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ArticleOriginal scientific text

Title

Saturating stiffness control of robot manipulators with bounded inputs

Authors 1, 2, 2, 3

Affiliations

  1. CONACYT—Ensenada Institute of Technology, Boulevard Tecnológico No. 150, Col. Ex Ejido Chapultepec, Ensenada, Baja California, 22780 Mexico
  2. Faculty of Sciences, Autonomous University of San Luis Potosí, Av. Salvador Nava S/N, San Luis Potosí, SLP, 78290 Mexico
  3. Robotics Engineering Department, Autonomous University of Aguascalientes, Prol. Mahatma Gandhi 6601, Aguascalientes, Ags., 20392 Mexico

Abstract

A saturating stiffness control scheme for robot manipulators with bounded torque inputs is proposed. The control law is assumed to be a PD-type controller, and the corresponding Lyapunov stability analysis of the closed-loop equilibrium point is presented. The interaction between the robot manipulator and the environment is modeled as spring-like contact forces. The proper behavior of the closed-loop system is validated using a three degree-of-freedom robotic arm.

Keywords

ENG
POL
bounded inputs, robot manipulator, saturation, stiffness control

Bibliography

  1. Aguiñaga-Ruiz, E., Zavala-Río, A., Santibáñez, V. and Reyes, F. (2009). Global trajectory tracking through static feedback for robot manipulators with bounded inputs, IEEE Transactions on Control Systems Technology 17(4): 934–944.
  2. Akdoğan, E. and Adli, M.A. (2011). The design and control of a therapeutic exercise robot for lower limb rehabilitation: Physiotherabot, Mechatronics 21(3): 509–522.
  3. Belter, D., Łabecki, P., Fankhauser, P. and Siegwart, R. (2016). RGB-D terrain perception and dense mapping for legged robots, International Journal of Applied Mathematics and Computer Science 26(1): 81–97, DOI: 10.1515/amcs-2016-0006.
  4. Canudas, C., Siciliano, B. and Bastin, G. (2012). Theory of Robot Control, Springer-Verlag, London.
  5. Caverly, R.J., Zlotnik, D.E., Bridgeman, L.J. and Forbes, J.R. (2014). Saturated proportional derivative control of flexible-joint manipulators, Robotics and Computer-Integrated Manufacturing 30(6): 658–666.
  6. Caverly, R.J., Zlotnik, D.E. and Forbes, J.R. (2016). Saturated control of flexible-joint manipulators using a Hammerstein strictly positive real compensator, Robotica 34(06): 1367–1382.
  7. Chávez-Olivares, C., Reyes, F. and González-Galván, E. (2015). On stiffness regulators with dissipative injection for robot manipulators, International Journal of Advanced Robotic Systems 12(65): 1–15.
  8. Chávez-Olivares, C., Reyes, F., González-Galván, E., Mendoza, M. and Bonilla, I. (2012). Experimental evaluation of parameter identification schemes on an anthropomorphic direct drive robot, International Journal of Advanced Robotic Systems 9(203): 1–18.
  9. Dario, P., Guglielmelli, E. and Allotta, B. (1994). Robotics in medicine, IEEE/RSJ/GI International Conference on Intelligent Robots and Systems: Advanced Robotic Systems and the Real World, IROS’94, Munich, Germany, Vol. 2, pp. 739–752.
  10. Dehghani, S., Taghirad, H. and Darainy,M. (2010). Self-tunning dynamic impedance control for human arm motion, 7th Iranian Conference of Biomedical Engineering (ICBME), Isfahan, Iran, pp. 1–5.
  11. Deneve, A., Moughamir, S., Afilal, L. and Zaytoon, J. (2008). Control system design of a 3-DOF upper limbs rehabilitation robot, Computer Methods and Programs in Biomedicine 89(2): 202–214.
  12. Djebrani, S., Benali, A. and Abdessemed, F. (2012). Modelling and control of an omnidirectional mobile manipulator, International Journal of Applied Mathematics and Computer Science 22(3): 601–616, DOI: 10.2478/v10006-012-0046-1.
  13. Dulęba, I. and Opałka, M. (2013). A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators, International Journal of Applied Mathematics and Computer Science 23(2): 373–382, DOI: 10.2478/amcs-2013-0028.
  14. Falaki, A. and Towhidkhah, F. (2012). Supervisory model predictive impedance control for human arm movement, 20th Iranian Conference on Electrical Engineering, Tehran, Iran, pp. 1562–1566.
  15. He, W., Dong, Y. and Sun, C. (2016). Adaptive neural impedance control of a robotic manipulator with input saturation, IEEE Transactions on Systems, Man, and Cybernetics: Systems 46(3): 334–344.
  16. Hogan, N. (1985). Impedance control: An approach to manipulation. I: Theory, II: Implementation, III: Applications, ASME Journal of Dynamic Systems, Measurement and Control 107(1): 1–24.
  17. Ju, M.S., Lin, C.C.K., Lin, D.H., Hwang, I.S. and Chen, S.M. (2005). A rehabilitation robot with force-position hybrid fuzzy controller: Hybrid fuzzy control of rehabilitation robot, IEEE Transactions on Neural Systems & Rehabilitation Engineering 13(3): 349–358.
  18. Kelly, R., Santibáñez, V. and Berghuis, H. (1997). Point-to-point robot control under actuator constraints, Control Engineering Practice 5(11): 1555–1562.
  19. Kelly, R., Santibáñez, V. and Loría, A. (2005). Control of Robot Manipulators in Joint Space, Springer-Verlag, London.
  20. Khalil, H. (2002). Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ.
  21. Kiguchi, K., Imada, Y. and Liyanaje, M. (2007). EMG-based neuro-fuzzy control of a 4-DOF upper-limb power-assist exoskeleton, 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Lyon, France, pp. 3040–3043.
  22. Kurfess, T. (2004). Robotics and Automation Handbook, CRC Press, Boca Raton, FL.
  23. Li, Y., Ge, S.S., Yang, C., Li, X. and Tee, K.P. (2011). Model-free impedance control for safe human–robot interaction, 2011 IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, pp. 6021–6026.
  24. López-Araujo, D.J., Zavala-Río, A., Santibáñez, V. and Reyes, F. (2013a). A generalized scheme for the global adaptive regulation of robot manipulators with bounded inputs, Robotica 31(7): 1103–1117.
  25. López-Araujo, D.J., Zavala-Río, A., Santibáñez, V. and Reyes, F. (2013b). Output-feedback adaptive control for the global regulation of robot manipulators with bounded inputs, International Journal of Control, Automation, and Systems 11(1): 105–115.
  26. López-Araujo, D. J., Zavala-Río, A., Santibáñez, V. and Reyes, F. (2015). A generalized global adaptive tracking control scheme for robot manipulators with bounded inputs, International Journal of Adaptive Control and Signal Processing 29(2): 180–200.
  27. Mendoza, M., Bonilla, I., Reyes, F. and González-Galván, E. (2012). A Lyapunov-based design tool of impedance controllers for robot manipulators, Kybernetika 48(6): 1136–1155.
  28. Mendoza, M., Zavala-Río, A., Santibáñez, V. and Reyes, F. (2015a). A generalised PID-type control scheme with simple for the global regulation of robot manipulators with tuning constrained inputs, International Journal of Control 88(10): 1995–2012.
  29. Mendoza, M., Zavala-Río, A., Santibáñez, V. and Reyes, F. (2015b). Output-feedback proportional-integral-derivative-type control with simple tuning for the global regulation of robot manipulators with input constraints, IET Control Theory and Applications 9(14): 2097–2106.
  30. Modares, H., Ranatunga, I., Lewis, F.L. and Popa, D.O. (2016). Optimized assistive human–robot interaction using reinforcement learning, IEEE Transactions on Cybernetics 46(3): 655–667.
  31. Santibáñez, V. and Kelly, R. (1996). Global regulation for robot manipulators under SP-SD feedback, 1996 IEEE International Conference on Robotics and Automation (ICRA), Minneapolis, MN, USA, pp. 927–932.
  32. Santibáñez, V., Kelly, R. and Reyes, F. (1998). A new set-point controller with bounded torques for robot manipulators, IEEE Transactions on Industrial Electronics 45(1): 126–133.
  33. Siciliano, B. and Villani, L. (2012). Robot Force Control, Springer-Verlag, London.
  34. Spong, M., Hutchinson, S. and Vidyasagar, M. (2005). Robot Modeling and Control, Wiley, New York, NY.
  35. Volpe, R. and Khosla, P. (1993). A theoretical and experimental investigation of explicit force control strategies for manipulators, IEEE Transactions on Automatic Control 38(11): 1634–1650.
  36. Xu, G., Song, A. and Li, H. (2011). Adaptive impedance control for upper-limb rehabilitation robot using evolutionary dynamic recurrent fuzzy neural network, Journal of Intelligent & Robotic Systems 62(3): 501–525.
  37. Yarza, A., Santibanez, V. and Moreno-Valenzuela, J. (2013). An adaptive output feedback motion tracking controller for robot manipulators: Uniform global asymptotic stability and experimentation, International Journal of Applied Mathematics and Computer Science 23(3): 599–611, DOI: 10.2478/amcs-2013-0045.
  38. Zavala-Río, A. and Santibáñez, V. (2006). Simple extensions of the PD-with-gravity-compensation control law for robot manipulators with bounded inputs, IEEE Transactions on Control Systems Technology 14(5): 958–965.
  39. Zavala-Río, A. and Santibáñez, V. (2007). A natural saturating extension of the PD-with-desired-gravity-compensation control law for robot manipulators with bounded inputs, IEEE Transactions on Robotics 23(2): 386–391.

Additional information

PL: Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).

International Journal of Applied Mathematics and Computer Science
2017/27/1
Export to PBN, Opens in new tab
Pages:
79-90
Main language of publication
English
Published
2017

DOI: 10.1515/amcs-2017-0006

Exact and natural sciences