Skip to main content
SpringerLink
Log in

Decentralized adaptive partitioned approximation control of high degrees-of-freedom robotic manipulators considering three actuator control modes

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

Partitioned approximation control is avoided in most decentralized control algorithms; however, it is essential to design a feedforward control term for improving the tracking accuracy of the desired references. In addition, consideration of actuator dynamics is important for a robot with high-velocity movement and highly varying loads. As a result, this work is focused on decentralized adaptive partitioned approximation control for complex robotic systems using the orthogonal basis functions as strong approximators. In essence, the partitioned approximation technique is intrinsically decentralized with some modifications. Three actuator control modes are considered in this study: (i) a torque control mode in which the armature current is well controlled by a current servo amplifier and the motor torque/current constant is known, (ii) a current control mode in which the torque/current constant is unknown, and (iii) a voltage control mode with no current servo control being available. The proposed decentralized control law consists of three terms: the partitioned approximation-based feedforward term that is necessary for precise tracking, the high gain-based feedback term, and the adaptive sliding gain-based term for compensation of modeling error. The passivity property is essential to prove the stability of local stability of the individual subsystem with guaranteed global stability. Two case studies are used to prove the validity of the proposed controller: a two-link manipulator and a six-link biped robot.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Notes

  1. ZMP can be defined as the ground reaction force wrench due to the foot–ground contact with zero horizontal moments. The ZMP location coincides with the location of the center of pressure for the balance walking; however, this is not the case for unbalanced walking. See [51,52,53,54,55,56,57,58,59,60,61] and the references therein for more details.

References

  1. Luh JYS, Walker MW, Paul RPC (1980) On-line computational scheme for mechanical manipulator. Trans ASME J Dyn Syst Meas Control 102:69–76

    Article  MathSciNet  Google Scholar 

  2. Hollerbach JM (1980) A recursive Lagrangian formulation of manipulator dynamics and comparative study of dynamics formulation complexity. IEEE Trans Syst Man Cybern SMC-10(11):730–736

    Article  MathSciNet  Google Scholar 

  3. Walker M, Orin DE (1982) Efficient dynamic computer simulation of robotic mechanisms. Trans ASME J Dyn Syst Meas Control 104:205–211

    Article  MATH  Google Scholar 

  4. Balafoutis CA, Patel RV (1989) Efficient computation of manipulator, inertia matrices and the direct dynamics problem. IEEE Trans Syst Man Cybern 19:1313–1321

    Article  Google Scholar 

  5. Angeles J, Ma O, Rojas A (1998) An algorithm for the inverse dynamics of n-axis general manipulator using Kane’s formulation of dynamical equations. Comput Math Appl 17(12):1545–1561

    Article  MATH  Google Scholar 

  6. Saha SK (1999) Dynamics of serial multibody systems using the decoupled natural orthogonal complement matrices. ASME J Appl Mech 66:986–996

    Article  Google Scholar 

  7. Featherstone R (1983) The calculation of robot dynamics using articulated-body inertias. Int J Robot Res 2(1):13–30

    Article  Google Scholar 

  8. Brandle H, Johanni R, Otter M (1986) A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass matrix. In: Proceeding of the IFAC/IFIP/IMACS international symposium on theory of robots, Vienna, pp 95–100

  9. Mohan A, Saha SK (2007) A recursive numerically stable and efficient simulation algorithm for serial robots. Int J Multibody Syst Dyn 17(4):291–319

    Article  MathSciNet  MATH  Google Scholar 

  10. Lee K, Chirikjian GS (2005) A new perspective on O (n) mass-matrix inversion for serial revolute manipulators. In: Proceeding of the IEEE international conference on robotics and automation, Barcelona, pp 4722–4726

  11. Featherstone R, Orin D (2000) Robot dynamics: equations and algorithms. In: IEEE international conference on robotics and automation, ICRA 1, pp 826–834

  12. Saha SK (2007) Recursive dynamics algorithms for serial, parallel and closed-chain multibody systems. In: Indo-US workshop on protein kinematics and protein conformations. IISC, Bangalore

  13. Fu KS, Gonzalez RC, Lee CSG (1987) Robotics: control, sensing, vision, and intelligence. McGraw-Hill, New York

    Google Scholar 

  14. Sandell NR, Varaiya P, Athans M, Safonov MG (1978) Survey of decentralized control methods for large scale systems. IEEE Trans Autom Control AC-23(2):108–128

    Article  MathSciNet  MATH  Google Scholar 

  15. Spong MW, Vidyasagar M (1989) Robot dynamics and control. Wiley, New York

    Google Scholar 

  16. Boha J, Belda K, Valasue M (2002) Decentralized control of redundant parallel robot construction. In; Proceeding of the 10th mediterranean conference on control and automation, Libson, pp 9–1

  17. Ohri J, Dewan L, Soni MK (2007) Tracking control of robots using decentralized robust PID control for friction and uncertainty compensation. In: Proceedings of the world congress on engineering and computer science, San Francisco

  18. Xu K (2010) Integrating centralized and decentralized approaches for multi-robot coordination. Dissertation, Mechanical and Aerospace Engineering, New Brunswick

  19. Leena G, Ray G (2012) A set of decentralized PID controller for an n-link robot manipulator. Indian Acad Sci 37:405–423

    MATH  Google Scholar 

  20. Liu M (1999) Decentralized control of robot manipulators: nonlinear and adaptive approaches. IEEE Trans Autom Control 44(2):357–363

    Article  MathSciNet  MATH  Google Scholar 

  21. Yang Z-J, Fukushima Y, Qin P (2012) Decentralized adaptive robust control of robot manipulators using disturbance observers. IEEE Trans Control Syst Technol 20(5):1357–1365

    Article  Google Scholar 

  22. Jasim IF, Plapper PW (2014) Enhanced decentralized robust adaptive control of robots with arbitrarily-switched unknown constraints. In: IEEE international conference on systems, man, and cybernetics, October 5–8, San Diego, pp 4027–4032

  23. Lewis FL, Yesildirek A, Liu K (1995) Neural net robot controller: structure and stability proofs. J Intell Robot Syst 13:1–23

    Article  Google Scholar 

  24. Lewis FL, Liu K, Yesildirek A (1995) Neural net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw 6(3):703–716

    Article  Google Scholar 

  25. Lewis FL, Yesildirek A, Liu K (1996) Multilayer neural net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw 7(2):1–12

    Article  Google Scholar 

  26. Liu J (2013) Radial basis function (RBF) neural network control for mechanical systems: design, analysis and Matlab simulation. Tsinghua University Press, Springer, Beijing, Berlin

    Book  MATH  Google Scholar 

  27. Al-Shuka HFN, Song R (2017) Adaptive hybrid regressor and approximation control of robotic manipulators in constrained space. Int J Mech Mechatron Eng IJMME-IJENS 17(3):11–21

    Google Scholar 

  28. Al-Shuka HFN, Song R (2018) Hybrid regressor and approximation-based adaptive control of robotic manipulators with contact-free motion. In: The 2nd IEEE advanced information management, communicates, electronic and automation control conference (IMCEC 2018), Beijing, pp 325–329

  29. Al-Shuka HFN, Song R (2018) Hybrid regressor and approximation-based adaptive control of piezoelectric flexible beams. In: The 2nd IEEE advanced information management, communicates, electronic and automation control conference (IMCEC 2018), Beijing, pp 330–334

  30. Huang A-C, Chien M-C (2010) Adaptive control of robot manipulators: a unified regressor-free approach. World Scientific, Singapore

    Book  MATH  Google Scholar 

  31. Ge SS, Lee TH, Harris CJ (1998) Adaptive neural network control of robotic manipulators. World Scientific, River Edge

    Book  Google Scholar 

  32. Al-Shuka HFN (2018) On local approximation-based adaptive control with applications to robotic manipulators and biped robots. Int J Dyn Control 6(1):339–353

    Article  MathSciNet  Google Scholar 

  33. Al-Shuka HFN, Song R (2019) Decentralized adaptive partitioned approximation control of robotic manipulators. In: Arakelian V, Wenger P (eds) ROMANSY 22—robot design, dynamics and control. CISM international centre for mechanical sciences (courses and lectures), vol 584. Springer, Cham

    Google Scholar 

  34. Panagi P, Polycarpou MM (2008) Decentralized adaptive approximation based control of a class of large-scale systems. In: American control conference westin seattle hotel, Seattle, pp 4191–4196

  35. Tan KK, Huang S, Lee TH (2009) Decentralized adaptive controller design of large-scale uncertain robotic systems. Automatica 45(1):161–166

    Article  MathSciNet  MATH  Google Scholar 

  36. Fateh MM, Fateh S (2012) Decentralized direct adaptive fuzzy control of robots using voltage control strategy. Nonlinear Dyn 70:1919–1930

    Article  MathSciNet  MATH  Google Scholar 

  37. Li T, Li R, Li J (2011) Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation. Neurocomputing 74:2277–2283

    Article  Google Scholar 

  38. Kim YT (2010) Decentralized adaptive fuzzy backstepping control of rigid-link electrically driven robots. Intell Autom Soft Comput 16(2):135–149

    Article  Google Scholar 

  39. Zhu L, Li Y (2010) Decentralized adaptive neural network control for reconfigurable manipulators. In: Chinese control and decision conference, pp 1760–1765

  40. Zhou Q, Li H, Shi P (2015) Decentralized adaptive fuzzy tracking control for robot finger dynamics. IEEE Trans Fuzzy Syst 23(3):501–510

    Article  Google Scholar 

  41. Zhu W-H (2010) Virtual decomposition control, toward hyper degrees of freedom robots. Springer, Berlin

    Book  MATH  Google Scholar 

  42. Kelly R, Santibáñez V, Loría A (2005) Control of robot manipulators in joint space. Springer, London

    Google Scholar 

  43. Vázquez LA, Jurado F, Alanís AY (2015) Decentralized identification and control in real-time of a robot manipulator via recurrent wavelet first-order neural network. Math Probl Eng 2015:12. https://doi.org/10.1155/2015/451049

    Article  MathSciNet  MATH  Google Scholar 

  44. Burden RL, Faires JD (1989) Numerical analysis, 4th edn. PWS Publishing Co., Boston

    MATH  Google Scholar 

  45. Mulero-Martínez JI (2007) Uniform bounds of the Coriolis/centripetal matrix of serial robot manipulators. IEEE Trans Rob 23(5):1083–1089

    Article  Google Scholar 

  46. Sciavicco L, Siciliano B, Villani L (1996) Lagrange and Newton–Euler dynamic modeling of a gear-driven robot manipulator with inclusion of motor inertia effects. Adv Robot 10(3):317–334

    Article  Google Scholar 

  47. Utkin VI, Poznyak AS (2013) Adaptive sliding mode control. In: Bandyopadhyay B, Janardhanan S, Spurgeon S (eds) Advances in sliding mode control. Lecture notes in control and information sciences, vol 440. Springer, Berlin

    Google Scholar 

  48. Ioannou P, Fidan B (2006) Adaptive control tutorial. SIAM, USA

    Book  MATH  Google Scholar 

  49. Farrell JA, Polycarpou MM (2006) Adaptive approximation based control: unifying neural, fuzzy and traditional adaptive approximation approaches. Wiley, New York

    Book  Google Scholar 

  50. Slotine J-J, Li W (1991) Applied nonlinear control. Pearson, London

    MATH  Google Scholar 

  51. Al-Shuka HFN (2014) Modeling, walking pattern generators and adaptive control of biped robot. PhD Dissertation, RWTH Aachen University, Department of Mechanical Engineering, IGM

  52. Al-Shuka HFN (2017) An overview on balancing and stabilization control of biped robots. GRIN Verlag, Munich. http://www.grin.com/en/e-book/375226/an-overview-on-balancing-and-stabilization-control-of-biped-robots

  53. Al-Shuka HFN, Corves BJ, Zhu W-H, Vanderborght B (2016) Multi-level control of zero moment point-based biped humanoid robots: a review. Robotica 34(11):2440–2466

    Article  Google Scholar 

  54. Al-Shuka HFN, Corves BJ, Vanderborght B, Zhu W-H (2015) Zero-moment point-based biped robot with different walking patterns. Int J Intell Syst Appl 7(1):31–41

    Google Scholar 

  55. Al-Shuka HFN, Corves BJ, Zhu W-H, Vanderborght B (2014) A simple algorithm for generating stable biped walking patterns. Int J Comput Appl 101(4):29–33

    Google Scholar 

  56. Al-Shuka HFN, Corves BJ, Zhu W-H (2014) Dynamic modeling of biped robot using Lagrangian and recursive Newton–Euler formulations. Int J Comput Appl 101(3):1–8

    Google Scholar 

  57. Al-Shuka HFN, Allmendinger F, Corves BJ, Zhu W-H (2014) Modeling, stability and walking pattern generators of biped robots: a review. Robotica 32(6):907–934

    Article  Google Scholar 

  58. Al-Shuka HFN, Corves BJ, Zhu W-H (2014) Function approximation technique-based adaptive virtual decomposition control for a serial-chain manipulator. Robotica 32(3):375–399

    Article  Google Scholar 

  59. Al-Shuka HFN, Corves BJ (2013) On the walking pattern generators of biped robot. J Autom Control 1(2):149–156

    Google Scholar 

  60. Al-Shuka HFN, Corves BJ, Zhu W-H (2013) On the dynamic optimization of biped robot. Lect Notes Softw Eng 1(3):237–243

    Article  Google Scholar 

  61. Al-Shuka HFN, Corves BJ, Vanderborght B, Zhu W-H (2013) Finite difference-based suboptimal trajectory planning of biped robot with continuous dynamic response. Int J Model Optim 3(4):337–343

    Article  Google Scholar 

  62. Vanderborght B (2010) Dynamic Stabilisation of the biped Lucy powered by actuators with controllable stiffness. Springer, Berlin

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, China

    Hayder F. N. Al-Shuka & R. Song

Authors
  1. Hayder F. N. Al-Shuka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hayder F. N. Al-Shuka.

Additional information

This paper is an extended version of the conference paper [33] in which the actuator dynamics were not considered and the focus was on torque control mode only.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Al-Shuka, H.F.N., Song, R. Decentralized adaptive partitioned approximation control of high degrees-of-freedom robotic manipulators considering three actuator control modes. Int. J. Dynam. Control 7, 744–757 (2019). https://doi.org/10.1007/s40435-018-0482-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-018-0482-3

Keywords

Search

Navigation