• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology

Article

Indian Journal of Science and Technology

Year: 2021, Volume: 14, Issue: 43, Pages: 3210-3226

Systematic Review

Dynamic modelling and control of flexible link manipulators: methods and scope- Part-1

Received Date:05 July 2021, Accepted Date:19 November 2021, Published Date:14 December 2021

Abstract

Objectives: This paper addresses two key issues in the area of flexible robotics. The issues are dynamic modelling and control of flexible link robots. A brief, yet, significant review is provided that addresses these issues. Methods: The various approaches used by researchers for dynamic modelling and control of flexible robots are presented. Besides that, methods used for achieving optimal control are also discussed. Findings: After a review of 153 research papers from the year 1975 to 2021, it has been found that a good dynamic model of flexible manipulator helps in reducing the control and computational efforts. Recent trends in research in the area of flexible manipulators are towards the use of sliding mode control and vision-based control techniques. Novelty: Inclusion of the effect of torsional vibrations besides lateral vibrations on the positional accuracy of flexible manipulators makes the current research work novel.

Keywords: Flexible manipulator; modelling; dynamics; control

References

  1. Dwivedy SK, Eberhard P. Dynamic analysis of flexible manipulators, a literature review. Mechanism and Machine Theory. 2006;41(7):749–777. doi: 10.1016/j.mechmachtheory.2006.01.014
  2. Benosman M, Le Vey G. Control of flexible manipulators: A survey. Robotica. 2004;22(5):533–545. doi: 10.1017/s0263574703005642
  3. Lochan K, Roy BK, 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
  4. Jing Z, Xu Q, Huang J. A review on kinematic analysis and dynamic stable control of space flexible manipulators. Aerospace Systems. 2019;2(1):1–14. doi: 10.1007/s42401-018-00024-4
  5. Tokhi MO, Azad AKM. Flexible Robot Manipulators: Modelling, Simulation and Control (2nd). Institution of Engineering and Technology. 2017. 10.1049/PBCE086E
  6. Li X, Zhang L, Jiang B, Fang J, Zheng Y. Research trends in China for macro-micro motion platform for microelectronics manufacturing industry. Journal of Advanced Mechanical Design, Systems, and Manufacturing. 2021;15(3):1–14. doi: 10.1299/jamdsm.2021jamdsm0032
  7. Book WJ, Maizza-Neto O, Whitney DE. Feedback Control of Two Beam, Two Joint Systems With Distributed Flexibility. Journal of Dynamic Systems, Measurement, and Control. 1975;97(4):424–431. doi: 10.1115/1.3426959
  8. Luh J, Walker M, Paul R. Resolved-acceleration control of mechanical manipulators. IEEE Transactions on Automatic Control. 1980;25(3):468–474. doi: 10.1109/tac.1980.1102367
  9. Book WJ, Majette M. Controller Design for Flexible, Distributed Parameter Mechanical Arms Via Combined State Space and Frequency Domain Techniques. Journal of Dynamic Systems, Measurement, and Control. 1983;105(4):245–254. doi: 10.1115/1.3140666
  10. Judd R, Falkenburg D. Dynamics of nonrigid articulated robot linkages. IEEE Transactions on Automatic Control. 1985;30(5):499–502. doi: 10.1109/tac.1985.1103978
  11. Bakr EM, Shabana AA. Geometrically nonlinear analysis of multibody systems. Computers & Structures. 1986;23(6):739–751. doi: 10.1016/0045-7949(86)90242-7
  12. De Luca A, Siciliano B. Closed-form dynamic model of planar multilink lightweight robots. IEEE Transactions on Systems, Man, and Cybernetics. 1991;21(4):826–839. doi: 10.1109/21.108300
  13. Li CJ, Sankar TS. Systematic methods for efficient modeling and dynamics computation of flexible robot manipulators. IEEE Transactions on Systems, Man, and Cybernetics. 1993;23(1):77–95. doi: 10.1109/21.214769
  14. Du H, Lim MK, Liew KM. A nonlinear finite element model for dynamics of flexible manipulators. Mechanism and Machine Theory. 1996;31(8):1109–1119. doi: 10.1016/0094-114x(96)84602-7
  15. Theodore RJ, Ghosal A. Modeling of flexible-link manipulators with prismatic joints. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics). 1997;27(2):296–305. doi: 10.1109/3477.558822
  16. Yüksel Ş, Aksoy TM. Flexural vibrations of a rotating beam subjected to different base excitations. Gazi University Journal of Science. 2009;22(1):33–40. Available from: https://dergipark.org.tr/en/pub/gujs/issue/7388/96768
  17. Ata AA, Fares WF, Sa’adeh MY. Dynamic Analysis of a Two-link Flexible Manipulator Subject to Different Sets of Conditions. Procedia Engineering. 2012;41:1253–1260. doi: 10.1016/j.proeng.2012.07.308
  18. Mishra N, Singh SP. Hybrid vibration control of a Two-Link Flexible manipulator. SN Applied Sciences. 2019;1(7). doi: 10.1007/s42452-019-0691-1
  19. Kumar P, Pratiher B. Influences of generic payload and constraint force on modal analysis and dynamic responses of flexible manipulator. Mechanics Based Design of Structures and Machines. 2020;0(0):1–19. doi: 10.1080/15397734.2020.1766980
  20. Sunada W, Dubowsky S. The Application of Finite Element Methods to the Dynamic Analysis of Flexible Spatial and Co-Planar Linkage Systems. Journal of Mechanical Design. 1981;103(3):643–651. doi: 10.1115/1.3254965
  21. Naganathan G, Soni AH. Non-linear flexibility studies for spatial manipulators. In: 1986 IEEE International Conference on Robotics and Automation. (pp. 359-64) Institute of Electrical and Electronics Engineers. 1986. 10.1109/ROBOT.1986.1087719
  22. Usoro PB, Nadira R, Mahil SS. A Finite Element/Lagrange Approach to Modeling Lightweight Flexible Manipulators. Journal of Dynamic Systems, Measurement, and Control. 1986;108(3):198–205. doi: 10.1115/1.3143768
  23. Simo JC, Vu-Quoc L. The role of non-linear theories in transient dynamic analysis of flexible structures. Journal of Sound and Vibration. 1987;119(3):487–508. doi: 10.1016/0022-460x(87)90410-x
  24. Chedmail P, Aoustin Y, Chevallereau C. Modelling and control of flexible robots. International Journal for Numerical Methods in Engineering. 1991;32(8):1595–1619. doi: 10.1002/nme.1620320806
  25. Gaultier PE, Cleghorn WL. A spatially translating and rotating beam finite element for modeling flexible manipulators. Mechanism and Machine Theory. 1992;27(4):415–433. doi: 10.1016/0094-114x(92)90033-e
  26. Alberts TE, Xia H, Chen Y. Dynamic Analysis to Evaluate Viscoelastic Passive Damping Augmentation for the Space Shuttle Remote Manipulator System. Journal of Dynamic Systems, Measurement, and Control. 1992;114(3):468–475. doi: 10.1115/1.2897370
  27. Hu FL, Ulsoy AG. Dynamic Modeling of Constrained Flexible Robot Arms for Controller Design. Journal of Dynamic Systems, Measurement, and Control. 1994;116(1):56–65. doi: 10.1115/1.2900681
  28. Stylianou M, Tabarrok B. Finite Element Analysis Of An Axially Moving Beam, Part II: Stability Analysis. Journal of Sound and Vibration. 1994;178(4):455–481. doi: 10.1006/jsvi.1994.1498
  29. Theodore RJ, Ghosal A. Robust control of multilink flexible manipulators. Mechanism and Machine Theory. 2003;38(4):367–377. doi: 10.1016/s0094-114x(02)00125-8
  30. Fotouhi R. Dynamic analysis of very flexible beams. Journal of Sound and Vibration. 2007;305(3):521–533. doi: 10.1016/j.jsv.2007.01.032
  31. Grazioso S, Sonneville V, Gironimo GD, Bauchau O, Siciliano B. A nonlinear finite element formalism for modelling flexible and soft manipulators. 2016 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR). 2016. doi: 10.1109/SIMPAR.2016.7862394
  32. Bamdad M, Feyzollahzadeh M. Computational efficient discrete time transfer matrix method for large deformation analysis of flexible manipulators. Mechanics Based Design of Structures and Machines. 2020;0(0):1–23. doi: 10.1080/15397734.2020.1830800
  33. Tirupathi RC, Ashok DB. Introduction to Finite Elements in Engineering. New Delhi. PHI Learning Private Limited. 2012.
  34. Kim YW. Dynamic analysis of Timoshenko beam subjected to support motions. Journal of Mechanical Science and Technology. 2016;30(9):4167–4176. Available from: http://link.springer.com/10.1007/s12206-016-0828-8
  35. Omolofe B, Adedowole A. Response characteristics of non-uniform beam with time-dependent boundary conditions and under the actions of travelling distributed masses. Journal of Applied Mathematics and Computational Mechanics. 2017;16(2):77–99. doi: 10.17512/jamcm.2017.2.07
  36. Matsuno F, Murachi T, Sakawa Y. Feedback control of decoupled bending and torsional vibrations of flexible beams. Journal of Robotic Systems. 1994;11(5):341–353. doi: 10.1002/rob.4620110502
  37. ElMaraghy WH, ElMaraghy HA, Zaki A, Massoud A. Design and Control of Robots with Flexibilities. CIRP Annals. 1994;43(1):359–362. doi: 10.1016/s0007-8506(07)62231-8
  38. Ubertini F. A contribution to the analysis of flexible link systems. International Journal of Solids and Structures. 2000;37(7):969–990. doi: 10.1016/s0020-7683(99)00106-7
  39. Yushu B, Zhihui G, Chao Y. Vibration Reduction of Open-chain Flexible Manipulators by Optimizing Independent Motions of Branch Links. Chinese Journal of Aeronautics. 2008;21(1):79–85. doi: 10.1016/s1000-9361(08)60011-4
  40. Connor WJO. Wave-based analysis and control of lump-modeled flexible robots. IEEE Transactions on Robotics. 2007;23(2):342–52. doi: 10.1109/TRO.2007.895061
  41. Gao Z, Yun C, Bian Y. Minimizing joint‐torques of the flexible redundant manipulator on the premise of vibration suppression. International Journal of Intelligent Computing and Cybernetics. 2008;1(4):634–645. doi: 10.1108/17563780810919168
  42. Bian Y, Gao Z, Yun C. Motion control of the flexible manipulator via controllable local degrees of freedom. Nonlinear Dynamics. 2009;55(4):373–384. doi: 10.1007/s11071-008-9370-2
  43. Kermani MR. Analytic Modal Analyses of a Partially Strengthened Timoshenko Beam. IEEE Transactions on Control Systems Technology. 2010;18(4):850–858. Available from: https://doi.org/10.1007/s11071-010-9897-x
  44. Vidoni R, Gasparetto A, Giovagnoni M. Design and implementation of an ERLS-based 3-D dynamic formulation for flexible-link robots. Robotics and Computer-Integrated Manufacturing. 2013;29(2):273–282. doi: 10.1016/j.rcim.2012.07.008
  45. Gasparetto A, Moosavi AK, Boscariol P, Giovagnoni M. Experimental Validation of a Dynamic Model for Lightweight Robots. International Journal of Advanced Robotic Systems. 2013;10(3):182. doi: 10.5772/55955
  46. Omer M. Dynamic boundary control of a Euler-Bernoulli beam. IEEE Transactions on Automatic Control. 1992;37(5):639–681. Available from: https://ieeexplore.ieee.org/document/135504
  47. Hillsley KL, Yurkovich S. Vibration control of a two-link flexible robot arm. Dynamics and Control. 1993;3(3):261–280. doi: 10.1007/bf01972699
  48. de Luca A, Siciliano B. Regulation of flexible arms under gravity. IEEE Transactions on Robotics and Automation. 1993;9(4):463–467. doi: 10.1109/70.246057
  49. Tso SK, Yang TW, Xu WL, Sun ZQ. Vibration control for a flexible-link robot arm with deflection feedback. International Journal of Non-Linear Mechanics. 2003;38(1):51–62. doi: 10.1016/s0020-7462(01)00040-3
  50. Monje CA, Ramos F, Vinagre BM, Feliu V. Tip position control of a lightweight flexible manipulator using a fractional order controller. IET Control Theory & Applications. 2007;1(5):1451–1460. doi: 10.1049/iet-cta:20060477
  51. Pereira E, Moheimani SOR, Aphale SS. Analog implementation of an integral resonant control scheme. Smart Materials and Structures. 2008;17(6):067001. doi: 10.1088/0964-1726/17/6/067001
  52. Chaoui H, Sicard P, Gueaieb W. ANN-Based Adaptive Control of Robotic Manipulators With Friction and Joint Elasticity. IEEE Transactions on Industrial Electronics. 2009;56(8):3174–3187. doi: 10.1109/tie.2009.2024657
  53. Korayem MH, Haghighi R, Korayem AH, Nikoobin A, Alamdari A. Determining maximum load carrying capacity of planar flexible-link robot: closed-loop approach. Robotica. 2010;28(7):959–973. doi: 10.1017/s0263574709990798
  54. Mamani G, Silva JMAD, Feliu-Batlle V. Least squares state estimator based sliding mode control of a very lightweight single-link flexible robot arm. 2009 IEEE International Conference on Mechatronics. 2009. doi: 10.1109/ICMECH.2009.4957205
  55. Liu G, Zhen WD, Du T, Yang J. Adaptive Control of Robotic Dynamic Systems Based on Fuzzy Basis Function Networks. 2010 International Conference on Artificial Intelligence and Computational Intelligence. 2010;2:263–269. doi: 10.1109/AICI.2010.177
  56. Díaz IM, Pereira E, Feliu V, Cela JJL. Concurrent Design of Multimode Input Shapers and Link Dynamics for Flexible Manipulators. IEEE/ASME Transactions on Mechatronics. 2010;15(4):646–651. doi: 10.1109/tmech.2009.2031434
  57. Takahashi K, Sasaki M. Remarks on tip angular position control of single-link flexible robot arm using modified Lyapunov function. 2010 IEEE International Conference on Mechatronics and Automation. 2010;p. 1024–1033. doi: 10.1109/ICMA.2010.5588105
  58. Macchelli A, Melchiorri C. A formal method for improving the transient behaviour of a non-linear flexible link. Mathematical and Computer Modelling of Dynamical Systems. 2011;17(1):3–18. doi: 10.1080/13873954.2010.537508
  59. Bossi L, Rottenbacher C, Mimmi G, Magni L. Multivariable predictive control for vibrating structures: An application. Control Engineering Practice. 2011;19(10):1087–1098. doi: 10.1016/j.conengprac.2011.05.003
  60. Kulakov F, Alferov GV, Efimova P, Chernakova S, Shymanchuk D. Modeling and control of robot manipulators with the constraints at the moving objects. 2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP). 2015;p. 102–105. doi: 10.1109/SCP.2015.7342075
  61. Zebin T, Alam MS. Dynamic modeling and fuzzy logic control of a two-link flexible manipulator using genetic optimization techniques. 2010 13th International Conference on Computer and Information Technology (ICCIT). 2010;p. 418–441. doi: 10.1109/ICCITECHN.2010.5723894
  62. Yin H, Kobayashi Y, Hoshino Y, Emaru T. Decomposed Dynamic Control for Flexible Manipulator in Consideration of Nonlinearity -Flexible Dynamic Control-. Journal of System Design and Dynamics. 2011;5(2):219–230. doi: 10.1299/jsdd.5.219
  63. Abe A, Komuro K. An energy saving open-loop control technique for flexible manipulators. 2011 IEEE International Conference on Mechatronics and Automation. 2011;p. 416–421. doi: 10.1109/ICMA.2011.5985694
  64. Loudini M. Modelling and Intelligent Control of an Elastic Link Robot Manipulator. International Journal of Advanced Robotic Systems. 2013;10(1):81. doi: 10.5772/51102
  65. Biglari H, Golmohammadi M, Hayati S, Hemmati S. Vibration reduction of a flexible robot link using a frictional damper. Journal of Vibration and Control. 2021;27(9-10):985–997. doi: 10.1177/1077546320936092
  66. Wasfy TM, Noor AK. Computational strategies for flexible multibody systems. Applied Mechanics Reviews. 2003;56(6):553–613. doi: 10.1115/1.1590354
  67. Bajodah AH, Hodges DH. Canonical Kane’s Equations of Motion for Discrete Dynamical Systems. AIAA Journal. 2019;57(10):4226–4240. doi: 10.2514/1.j057603
  68. Xu Y, Teng Z, Yao J, Zhou Y, Zhao Y. Elastodynamic analysis of a novel motion-decoupling forging manipulator. Mechanism and Machine Theory. 2020;147:103771. doi: 10.1016/j.mechmachtheory.2019.103771
  69. Vlase S, Negrean I, Marin M, Năstac S. Kane’s Method-Based Simulation and Modeling Robots with Elastic Elements, Using Finite Element Method. Mathematics. 2020;8(5):805. doi: 10.3390/math8050805
  70. Zhang Z, Wang T, Shabana AA. Development and implementation of geometrically accurate reduced-order models: Convergence properties of planar beams. Journal of Sound and Vibration. 2019;439:457–478. doi: 10.1016/j.jsv.2018.06.005
  71. Ghorbani H, Tarvirdizadeh B, Alipour K, Hadi A. Near-time-optimal motion control for flexible-link systems using absolute nodal coordinates formulation. Mechanism and Machine Theory. 2019;140:686–710. doi: 10.1016/j.mechmachtheory.2019.06.032
  72. Meier C, Popp A, Wall WA. Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff–Love Theory Versus Simo–Reissner Theory. Archives of Computational Methods in Engineering. 2019;26(1):163–243.
  73. Chhang S, Sansour C, Hjiaj M, Battini JM. An energy-momentum co-rotational formulation for nonlinear dynamics of planar beams. Computers & Structures. 2017;187:50–63. doi: 10.1016/j.compstruc.2017.03.021
  74. Gaonkar AK, Kulkarni SS. Model order reduction for dynamic simulation of slender beams undergoing large rotations. Computational Mechanics. 2017;59(5):809–829. doi: 10.1007/s00466-017-1374-7
  75. Warminski J, Kloda L, Latalski J, Mitura A, Kowalczuk M. Nonlinear vibrations and time delay control of an extensible slowly rotating beam. Nonlinear Dynamics. 2021;103(4):3255–3281. doi: 10.1007/s11071-020-06079-3
  76. Kloda L, Lenci S, Warminski J. Hardening vs. softening dichotomy of a hinged-simply supported beam with one end axial linear spring: Experimental and numerical studies. International Journal of Mechanical Sciences. 2020;178:105588. doi: 10.1016/j.ijmecsci.2020.105588
  77. Guillot V, Givois A, Colin M, Thomas O, Ture Savadkoohi A, Lamarque CH. Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches. Journal of Vibration and Control. 2020;26(13-14):1119–1132. doi: 10.1177/1077546320910536
  78. Abdeljawad T, Mahariq I, Kavyanpoor M, Ghalandari M, Nabipour N. Identification of nonlinear normal modes for a highly flexible beam. Alexandria Engineering Journal. 2020;59(4):2419–2427. doi: 10.1016/j.aej.2020.03.004
  79. Acar GD, Feeny BF. Bend‐bend‐twist vibrations of a wind turbine blade. Wind Energy. 2018;21(1):15–28. doi: 10.1002/we.2141
  80. Banerjee AK, Lemak ME. Multi-flexible body dynamics capturing motion-induced stiffness. Journal of Applied Mechanics. 1991;58(3):766–75.
  81. Meghdari G. Dynamics of flexible manipulators. Journal of Engineering, Islamic Republic of Iran. 1994;7:19–32.
  82. Theodore RJ, Ghosal A. Comparison of the Assumed Modes and Finite Element Models for Flexible Multilink Manipulators. The International Journal of Robotics Research. 1995;14(2):91–111. doi: 10.1177/027836499501400201
  83. Zimmert N, Pertsch A, Sawodny O. 2-DOF Control of a Fire-Rescue Turntable Ladder. IEEE Transactions on Control Systems Technology. 2012;20(2):438–452. doi: 10.1109/tcst.2011.2116021
  84. Wang FY, Gao Y. On Frequency Sensitivity and Mode Orthogonality of Flexible Robotic Manipulators. IEEE/CAA Journal of Automatica Sinica. 2016;3(4):394–397.
  85. Oetinger D, Knierim KL, Sawodny O. Parameter identification and controller design for high-rack feeder systems and fork lifts. 2016 IEEE International Conference on Automation Science and Engineering (CASE). 2016;p. 509–523.
  86. Mishra N, Singh SP. Dynamic Analysis of Two-Link Flexible Manipulator Using Fem Undergoing Bending-Torsional Vibrations. ACTA TECHNICA NAPOCENSIS - Series: APPLIED MATHEMATICS, MECHANICS, and ENGINEERING. 2019;62(3):431–479. Available from: https://atna-mam.utcluj.ro/index.php/Acta/article/view/1223
  87. Coleman MP, Vibration, Of, Single-Link Flexible Manipulator. Journal of Sound and Vibration. 1998;212(1):109–129.
  88. Halevi Y. Control of Flexible Structures Governed by the Wave Equation Using Infinite Dimensional Transfer Functions. Journal of Dynamic Systems, Measurement, and Control. 2005;127(4):579–588. doi: 10.1115/1.2098895
  89. Connor O, WJ. Wave-like modelling of cascaded, lumped, flexible systems with an arbitrarily moving boundary. Journal of Sound and Vibration. 2011;330(13):3070–83.
  90. O’connor WJ, Habibi H. Wave-based control of under-actuated flexible structures with strong external disturbing forces. International Journal of Control. 2015;88(9):1818–1847.
  91. Mayo J, Dominguez J, Shabana AA. Geometrically Nonlinear Formulations of Beams in Flexible Multibody Dynamics. Journal of Vibration and Acoustics. 1995;117(4):501–509. doi: 10.1115/1.2874490
  92. Chen T, Shan J. Distributed Control of Multiple Flexible Manipulators With Unknown Disturbances and Dead-Zone Input. IEEE Transactions on Industrial Electronics. 2020;67(11):9937–9947. doi: 10.1109/tie.2019.2955417
  93. Najafi M, Dehgolan FR. Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint. Aerospace, Industrial, Mechatronic and Manufacturing Engineering. 2017;11(4):780–789.
  94. Mohan A. 2006.
  95. Scaglioni B, Bascetta L, Baur M, Ferretti G. Closed-form control oriented model of highly flexible manipulators. Applied Mathematical Modelling. 2017;52:174–185. doi: 10.1016/j.apm.2017.07.034
  96. Mohan A, Saha SK. A recursive, numerically stable, and efficient simulation algorithm for serial robots. Multibody System Dynamics. 2007;17(4):291–319. doi: 10.1007/s11044-007-9044-8
  97. Saha SK, Shah SV, Nandihal PV. Evolution of the DeNOC-based dynamic modelling for multibody systems. Mechanical Sciences. 2013;4(1):1–20. doi: 10.5194/ms-4-1-2013
  98. Jia S, Jia Y, Xu S, Hu Q. Maneuver and Active Vibration Suppression of Free-flying Space Robot. IEEE Transactions on Aerospace and Electronic Systems. 2017;1(1):1. doi: 10.1109/taes.2017.2775780
  99. Lismonde A, Sonneville V, Brüls O. A geometric optimization method for the trajectory planning of flexible manipulators. Multibody System Dynamics. 2019;47(4):347–362. doi: 10.1007/s11044-019-09695-z
  100. Bian Y, Gao Z, Lv X, Fan M. Theoretical and experimental study on vibration control of flexible manipulator based on internal resonance. Journal of Vibration and Control. 2018;24(15):3321–3337. doi: 10.1177/1077546317704792
  101. Rahmani B, Belkheiri M. Adaptive neural network output feedback control for flexible multi-link robotic manipulators. International Journal of Control. 2019;92(10):2324–2338. doi: 10.1080/00207179.2018.1436774
  102. Chen B, Huang J. Decreasing infinite-mode vibrations in single-link flexible manipulators by a continuous function. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering. 2017;231(6):436–446. doi: 10.1177/0959651817708489
  103. Lochan K, Roy BK, 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
  104. Wang Y, Cao Y, Xia H. Optimized continuous nonsingular terminal sliding mode control of uncertain flexible manipulators. 34th Chinese Control Conference. 2015;p. 3392–3397.
  105. Yang HJ, Tan M. Sliding Mode Control for Flexible-link Manipulators Based on Adaptive Neural Networks. International Journal of Automation and Computing. 2018;15(2):239–248. doi: 10.1007/s11633-018-1122-2
  106. Aghababa MP, Saif M. 2021. Available from: https://doi.org/10.1177/09596518211014328
  107. Zhang C, Yang T, Sun N, Fang Y. An Adaptive Fuzzy Control Method of Single-Link Flexible Manipulators with Input Dead-Zones. International Journal of Fuzzy Systems. 2020;22(8):2521–2533. doi: 10.1007/s40815-020-00962-2
  108. Bastos G. A stable reentry trajectory for flexible manipulators. International Journal of Control. 2019;0(0):1–12. Available from: https://doi.org/10.1080/00207179.2019.1644538
  109. Ettefagh MH, Naraghi M, Towhidkhah F. Position Control of a Flexible Joint via Explicit Model Predictive Control: An Experimental Implementation. Emerging Science Journal. 2019;3(3):146–156. doi: 10.28991/esj-2019-01177
  110. O’Connor WJ, Ramos de la Flor F, McKeown DJ, Feliu V. Wave-based control of non-linear flexible mechanical systems. Nonlinear Dynamics. 2009;57(1-2):113–123. doi: 10.1007/s11071-008-9425-4
  111. Obe OO. Genetic Algorithm Based Optimal Trajectories Planning for Robot Manipulators on Assigned Paths. International Journal of Emerging Trends in Engineering Research. 2020;8(8):4888–93.
  112. Sangdani MH, Tavakolpour-Saleh AR, Lotfavar A. Genetic algorithm-based optimal computed torque control of a vision-based tracker robot: Simulation and experiment. Engineering Applications of Artificial Intelligence. 2018;67:24–38. doi: 10.1016/j.engappai.2017.09.014
  113. Wu D, Zhang W, Qin M, Xie B. Interval Search Genetic Algorithm Based on Trajectory to Solve Inverse Kinematics of Redundant Manipulators and Its Application. 2020 IEEE International Conference on Robotics and Automation (ICRA). 2020;p. 7088–94.
  114. Yang C, Xu Y, Zhou L, Sun Y. Model-Free Composite Control of Flexible Manipulators Based on Adaptive Dynamic Programming. Complexity. 2018;2018:1–9. doi: 10.1155/2018/9720309
  115. Kiang CT, Spowage A, Yoong CK. Review of Control and Sensor System of Flexible Manipulator. Journal of Intelligent & Robotic Systems. 2015;77(1):187–213. doi: 10.1007/s10846-014-0071-4
  116. Riekert Z, Helbig M. Solving Inverse Kinematics with Vector Evaluated Particle Swarm Optimization. Lecture Notes in Computer Science. 2017;p. 225–237.
  117. Shah P, Agashe S. Design of Controller for a Higher Order System Without Using Model Reduction Methods. Progress in Fractional Differentiation and Applications. 2017;3:289–304. doi: 10.18576/pfda/030405
  118. Khan MU, Kara T. Adaptive Control of a Two-Link Flexible Manipulator Using a Type-2 Neural Fuzzy System. Arabian Journal for Science and Engineering. 2020;45(3):1949–1960. doi: 10.1007/s13369-020-04341-9
  119. Kalyoncu M, Botsalı FM. Lateral and Torsional Vibration Analysis of Elastic Robot Manipulators With Prismatic Joint. Engineering Technology Conference on Energy, Parts A and B. 2002;p. 949–56.
  120. Chen B, Huang J, Ji JC. Control of flexible single-link manipulators having Duffing oscillator dynamics. Mechanical Systems and Signal Processing. 2019;121:44–57. doi: 10.1016/j.ymssp.2018.11.014
  121. Chen G, Liu D, Wang Y, Jia Q, Liu X. Contact Force Minimization for Space Flexible Manipulators Based on Effective Mass. Journal of Guidance, Control, and Dynamics. 2019;42(8):1870–1877. doi: 10.2514/1.g003987
  122. Mishra N, Singh SP, Nakra BC. Dynamic modelling of two link flexible manipulator using Lagrangian assumed modes method. Global Journal of Multidisciplinary Studies. 2015;4:93–105.
  123. Hussein MT. A review on vision-based control of flexible manipulators. Advanced Robotics. 2015;29(24):1575–1585. Available from: https://doi.org/10.1080/01691864.2015.1078743
  124. He W, Gao H, Zhou C, Yang C, Li Z. Reinforcement Learning Control of a Flexible Two-Link Manipulator: An Experimental Investigation. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2021;51(12):7326–7336. doi: 10.1109/tsmc.2020.2975232

Copyright

© 2021 Mishra & Singh. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)

DON'T MISS OUT!

Subscribe now for latest articles and news.