, M., Zhang, C., and Li, G. (2019). Dong, J, , He, B., Ma, M., Zhang, C., and Li, G. Open-Closed-Loop PD Iterative Learning Control Corrected With the Angular Relationship of Output Vectors for a Flexible Manipulator. IEEE Access. 7:167815--167822. doi:10.1109/ACCESS.2019.2930559
[38] Dwivedy, S.K. and Eberhard, P. (2006). Dwivedy, S, K. and Eberhard, P. Dynamic analysis of flexible manipulators, a literature review. Mechanism and Machine Theory. 41(7):749--777. doi:10.1016/j.mechmachtheory.2006.01.014
[39] Esfandiar, H., Korayem, M.H., and Haghpanahi, M. (2017). Esfandiar, H, , Korayem, M.H., and Haghpanahi, M. Large deformation modeling of flexible manipulators to determine allowable load. Structural Engineering and Mechanics. 62(5):619--629. .
[40] Fareh, R., Al-Shabi, M., Bettayeb, M., and Ghommam, J. (2020). Fareh, R, , Al-Shabi, M., Bettayeb, M., and Ghommam, J. Robust Active Disturbance Rejection Control for Flexible Link Manipulator. Robotica. 38(1):118--135. doi:10.1017/S026357471900050X
[41] Gao, H., He, W., Zhou, C., and Sun, C. (2018). Gao, H, , He, W., Zhou, C., and Sun, C. Neural Network Control of a Two-Link Flexible Robotic Manipulator Using Assumed Mode Method. IEEE Transactions on Industrial Informatics. 15(2):755--765. doi:10.1109/TII.2018.2818120
[42] Garcia-Perez, O.A., Silva-Navarro, G., and Peza-Solis, J.F. (2019). Garcia-Perez, O, A., Silva-Navarro, G., and Peza-Solis, J.F. Flexible-link robots with combined trajectory tracking and vibration control. Applied Mathematical Modelling. 70:285--298. doi:10.1016/j.apm.2019.01.035
[43] Ghasemi, A.H. (2017). Ghasemi, A, H. Slewing and vibration control of a single-link flexible manipulator using filtered feedback linearization. Journal of Intelligent Material Systems and Structures. 28(20):2887--2895. doi:10.1177/1045389X17704067
[44] Giorgio, I. and Del Vescovo, D.D. (2018). Giorgio, I, and Del Vescovo, D.D. Non-linear lumped-parameter modeling of planar multi-link manipulators with highly flexible arms. Robotics. 7(4):1--13. doi:10.3390/robotics7040060
[45] He, W., He, X., and Sun, C. (2017). He, W, , He, X., and Sun, C. Vibration Control of an Industrial Moving Strip in the Presence of Input Deadzone. IEEE Transactions on Industrial Electronics, 2017. 64(6):4680--4689. doi:10.1109/TIE.2017.2674592
[46] He, W., He, X., Zou, M., and Li, H. (2018). He, W, , He, X., Zou, M., and Li, H. PDE Model-Based Boundary Control Design for a Flexible Robotic Manipulator with Input Backlash. IEEE Transactions on Control Systems Technology. 27(2):790--797. doi:10.1109/TCST.2017.2780055
[47] He, X., He, W., and Sun, C. (2017). He, X, , He, W., and Sun, C. Robust adaptive vibration control for an uncertain flexible Timoshenko robotic manipulator with input and output constraints. International Journal of Systems Science, 2017. 48(13):2860--2870. doi:10.1080/00207721.2017.1360963
[48] Heidari, H.R., Korayem, M.H., Haghpanahi, M., and Feliu Batlle, V. (2011). Heidari, H, R., Korayem, M.H., Haghpanahi, M., and Feliu Batlle, V. A new nonlinear finite element model for the dynamic modeling of flexible link manipulators undergoing large deflections. In 2011 IEEE International Conference on Mechatronics. pages 375--380. doi:10.1109/ICMECH.2011.5971314
[49] Huan, G. and Xian, W.Q. (2017). Huan, G, and Xian, W.Q. Observer based tracking control of flexible manipulator. In 2017 2nd International Conference on Advanced Robotics and Mechatronics (ICARM). pages 662--666. doi:10.1109/ICARM.2017.8273241
[50] Hussein, M.T. (2015). Hussein, M, T. A review on vision-based control of flexible manipulators. Advanced Robotics. 29(24):1575--1585. doi:10.1080/01691864.2015.1078743
[51] Jia, S., Jia, Y., Xu, S., and Hu, Q. (2017). Jia, S, , Jia, Y., Xu, S., and Hu, Q. Maneuver and Active Vibration Suppression of Free-Flying Space Robot. IEEE Transactions on Aerospace and Electronic Systems. 54(3):1115--1134. doi:10.1109/TAES.2017.2775780
[52] Jiang, T., Liu, J., and He, W. (2017). Jiang, T, , Liu, J., and He, W. A robust observer design for a flexible manipulator based on a PDE model. Journal of Vibration and Control. 23(6):871--882. doi:10.1177/1077546315587443
[53] Jiang, T., Liu, J., and He, W. (2018). Jiang, T, , Liu, J., and He, W. Boundary control for a flexible manipulator with a robust state observer. JVC/Journal of Vibration and Control. 24(2):260--271. doi:10.1177/1077546316635343
[54] Jing, Z., Xu, Q., and Huang, J. (2019). Jing, Z, , Xu, Q., and Huang, J. A review on kinematic analysis and dynamic stable control of space flexible manipulators. Aerospace Systems. 2(1):1--14. doi:10.1007/s42401-018-00024-4
[55] Jonker, J.B. and Aarts, R.G. (2001). Jonker, J, B. and Aarts, R.G. A Perturbation Method for Dynamic Analysis and Simulation of Flexible Manipulators. Multibody System Dynamics. 6(3):245--266. doi:10.1023/A:1012070525137
[56] Ju, J.Y., Li, W., Liu, Y., and Zhang, C. (2019). Ju, J, Y., Li, W., Liu, Y., and Zhang, C. Master-slave integrated control for the transverse vibration of a translational flexible manipulator based on input shaping and state feedback. Shock and Vibration. 2019. doi:10.1155/2019/8419591
[57] Kane, T.R. and Levinson, D.A. (1980). Kane, T, R. and Levinson, D.A. Formulation of Equations of Motion for Complex Spacecraft. Journal of Guidance and Control. 3(2):99--112. doi:10.2514/3.55956
[58] Kane, T.R. and Levinson, D.A. (1985). Kane, T, R. and Levinson, D.A. Dynamics, theory and applications. McGraw Hill. .
[59] Khadem, S.E. and Pirmohammadi, A.A. (2003). Khadem, S, E. and Pirmohammadi, A.A. Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics. 33(2):237--249. doi:10.1109/TSMCB.2003.810439
[60] Kiang, C.T., Spowage, A., and Yoong, C.K. (2015). Kiang, C, T., Spowage, A., and Yoong, C.K. Review of Control and Sensor System of Flexible Manipulator. Journal of Intelligent and Robotic Systems: Theory and Applications. 77(1):187--213. doi:10.1007/s10846-014-0071-4
[61] Kim, J.S. and Uchiyama, M. (2003). Kim, J, S. and Uchiyama, M. Vibration mechanism of constrained spatial flexible manipulators. JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing. 46(1):123--128. doi:10.1299/jsmec.46.123
[62] Kivila, A., Book, W., and Singhose, W. (2017). Kivila, A, , Book, W., and Singhose, W. Exact Modeling of n-Link Spatial Serial Structures Using Transfer Matrices. Journal of Dynamic Systems, Measurement, and Control. 139(11). doi:10.1115/1.4036555
[63] Korayem, M.H., Haghpanahi, M., Rahimi, H.N., and Nikoobin, A. (2009). Korayem, M, H., Haghpanahi, M., Rahimi, H.N., and Nikoobin, A. Finite element method and optimal control theory for path planning of elastic manipulators. Studies in Computational Intelligence. 199:117--126. doi:10.1007/978-3-642-00909-9_12
[64] Korayem, M.H., Rahimi, H.N., and Nikoobin, A. (2012). Korayem, M, H., Rahimi, H.N., and Nikoobin, A. Mathematical modeling and trajectory planning of mobile manipulators with flexible links and joints. Applied Mathematical Modelling. 36(7):3229--3244. doi:10.1016/j.apm.2011.10.002
[65] Korayem, M.H. and Shafei, A.M. (2007). Korayem, M, H. and Shafei, A.M. Inverse dynamic equation of motion for flexible link manipulators using recursive gibbs-appell formulation. In 2007 IEEE International Conference on Robotics and Biomimetics (ROBIO). pages 2160--2165. doi:10.1109/ROBIO.2007.4522504
[66] Krauss, R. (2019). Krauss, R, An Improved Approach for Spatial Discretization of Transfer Matrix Models of Flexible Structures. In 2019 American Control Conference (ACC). pages 3123--3128, 2019. doi:10.23919/ACC.2019.8814650
[67] Krauss, R. and Okasha, M. (2013). Krauss, R, and Okasha, M. Discrete-time transfer matrix modeling of flexible robots under feedback control. Proceedings of the American Control Conference. pages 4104--4109. doi:10.1109/acc.2013.6580469
[68] Krauss, R.W. (2012). Krauss, R, W. Computationally efficient modeling of flexible robots using the transfer matrix method. JVC/Journal of Vibration and Control. 18(5):596--608. doi:10.1177/1077546311408466
[69] Krauss, R.W. and Book, W.J. (2007). Krauss, R, W. and Book, W.J. A Python Module for Modeling and Control Design of Flexible Robots. Computing in Science Engineering. 9(3):41--45. doi:10.1109/MCSE.2007.44
[70] Kurfess, T.R. (2018). Kurfess, T, R. Robotics and automation handbook. CRC press. .
[71] Li, C.. and Sankar, T.S. (1993). Li, C, . and Sankar, T.S. Systematic methods for efficient modeling and dynamics computation of flexible robot manipulators. IEEE Transactions on Systems, Man, and Cybernetics. 23(1):77--95. doi:10.1109/21.214769
[72] Li, H. and Zhang, X. (2016). Li, H, and Zhang, X. A Method for Modeling Flexible Manipulators: Transfer Matrix Method with Finite Segments. International Journal of Computer and Information Engineering, 2016. 10(6):1086--1093. .
[73] Li, L., Cao, F., and Liu, J. (2020). Li, L, , Cao, F., and Liu, J. Vibration control of flexible manipulator with unknown control direction. International Journal of Control. 0(0):1--13. doi:10.1080/00207179.2020.1731609
[74] Li, Z., Feiling, J., Ren, H., and Yu, H. (2015). Li, Z, , Feiling, J., Ren, H., and Yu, H. A Novel Tele-Operated Flexible Robot Targeted for Minimally Invasive Robotic Surgery. Engineering. 1(1):073--078. doi:10.15302/J-ENG-2015011
[75] Liu, J. and He, W. (2018). Liu, J, and He, W. Boundary Control for Flexible Manipulator Using Singular Perturbation. In Distributed Parameter Modeling and Boundary Control of Flexible Manipulators, pages 27--43. Springer Singapore, Singapore. doi:10.1007/978-981-10-8300-6_4
[76] Liu, Z. and Liu, J. (2017). Liu, Z, and Liu, J. Boundary Control of a Flexible Robotic Manipulator With Output Constraints. Asian Journal of Control. 19(1):332--345. doi:10.1002/asjc.1342
[77] Liu, Z. and Liu, J. (2018). Liu, Z, and Liu, J. Adaptive Iterative Learning Boundary Control of a Flexible Manipulator with Guaranteed Transient Performance. Asian Journal of Control. 20(3):1027--1038. doi:10.1002/asjc.1379
[78] Liu, Z., Liu, J., and He, W. (2016). Liu, Z, , Liu, J., and He, W. Adaptive boundary control of a flexiblemanipulator with input saturation. International Journal of Control. 89(6):1191--1202. doi:10.1080/00207179.2015.1125022
[79] Liu, Z., Liu, J., and He, W. (2017). Liu, Z, , Liu, J., and He, W. Partial differential equation boundary control of a flexible manipulator with input saturation. International Journal of Systems Science. 48(1):53--62. doi:10.1080/00207721.2016.1152416
[80] Liu, Z., Liu, J., and He, W. (2018). Liu, Z, , Liu, J., and He, W. Dynamic modeling and vibration control for a nonlinear 3-dimensional flexible manipulator. International Journal of Robust and Nonlinear Control. 28(13):3927--3945. doi:10.1002/rnc.4113
[81] Lochan, K. and Roy, B.K. (2018). Lochan, K, and Roy, B.K. Second-order SMC for tip trajectory tracking and tip deflection suppression of an AMM modelled nonlinear TLFM. International Journal of Dynamics and Control. 6(3):1310--1318. doi:10.1007/s40435-017-0371-1
[82] Lochan, K., Roy, B.K., and Subudhi, B. (2016). Lochan, K, , Roy, B.K., and Subudhi, B. A review on two-link flexible manipulators. Annual Reviews in Control, 2016. 42:346--367. doi:10.1016/j.arcontrol.2016.09.019
[83] Lochan, K., Roy, B.K., and Subudhi, B. (2016). Lochan, K, , Roy, B.K., and Subudhi, B. SMC controlled chaotic trajectory tracking of two-link flexible manipulator with PID sliding surface. IFAC-PapersOnLine, 2016. 49(1):219--224. doi:10.1016/j.ifacol.2016.03.056
[84] Lochan, K., Roy, B.K., and Subudhi, B. (2019). Lochan, K, , Roy, B.K., and Subudhi, B. Use of memristive chaotic signal as a desired trajectory for a two-link flexible manipulator using contraction theory based on a composite control technique. European Physical Journal: Special Topics. 228(10):2215--2231. doi:10.1140/epjst/e2019-900038-5
[85] Lochan, K., Singh, J.P., and Roy, B.K. (2020). Lochan, K, , Singh, J.P., and Roy, B.K. Tracking control and deflection suppression of an AMM modelled TLFM using backstepping based adaptive SMC technique, volume 581. Springer Singapore. doi:10.1007/978-981-13-9419-5_4
[86] Lou, J., Liao, J., Wei, Y., Yang, Y., and Li, G. (2017). Lou, J, , Liao, J., Wei, Y., Yang, Y., and Li, G. Experimental identification and vibration control of a piezoelectric flexible manipulator using optimal multi-poles placement control. Applied Sciences (Switzerland). 7(3). doi:10.3390/APP7030309
[87] Luca, A.D. and Siciliano, B. (1991). Luca, A, D. and Siciliano, B. Closed-Form Dynamic Model of Planar Multilink Lightweight Robots. IEEE Transactions on Systems, Man and Cybernetics. 21(4):826--839. doi:10.1109/21.108300
[88] Ma Xiang-feng and Xu Xiang-rong. (1988). Ma Xiang-feng and Xu Xiang-rong, A further study on kane's equations approach of robots dynamics. In Proceedings of the 1988 IEEE International Conference on Systems, Man, and Cybernetics, volume1. pages 107--112. doi:10.1109/ICSMC.1988.754252
[89] Malvezzi, F., Orsino, R. M.M., and Coelho, T. A.H. (2019). Malvezzi, F, , Orsino, R. M.M., and Coelho, T. A.H. Lagrange's, Maggi's and Kane's Equations Applied to the Dynamic Modelling of Serial Manipulator. In A.d.T. Fleury, D.A. Rade, and P.R.G. Kurka, editors, Proceedings of DINAME 2017. Springer International Publishing, Cham, pages 291--304. .
[90] Matsuno, F. and Yamamoto, K. (1993). Matsuno, F, and Yamamoto, K. Dynamic hybrid position/force control of a flexible manipulator. In [1993.
[91] Meghdari, A. and Fahimi, F. (2001). Meghdari, A, and Fahimi, F. On the First-Order Decoupling of Dynamical Equations of Motion for Elastic Multibody Systems as Applied to a Two-Link Flexible Manipulator. Multibody System Dynamics. 5(1):1--20. doi:10.1023/A:1026576603498
[92] Mehria, F. and Foruzantabarb, A. (2019). Mehria, F, and Foruzantabarb, A. Control of Flexible Link Robot using a Closed Loop Input-Shaping Approach. Journal of Artificial Intelligence in Electrical Engineering, 2019. 8(29):41--52. .
[93] Meng, Q.X., Lai, X.Z., Wang, Y.W., and Wu, M. (2018). Meng, Q, X., Lai, X.Z., Wang, Y.W., and Wu, M. A fast stable control strategy based on system energy for a planar single-link flexible manipulator. Nonlinear Dynamics. 94(1):615--626. doi:10.1007/s11071-018-4380-1
[94] Meng, T. and He, W. (2020). Meng, T, and He, W. ILC for a Flexible Single-Link Manipulator, pages 109--128. Springer Singapore, Singapore. doi:10.1007/978-981-15-2784-5_5
[95] Moh. Khairudin, M.K. (2008). Moh, Khairudin, M.K. Dynamic Modelling of a Flexible Link Manipulator Robot Using Amm. TELKOMNIKA (Telecommunication Computing Electronics and Control). 6(3):185. doi:10.12928/telkomnika.v6i3.566
[96] Mohamed, Z., Khairudin, M., Husain, A.R., and Subudhi, B. (2016). Mohamed, Z, , Khairudin, M., Husain, A.R., and Subudhi, B. Linear matrix inequality-based robust proportional derivative control of a two-link flexible manipulator. JVC/Journal of Vibration and Control. 22(5):1244--1256. doi:10.1177/1077546314536427
[97] Mosayebi, M., Ghayour, M., and Sadigh, M.J. (2012). Mosayebi, M, , Ghayour, M., and Sadigh, M.J. A nonlinear high gain observer based input-output control of flexible link manipulator. Mechanics Research Communications. 45:34--41. doi:10.1016/j.mechrescom.2012.06.004
[98] Newman, D. and Vaughan, J. (2018). Newman, D, and Vaughan, J. Concurrent Design of Linear Control with Input Shaping for a Two-Link Flexible Manipulator Arm. IFAC-PapersOnLine. 51(14):66--71. doi:10.1016/j.ifacol.2018.07.200
[99] Njeri, W., Sasaki, M., and Matsushita, K. (2018). Njeri, W, , Sasaki, M., and Matsushita, K. Enhanced vibration control of a multilink flexible manipulator using filtered inverse controller. ROBOMECH Journal. 5(1):1--19. doi:10.1186/s40648-018-0125-7
[100] Njeri, W., Sasaki, M., and Matsushita, K. (2019). Njeri, W, , Sasaki, M., and Matsushita, K. Gain Tuning for High-Speed Vibration Control of a Multilink Flexible Manipulator Using Artificial Neural Network. Journal of Vibration and Acoustics. 141(4). doi:10.1115/1.4043241
[101] O'Connor, W.J. (2008). O'Connor, W, J. Wave-based Control of Flexible Mechanical Systems, pages 25--34. Springer Berlin Heidelberg, Berlin, Heidelberg. doi:10.1007/978-3-540-79142-3_3
[102] Ouyang, Y., He, W., and Li, X. (2017). Ouyang, Y, , He, W., and Li, X. Reinforcement learning control of a singlelink flexible robotic manipulator. IET Control Theory and Applications. 11(9):1426--1433. doi:10.1049/iet-cta.2016.1540
[103] Pappalardo, C.M. and Guida, D. (2018). Pappalardo, C, M. and Guida, D. Development of a new inertial-based vibration absorber for the active vibration control of flexible structures. Engineering Letters. 26(3):372--385. .
[104] Pradhan, S.K. and Subudhi, B. (2020). Pradhan, S, K. and Subudhi, B. Position control of a flexible manipulator using a new nonlinear self-Tuning PID controller. IEEE/CAA Journal of Automatica Sinica. 7(1):136--149. doi:10.1109/JAS.2017.7510871
[105] Pucher, F., Gattringer, H., and Muller, A. (2019). Pucher, F, , Gattringer, H., and Muller, A. Collision detection for flexible link robots using accelerometers. IFAC-PapersOnLine. 52(16):514--519. doi:10.1016/j.ifacol.2019.12.013
[106] Pucher, F., Gattringer, H., and Muller, A. (2020). Pucher, F, , Gattringer, H., and Muller, A. Investigation of the Behavior of Vibration-Damped Flexible Link Robots in End-Effector Contact: Simulation and Experiment. In A.Kecskemethy and F.Geu Flores, editors, Multibody Dynamics 2019. Springer International Publishing, Cham, pages 139--146, 2020. .
[107] Qiu, Z.-c., Li, C., and min Zhang, X. (2019). Qiu, Z, -c., Li, C., and min Zhang, X. Experimental study on active vibration control for a kind of two-link flexible manipulator. Mechanical Systems and Signal Processing. 118:623--644. doi:10.1016/j.ymssp.2018.09.001
[108] Qiu, Z.-c. and Zhang, W.-z. (2019). Qiu, Z, -c. and Zhang, W.-z. Trajectory planning and diagonal recurrent neural network vibration control of a flexible manipulator using structural light sensor. Mechanical Systems and Signal Processing. 132:563--594. doi:10.1016/j.ymssp.2019.07.014
[109] Rahimi, H.N. and Nazemizadeh, M. (2014). Rahimi, H, N. and Nazemizadeh, M. Dynamic analysis and intelligent control techniques for flexible manipulators: A review. Advanced Robotics. 28(2):63--76. doi:10.1080/01691864.2013.839079
[110] Reddy, M. P.P. and Jacob, J. (2017). Reddy, M, P.P. and Jacob, J. Vibration control of flexible link manipulator using SDRE controller and Kalman filtering. Studies in Informatics and Control. 26(2):143--150. doi:10.24846/v26i2y201702
[111] Ren, S., Chu, M., and Jia, Q. (2016). Ren, S, , Chu, M., and Jia, Q. Position inner loop impedance control of flexible link and flexible joint. In 2016 4th International Conference on Sensors, Mechatronics and Automation (ICSMA 2016). Atlantis Press. doi:https://doi.org/10.2991/icsma-16.2016.81
[112] Rigatos, G. and Busawon, K. (2018). Rigatos, G, and Busawon, K. Flexible-Link Robots, pages 271--300. Springer International Publishing, Cham. doi:10.1007/978-3-319-77851-8_5
[113] Ripamonti, F., Orsini, L., and Resta, F. (2017). Ripamonti, F, , Orsini, L., and Resta, F. A Nonlinear Sliding Surface in Sliding Mode Control to Reduce Vibrations of a Three-Link Flexible Manipulator. Journal of Vibration and Acoustics. 139(5). doi:10.1115/1.4036502
[114] Runciman, M., Darzi, A., and Mylonas, G.P. (2019). Runciman, M, , Darzi, A., and Mylonas, G.P. Soft Robotics in Minimally Invasive Surgery. Soft Robotics. 6(4):423--443. doi:10.1089/soro.2018.0136
[115] Sabatini, M., Gasbarri, P., Monti, R., and Palmerini, G.B. (2012). Sabatini, M, , Gasbarri, P., Monti, R., and Palmerini, G.B. Vibration control of a flexible space manipulator during on orbit operations. Acta Astronautica. 73:109--121. doi:10.1016/j.actaastro.2011.11.012
[116] Saeed, A., Malik, F.M., Ullah, H., Akbar, Z.A., and Mazhar, N. (2019). Saeed, A, , Malik, F.M., Ullah, H., Akbar, Z.A., and Mazhar, N. Model-Based Control of Planar Rigid-Flexible Manipulator. In 2019 IEEE 7th Conference on Systems, Process and Control (ICSPC), December. IEEE, pages 122--126. .
[117] Sahu, U.K., Mishra, A., Sahu, B., Pradhan, P.P., Patra, D., and Subudhi, B. (2019). Sahu, U, K., Mishra, A., Sahu, B., Pradhan, P.P., Patra, D., and Subudhi, B. Vision-Based Tip Position Control of a Single-Link Robot Manipulator. SSRN Electronic Journal, 2019. pages 1416--1422. doi:10.2139/ssrn.3356203
[118] Sahu, U.K. and Patra, D. (2016). Sahu, U, K. and Patra, D. Observer based backstepping method for tip tracking control of 2-DOF Serial Flexible Link Manipulator. In 2016 IEEE Region 10 Conference (TENCON). pages 3563--3568, 2016. doi:10.1109/TENCON.2016.7848721
[119] Sahu, U.K., Subudhi, B., and Patra, D. (2019). Sahu, U, K., Subudhi, B., and Patra, D. Sampled-data extended state observer-based backstepping control of two-link flexible manipulator. Transactions of the Institute of Measurement and Control, 2019. 41(13):3581--3599. doi:10.1177/0142331219832954
[120] Sayahkarajy, M., Mohamed, Z., and Mohd Faudzi, A.A. (2016). Sayahkarajy, M, , Mohamed, Z., and Mohd Faudzi, A.A. Review of modelling and control of flexible-link manipulators. Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering. 230(8):861--873. doi:10.1177/0959651816642099
[121] Scaglioni, B., Bascetta, L., Baur, M., and Ferretti, G. (2017). Scaglioni, B, , Bascetta, L., Baur, M., and Ferretti, G. Closed-form control oriented model of highly flexible manipulators. Applied Mathematical Modelling. 52:174--185. doi:10.1016/j.apm.2017.07.034
[122] Schnelle, F. and Eberhard, P. (2017). Schnelle, F, and Eberhard, P. Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters. Acta Mechanica Sinica. 33(3):529--542. doi:10.1007/s10409-017-0669-4
[123] Si, Y., Pu, J., and Sun, L. (2017). Si, Y, , Pu, J., and Sun, L. A fast terminal sliding mode control of two-link flexible manipulators for trajectory tracking. In 2017 Chinese Automation Congress (CAC). pages 6387--6391, 2017. doi:10.1109/CAC.2017.8243928
[124] Singh, N. and Rajendran, S. (2016). Singh, N, and Rajendran, S. Integral Fast Output Sampling control for Flexible Link Manipulators with LMI approach. In 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES). pages 1--6. doi:10.1109/ICPEICES.2016.7853698
[125] Singh, V.K. and Ohri, J. (2018). Singh, V, K. and Ohri, J. Simultaneous control of position and vibration of flexible link manipulator by nature-inspired algorithms. In 2018 IEEE 8th Power India International Conference (PIICON). pages 1--6. doi:10.1109/POWERI.2018.8704403
[126] Singla, A. and Singh, A. (2019). Singla, A, and Singh, A. Dynamic Modeling of Flexible Robotic Manipulators. In N.Yadav, A.Yadav, J.C. Bansal, K.Deep, and J.H. Kim, editors, Harmony Search and Nature Inspired Optimization Algorithms. Springer Singapore, Singapore, pages 819--834. .
[127] Sira-Ramirez, H., Luviano-Juarez, A., Ramirez-Neria, M., and Zurita-Bustamante, E.W. (2017). Sira-Ramirez, H, , Luviano-Juarez, A., Ramirez-Neria, M., and Zurita-Bustamante, E.W. Chapter 4 - Extensions of ADRC. In H.Sira-Ramirez, A.Luviano-Juarez, M.Ramirez-Neria, and E.W. Zurita-Bustamante, editors, Active Disturbance Rejection Control of Dynamic Systems, pages 109--172. Butterworth-Heinemann. doi:https://doi.org/10.1016/B978-0-12-849868-2.00004-6
[128] Suarez, A., Giordano, A.M., Kondak, K., Heredia, G., and Ollero, A. (2018). Suarez, A, , Giordano, A.M., Kondak, K., Heredia, G., and Ollero, A. Flexible link long reach manipulator with lightweight dual arm: Soft-collision detection, reaction, and obstacle localization. In 2018 IEEE International Conference on Soft Robotics (RoboSoft). pages 406--411. doi:10.1109/ROBOSOFT.2018.8404953
[129] Subedi, D., Tyapin, I., and Hovland, G. (2020). Subedi, D, , Tyapin, I., and Hovland, G. Modeling and Analysis of Flexible Bodies Using Lumped Parameter Method. 2020 IEEE 11th International Conference on Mechanical and Intelligent Manufacturing Technologies (ICMIMT). pages 161--166. doi:10.1109/icmimt49010.2020.9041188
[130] Sun, C., Gao, H., He, W., and Yu, Y. (2018). Sun, C, , Gao, H., He, W., and Yu, Y. Fuzzy Neural Network Control of a Flexible Robotic Manipulator Using Assumed Mode Method. IEEE Transactions on Neural Networks and Learning Systems, 2018. 29(11):5214--5227. doi:10.1109/TNNLS.2017.2743103
[131] Sun, C., He, W., and Hong, J. (2016). Sun, C, , He, W., and Hong, J. Neural Network Control of a Flexible Robotic Manipulator Using the Lumped Spring-Mass Model. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2016. 47(8):1863--1874. doi:10.1109/TSMC.2016.2562506
[132] Tahir, N.M., Hassan, S.M., Mohamed, Z., and Ibrahim, A.G. (2017). Tahir, N, M., Hassan, S.M., Mohamed, Z., and Ibrahim, A.G. Output based input shaping for optimal control of single link flexible manipulator. International Journal on Smart Sensing and Intelligent Systems. 10(2):367--386. doi:10.21307/ijssis-2017-216
[133] Theodore, R.J. and Ghosal, A. (1995). Theodore, R, J. and Ghosal, A. Comparison of the Assumed Modes and Finite Element Models for Flexible Multilink Manipulators. The International Journal of Robotics Research. 14(2):91--111. doi:10.1177/027836499501400201
[134] Tian, L., Wang, J., and Mao, Z. (2002). Tian, L, , Wang, J., and Mao, Z. Constrained motion control of flexible manipulators based on a dynamic neural network. Proceedings of the IEEE International Conference on Industrial Technology. 2(3):678--683. doi:10.1109/ICIT.2002.1189246
[135] Tokhi, M.O. and Azad, A. K.M. (2008). Tokhi, M, O. and Azad, A. K.M. Flexible robot manipulators: modelling, simulation and control, volume68. Iet. .
[136] Wang, B., Li, S., and Liu, Z. (2020). Wang, B, , Li, S., and Liu, Z. Robust Adaptive Position/Force Control for Flexible-Link with Flexible-Joint Manipulator. In R.Wang, Z.Chen, W.Zhang, and Q.Zhu, editors, Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019). Springer Singapore, Singapore, pages 1215--1227. .
[137] Wang, J., Pi, Y., Hu, Y., Zhu, Z., and Zeng, L. (2017). Wang, J, , Pi, Y., Hu, Y., Zhu, Z., and Zeng, L. Adaptive simultaneous motion and vibration control for a multi flexible-link mechanism with uncertain general harmonic disturbance. Journal of Sound and Vibration. 408:60--72. doi:10.1016/j.jsv.2017.07.024
[138] Wang, L., Zhang, D., Liu, J., Huang, H., and Shi, Q. (2018). Wang, L, , Zhang, D., Liu, J., Huang, H., and Shi, Q. Adaptive Fault-Tolerant Control for a Flexible Manipulator of Output-Constrained. In 2018 IEEE 8th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER). pages 1048--1052. .
[139] Wanner, J. and Sawodny, O. (2019). Wanner, J, and Sawodny, O. A lumped parameter model of the boom of a mobile concrete pump. 2019 18th European Control Conference, ECC 2019. pages 2808--2813. doi:10.23919/ECC.2019.8796004
[140] Wei, J., Cao, D., Liu, L., and Huang, W. (2017). Wei, J, , Cao, D., Liu, L., and Huang, W. Global mode method for dynamic modeling of a flexible-link flexible-joint manipulator with tip mass. Applied Mathematical Modelling. 48:787--805. doi:10.1016/j.apm.2017.02.025
[141] Xu, B. (2017). Xu, B, Composite learning control of flexible-link manipulator using NN and DOB. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017. 48(11):1979--1985. doi:10.1109/TSMC.2017.2700433
[142] Xu, Q., Wang, W., Xia, H., Wang, Y., and Feng, Y. (2018). Xu, Q, , Wang, W., Xia, H., Wang, Y., and Feng, Y. Second-Order Non-Singular Terminal Sliding Mode Optimal Control of Uncertain Flexible Manipulator. In 2018 IEEE 8th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER). pages 1376--1381. doi:10.1109/CYBER.2018.8688134
[143] Yanan, L., Deshan, M., Houde, L., Xueqian, W., and Bin, L. (2017). Yanan, L, , Deshan, M., Houde, L., Xueqian, W., and Bin, L. Modeling and control of a two-link flexible space manipulator using the wave-based method. Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017. 0:512--519. doi:10.1109/CCDC.2017.7978148
[144] Yang, C., Xu, Y., Zhou, L., and Sun, Y. (2018). Yang, C, , Xu, Y., Zhou, L., and Sun, Y. Model-free composite control of flexible manipulators based on adaptive dynamic programming. Complexity, 2018. 2018. doi:10.1155/2018/9720309
[145] Yang, H., Liu, J., and Lan, X. (2015). Yang, H, , Liu, J., and Lan, X. Observer design for a flexible-link manipulator with PDE model. Journal of Sound and Vibration. 341:237--245. doi:10.1016/j.jsv.2014.12.033
[146] Yang, H.J., Liu, J.K., and He, W. (2018). Yang, H, J., Liu, J.K., and He, W. Distributed disturbance-observer-based vibration control for a flexible-link manipulator with output constraints. Science China Technological Sciences, 2018. 61(10):1528--1536. doi:10.1007/s11431-017-9280-1
[147] Yang, H.-J. and Tan, M. (2018). Yang, H, -J. and Tan, M. Sliding Mode Control for Flexible-link Manipulators Based on Adaptive Neural Networks. International Journal of Automation and Computing. 15(2):239--248. doi:10.1007/s11633-018-1122-2
[148] Yang, Y., Liu, Z., and Ma, G. (2019). Yang, Y, , Liu, Z., and Ma, G. Adaptive Distributed Control of a Flexible Manipulator Using an Iterative Learning Scheme. IEEE Access. 7:145934--145943. doi:10.1109/ACCESS.2019.2946018
[149] Zhang, C., Yang, T., Sun, N., and Zhang, J. (2019). Zhang, C, , Yang, T., Sun, N., and Zhang, J. A Simple Control Method of Single-Link Flexible Manipulators. 3rd International Symposium on Autonomous Systems, ISAS 2019, 2019. pages 300--304. doi:10.1109/ISASS.2019.8757711
[150] Zhang, D.-g. and Zhou, S.-f. (2006). Zhang, D, -g. and Zhou, S.-f. Dynamic analysis of flexible-link and flexible-joint robots. Applied Mathematics and Mechanics. 27(5):695--704. doi:10.1007/s10483-006-0516-1
[151] Zhang, L. and Liu, J. (2012). Zhang, L, and Liu, J. Nonlinear PDE observer design for a flexible two-link manipulator. In 2012 American Control Conference (ACC). pages 5336--5341, 2012. doi:10.1109/ACC.2012.6314625
[152] Zhang, L. and Liu, J. (2012). Zhang, L, and Liu, J. Observer-based partial differential equation boundary control for a flexible two-link manipulator in task space. IET Control Theory Applications, 2012. 6(13):2120--2133. doi:10.1049/iet-cta.2011.0545
[153] Zhang, L. and Liu, J. (2012). Zhang, L, and Liu, J. Optimal trajectory control of flexible two-link manipulator based on PDE model. Proceedings of the IEEE Conference on Decision and Control, 2012. pages 4406--4411. doi:10.1109/CDC.2012.6427070
[154] Zhang, L. and Liu, J. (2013). Zhang, L, and Liu, J. Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model. IET Control Theory and Applications. 7(1):43--51. doi:10.1049/iet-cta.2011.0593
[155] Zhang, X., Xu, W., and Nair, S.S. (2004). Zhang, X, , Xu, W., and Nair, S.S. Comparison of some modeling and control issues for a flexible two link manipulator. ISA Transactions. 43(4):509--525. doi:10.1016/s0019-0578(07)60165-7
[156] Zhang, X., Xu, W., Nair, S.S., and Chellaboina, V.S. (2005). Zhang, X, , Xu, W., Nair, S.S., and Chellaboina, V.S. PDE Modeling and Control of a Flexible Two-Link Manipulator. IEEE Transactions on Control Systems Technology. 13(2):301--312. doi:10.1109/TCST.2004.842446
[157] Zhang, X. and Yu, Y.Q. (2001). Zhang, X, and Yu, Y.Q. Motion control of flexible robot manipulators via optimizing redundant configurations. Mechanism and Machine Theory. 36(7):883--892. doi:10.1016/S0094-114X(01)00020-9
[158] Zhang, Y., Li, Q., Zhang, W., Liu, Y., and Xue, Z. (2019). Zhang, Y, , Li, Q., Zhang, W., Liu, Y., and Xue, Z. Weighted Multiple Neural Network Boundary Control for a Flexible Manipulator With Uncertain Parameters. IEEE Access, 2019. 7:57633--57641. doi:10.1109/ACCESS.2019.2914077
[159] Zhao, Z., He, X., and Ahn, C.K. (2019). Zhao, Z, , He, X., and Ahn, C.K. Boundary Disturbance Observer-Based Control of a Vibrating Single-Link Flexible Manipulator. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. pages 1--9. doi:10.1109/TSMC.2019.2912900


BibTeX:
@article{MIC-2020-3-2,
  title={{Review on Modeling and Control of Flexible Link Manipulators}},
  author={Subedi, Dipendra and Tyapin, Ilya and Hovland, Geir},
  journal={Modeling, Identification and Control},
  volume={41},
  number={3},
  pages={141--163},
  year={2020},
  doi={10.4173/mic.2020.3.2},
  publisher={Norwegian Society of Automatic Control}
};