Saturating stiffness control of robot manipulators with bounded inputs
María del Carmen Rodríguez-Liñán ; Marco Mendoza ; Isela Bonilla ; César A. Chávez-Olivares
International Journal of Applied Mathematics and Computer Science, Tome 27 (2017), p. 79-90 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2017-01-01
EUDML-ID : urn:eudml:doc:288097
@article{bwmeta1.element.bwnjournal-article-amcv27i1p79bwm,
     author = {Mar\'\i a del Carmen Rodr\'\i guez-Li\~n\'an and Marco Mendoza and Isela Bonilla and C\'esar A. Ch\'avez-Olivares},
     title = {Saturating stiffness control of robot manipulators with bounded inputs},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {27},
     year = {2017},
     pages = {79-90},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv27i1p79bwm}
}
María del Carmen Rodríguez-Liñán; Marco Mendoza; Isela Bonilla; César A. Chávez-Olivares. Saturating stiffness control of robot manipulators with bounded inputs. International Journal of Applied Mathematics and Computer Science, Tome 27 (2017) pp. 79-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv27i1p79bwm/

[000] 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.

[001] 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.

[002] 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. | Zbl 1336.93111

[003] Canudas, C., Siciliano, B. and Bastin, G. (2012). Theory of Robot Control, Springer-Verlag, London. | Zbl 0854.70001

[004] Caverly, R.J., Zlotnik, D.E., Bridgeman, L.J. and Forbes, J.R. (2014). Saturated proportional derivative control of flexible-joint manipulators, Robotics and ComputerIntegrated Manufacturing 30(6): 658-666.

[005] 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.

[006] 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.

[007] 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.

[008] 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.

[009] 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.

[010] 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.

[011] 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. | Zbl 1302.93153

[012] 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.

[013] 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.

[014] 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.

[015] 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. | Zbl 0566.93025

[016] 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.

[017] Kelly, R., Santibáñez, V. and Berghuis, H. (1997). Point-to-point robot control under actuator constraints, Control Engineering Practice 5(11): 1555-1562.

[018] Kelly, R., Santibáñez, V. and Loría, A. (2005). Control of Robot Manipulators in Joint Space, Springer-Verlag, London.

[019] Khalil, H. (2002). Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ. | Zbl 1003.34002

[020] 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.

[021] Kurfess, T. (2004). Robotics and Automation Handbook, CRC Press, Boca Raton, FL.

[022] 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.

[023] 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.

[024] 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.

[025] 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. | Zbl 1337.93058

[026] 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. | Zbl 1255.68163

[027] 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. | Zbl 1334.93129

[028] 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.

[029] 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.

[030] 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.

[031] 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.

[032] Siciliano, B. and Villani, L. (2012). Robot Force Control, Springer-Verlag, London. | Zbl 0940.93006

[033] Spong, M., Hutchinson, S. and Vidyasagar, M. (2005). Robot Modeling and Control, Wiley, New York, NY.

[034] 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.

[035] 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. | Zbl 1245.93095

[036] 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. | Zbl 1279.93078

[037] 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.

[038] 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.