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Challenges and New Frontiers in the Field of Underactuated Mechanical Systems Control

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Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems

Abstract

This concluding chapter epitomizes the major work described in this book. Comprehensive analysis on the generalized formulation of a novel block backstepping control law, and detailed description of its applications on ten different underactuated systems have been studied in the last three chapters.

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References

  1. Chatterjee D, Patra A, Joglekar HK (2002) Swing-up and stabilization of a cart pendulum system under restricted cart track length. Syst Control Lett 47(4):355–364

    Article  MathSciNet  MATH  Google Scholar 

  2. Fantoni I, Lozano R (2002) Stabilization of the Furuta pendulum around its homoclinic orbit. Int J Control 75(6):390–398

    Article  MathSciNet  MATH  Google Scholar 

  3. Freidovich L, Shiriaev A, Gordillo F, Gómez-Estern F, Aracil J (2009) Partial-energy shaping control for orbital stabilization of high-frequency oscillations of the Furuta pendulum. IEEE Trans Control Syst Technol 17(4):853–858

    Article  Google Scholar 

  4. Jiang ZP, Hill DJ, Guo Y (1998) Stabilization and tracking via output feedback for the nonlinear benchmark system. Automatica 34(7):907–915

    Article  MathSciNet  MATH  Google Scholar 

  5. Luca AD, Mattone R, Orilo G (1996) Control of underactuated mechanical systems: application to the planar 2R robot. Paper presented at the international conference on decision and control, Kobe, Japan, pp 1455–1460

    Google Scholar 

  6. Notarstefano G, Hauser J, Frezza R (2005) Trajectory manifold exploration for the PVTOL aircraft. Paper presented at IEEE conference on decision and control and European control conference, Seville, Spain, pp 5848–5853

    Google Scholar 

  7. Olfati RS (2001) Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles, Ph.D. thesis, Department of Electrical Engineering and Computer, Massachusetts Institute of Technology

    Google Scholar 

  8. Oriolo G, Nakamura T (1991) Control of mechanical systems with second-order nonholonomic constraints: Underactuated manipulators. Paper presented at the international conference on decision and control, Brighton, UK, pp 2398–2403

    Google Scholar 

  9. Viola G, Ortega R, Banavar R, Acosta JA, Astolfi A (2007) Total energy shaping control of mechanical systems: simplifying the matching equations via coordinate changes. IEEE Trans Autom Control 52(6):1093–1099

    Article  MathSciNet  MATH  Google Scholar 

  10. White WN, Foss M, Guo X (2006) A direct Lyapunov approach for a class of underactuated mechanical systems. Paper presented at the American control conference, Minneapolis, Minnesota, USA 103–110:2006

    Google Scholar 

  11. Wood R, Cazzolato B (2007) An alternative nonlinear control law for the global stabilization of the PVTOL vehicle. IEEE Trans Autom Control 52(7):1282–1287

    Article  MathSciNet  Google Scholar 

  12. Egeland O, Dalsmo M, Sordalen OJ (1996) Feedback control of a nonholonomic underwater vehicle with constant desired configuration. Int J Robot Res 15(1):24–35

    Article  Google Scholar 

  13. Kim Y, Kim SH, Kwak YK (2005) Dynamic analysis of a nonholonomic two-wheeled inverted pendulum robot. J Intell Robot Syst 44(1):25–46

    Article  Google Scholar 

  14. Olfati-Saber R, Megretski A (1998) Controller design for a class of underactuated nonlinear systems. Paper presented at the 37th international conference on decision and control, Tampa, FL, vol 4, pp 4182–4187

    Google Scholar 

  15. Pavlov A, Janssen B, van de Wouw N, Nijmeijer H (2007) Experimental output regulation for a nonlinear benchmark system. IEEE Trans Control Syst Technol 15(4):786–793

    Article  Google Scholar 

  16. Shiriaev AS, Freidovich LB, Robertsson A, Johansson R, Sandberg A (2007) Virtual holonomic-constraints-based design of stable oscillations of Furuta pendulum: theory and experiments. IEEE Trans Robot 23(4):827–832

    Article  Google Scholar 

  17. Spong MW (1994) Partial feedback linearization of underactuated mechanical systems. Paper presented at IEEE/RSJ/GI international conference on intelligent robots and systems, Munich, Germany, pp 314–321

    Google Scholar 

  18. Spong M (1995) The swing-up control problem for the Acrobot. IEEE Control Syst Mag 47(1):49–55

    Article  Google Scholar 

  19. Spong MW (1996) Energy based control of a class of underactuated mechanical systems. Paper presented at the IFAC world congress, San Francisco, CA, USA, pp 431–435

    Google Scholar 

  20. Spong M, Praly L (1996) Control of underactuated mechanical systems using switching and saturation. In Morse AS (ed) Paper presented on control using logic-based switching (Lecture Notes no. 222). Springer, Berlin, pp 162–172

    Google Scholar 

  21. Wang WJ, Lin HR (1999) Fuzzy control design for the trajectory tracking on uncertain nonlinear systems. IEEE Trans Fuzzy Syst 7(1):53–62

    Article  Google Scholar 

  22. Albahkali T, Mukherjee R, Das T (2009) Swing-up control of the pendubot: an impulse momentum approach. IEEE Trans Robot 25(4):975–982

    Article  Google Scholar 

  23. Al-Hiddabi SA, McClamroch NH (2002) Tracking and maneuver regulation control for nonlinear non-minimum phase systems: application to flight control. IEEE Trans Control Syst Technol 10(6):780–792

    Article  Google Scholar 

  24. Jankovic M, Fontaine D, Kokotovic PV (1996) TORA example: cascade and passivity based control designs. IEEE Trans Control Syst Technol 4(3):292–297

    Article  Google Scholar 

  25. Pathak K, Franch J, Agrawal SK (2005) Velocity and position control of a wheeled inverted pendulum by partial feedback linearization. IEEE Trans Robot 21(3):505–513

    Article  Google Scholar 

  26. Liu Y, Yu H (2013) A survey of underactuated mechanical systems. IET Control Theory Appl 7(7):921–935

    Article  MathSciNet  Google Scholar 

  27. Abdessameuda A, Tayebi A (2010) Global trajectory tracking control of VTOL-UAVs without linear velocity measurements. Automatica 46(6):1053–1059

    Article  MathSciNet  MATH  Google Scholar 

  28. Aguiar AP, Hespanha JP (2003) Position tracking of underactuated vehicles. Paper presented at American control conference, Denver, Co, 3, 1988–1993

    Google Scholar 

  29. Avis JM, Nersesov SG, Nathan R, Ashrafiuon H, Muske KR (2010) A comparison study of nonlinear control techniques for the RTAC system. Nonlinear Anal Real World Appl 11(4):2647–2658

    Article  MathSciNet  MATH  Google Scholar 

  30. Bi FY, Wei YJ, Zhang JZ, Cao W (2010) Position-tracking control of underactuated autonomous underwater vehicles in the presence of unknown ocean currents. IET Control Theory Appl 4(11):2369–2380

    Article  MathSciNet  Google Scholar 

  31. Chang DE (2010) Stabilizability of controlled Lagrangian systems of two degrees of freedom and one degree of under-actuation by the energy-shaping method. IEEE Trans Autom Control 55(8):1888–1893

    Article  MathSciNet  Google Scholar 

  32. Consolini L, Maggiore M, Nielsen C, Tosques M (2010) Path following for the PVTOL aircraft. Automatica 46(8):1284–1296

    Article  MathSciNet  MATH  Google Scholar 

  33. Consolini L, Tosques M (2007) On the VTOL exact tracking with bounded internal dynamics via a Poincar´e map approach. IEEE Trans Autom Control 52(9):1757–1762

    Article  MathSciNet  Google Scholar 

  34. De Luca RMA, Iannitti S, Oriolo G (2001) Control problems in underactuated manipulators. Paper presented at IEEE/ASME international conference on advanced intelligent mechatronics, Como, Italy, pp 8–12

    Google Scholar 

  35. Do KD, Jiang ZP, Pan J (2002) Underactuated ship global tracking under relaxed conditions. IEEE Trans Autom Control 47(9):1529–1536

    Article  MathSciNet  Google Scholar 

  36. Do KD, Jiang ZP, Pan J (2003) On global tracking control of a VTOL aircraft without velocity measurements. IEEE Trans Autom Control 48(12):2212–2217

    Article  MathSciNet  Google Scholar 

  37. Dong W, Farrell JA (2008) Formation control of multiple underactuated surface vessels. IET Control Theory Appl 2(2):1077–1085

    Article  MathSciNet  Google Scholar 

  38. Fahimi F (2007) Sliding-mode formation control for underactuated surface vessels. IEEE Trans Robot 23(3):617–622

    Article  Google Scholar 

  39. Fantoni I, Lozano R, Spong MW (2000) Energy based control of the Pendubot. IEEE Trans Autom Control 45(4):725–729

    Article  MathSciNet  MATH  Google Scholar 

  40. Fantoni I, Lozano R (2001) Nonlinear control for underactuated mechanical systems. Springer-Verlag, London

    MATH  Google Scholar 

  41. Gao A, Zhang X, Chen H, Zhao J (2009) Energy-based control design of an underactuated 2-dimensional TORA system. Paper presented at the IEEE/RSJ international conference on intelligent robots and systems, St. Louis, USA, pp 1296–1301

    Google Scholar 

  42. Ghommam J, Mnif F, Derbel N (2010) Global stabilisation and tracking control of underactuated surface vessels. IET Control Theory Appl 4(1):71–88

    Article  MathSciNet  Google Scholar 

  43. Gruszka A, Malisoff, M, Mazenc F (2011) On tracking for the PVTOL model with bounded feedbacks. Paper presented at American control conference, San Francisco, CA, USA, pp 1428–1433

    Google Scholar 

  44. Jafari R, Mathis FB, Mukherjee R (2011) Swing-up control of the acrobot: an impulse momentum approach. Paper presented at American control conference, San Francisco, CA, USA, pp 262–267

    Google Scholar 

  45. Jiang ZP, Kanellakopoulos I (2000) Global output-feedback tracking for a benchmark nonlinear system. IEEE Trans Autom Control 45(5):1023–1027

    Article  MathSciNet  MATH  Google Scholar 

  46. Lai XZ, She JH, Yang SX, Wu M (2009) Comprehensive unified control strategy for underactuated two-link manipulators. IEEE Trans Syst Man Cybern B 39(2):389–398

    Google Scholar 

  47. Lopez-Martinez M, Acosta JA, Cano JM (2010) Non-linear sliding mode surfaces for a class of underactuated mechanical systems. IET Control Theory Appl 4(10):2195–2204

    Google Scholar 

  48. Lozano R, Castillo P, Dzul A (2004) Global stabilization of the PVTOL: real-time application to a mini-aircraft. Int J Control 77(8):735–740

    Google Scholar 

  49. Yu R, Zhu Q, Xia G, Liu Z (2012) Sliding mode tracking control of an underactuated surface vessel. IET Control Theory Appl 6(3):461–466

    Article  MathSciNet  Google Scholar 

  50. Marconi L, Isidori A, Serrani A (2002) Autonomous vertical landing on an oscillating platform: an internal-model based approach. Automatica 38(1):21–32

    Article  MathSciNet  MATH  Google Scholar 

  51. Martin P, Devasia S, Paden B (1996) A different look at output tracking: control of a VTOL aircraft. Automatica 32(1):101–107

    Article  MATH  Google Scholar 

  52. McNich LC, Ashrafiuon H, Muske KR (2010) Sliding mode set-point control of an underactuated surface vessel: simulation and experiment. Paper presented at American control conference, Baltimore, MD, USA, pp 5212–5217

    Google Scholar 

  53. Mori S, Nishiharaa H, Furuta K (1976) Control of unstable mechanical system Control of pendulum. Int J Control 23(5):673–692

    Article  Google Scholar 

  54. Nair S, Leonard NE (2002) A normal form for energy shaping: application to the Furuta pendulum. Paper presented at the 41th international conference on decision and control, vol 1, pp 516–521

    Google Scholar 

  55. Ortega R , Spong MW, G´omez-Estern F, Blankenstein G (2002) Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment, IEEE Trans Autom Control (47)8:1218–1232

    Google Scholar 

  56. Rudra S, Barai RK, Maitra M (2014) Nonlinear state feedback controller design for underactuated mechanical system: a modified block backstepping approach. ISA Trans 53(2):317–326

    Article  Google Scholar 

  57. Van der Schaft J (1999) L2-Gain and passivity in nonlinear control. Springer-Verlag, New York

    Google Scholar 

  58. Setlur P, Dawson D, Fang Y, Costic B (2001) Nonlinear tracking control of the VTOL aircraft. Paper presented at the international conference on decision and control, Orlando, USA, pp 4592–4597

    Google Scholar 

  59. Spong MW (1998) Underactuated mechanical systems, control problems in robotics and automation, vol 230. Springer-Verlag, Berlin, pp 135–150

    Google Scholar 

  60. Wan J, Bernstein DS, Coppola VT (1994) Global stabilization of the oscillating eccentric rotor. Paper presented at the international conference on decision and control, Orlando, USA, pp 4024–4029

    Google Scholar 

  61. Wang W, Yi J, Zhao D, Liu D (2004) Design of a stable sliding mode controller for a class of second-order underactuated systems. IEEE Proc Control Theory April 151(6):683–690

    Google Scholar 

  62. Ye H, Wang H (2007) Stabilization of a PVTOL aircraft and an inertia wheel pendulum using saturation technique. IEEE Trans Control Syst Technol 15(6):1143–1150

    Article  MathSciNet  Google Scholar 

  63. Zavala-Rio A, Fantoni I, Lozano R (2003) Global stabilization of a PVTOL aircraft model with bounded inputs. Int J Control 76(18):1833–1844

    Article  MathSciNet  MATH  Google Scholar 

  64. Zhixiang T, Hongtao W, Chun F (2010) Hierarchical adaptive backstepping sliding mode control for under actuated space robot. In: International conference on informatics in control, automation and robotics, pp 500–503

    Google Scholar 

  65. Zhang M, Tarn T (2002) Hybrid control of the Pendubot. IEEE/ASME Trans Mechatronics 7(1):79–86

    Article  Google Scholar 

  66. Zhao J, Spong MW (2001) Hybrid control for global stabilization of the cart-pendulum system. Automatica 37(12):1941–1951

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Shubhobrata Rudra .

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Rudra, S., Barai, R.K., Maitra, M. (2017). Challenges and New Frontiers in the Field of Underactuated Mechanical Systems Control. In: Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems. Springer, Singapore. https://doi.org/10.1007/978-981-10-1956-2_6

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  • DOI: https://doi.org/10.1007/978-981-10-1956-2_6

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