Abstract
Rapid development of biological science and technologies will further improve the active applications of control engineering by advanced biomimetic and biologically inspired research. First of all, it has promoted a biologically inspired control synergy approach that allows the resolution of redundancy of a given robotized system. In particular, the actuator redundancy control problem has been stated and solved by using Pontryagin’s maximum principle, where control synergy was established at the coordination level. Besides, fractional calculus (FC), is a mathematical topic with more than 300 years old history, in recent years there have been extensive research activities related to applications of FC in many areas of science and engineering. Here, they are presented by the advanced algorithms of PID control based on FC, tuned by genetic algorithms, in the position control of robotic system with 3 DOFs driven by DC motors. Also, a chattering-free fractional \( PD^{\alpha } \) sliding-mode controller in the control of a given robotic system has been proposed and realized. The effectiveness of the proposed optimal fractional order controls are demonstrated by the given robot. Finally, it is shown that one can obtain analytical expressions for generalized forces of the magnetorheological damping elements of fractional order which are used for obtaining better model of (bio)robotic systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Astrom, K. and T. Hagglund: PID controllers: theory, design, and tuning, Instrument Society of America, North Carolina (1995)
Bar-Cohen,Y.: Biomimetics-Biologically Inspired Technologies, CRC Press, Taylor & Francis Group, Boca Raton:FL, pp.399–425 (2006)
Batalov S.A, M. Lazarevic,A.Hace, K. Jezernik,A Chattering-free Fractional PDa Sliding-mode Control of a 3-DOF Robot System Driven by DC motors, 5’th FDA2012, pp.77,Nanjing, China,May 20, (2012)
Bernstein,A.:The Coordination and Regulation of Movements,Oxford Perg., 77–92 (1961)
Cajić,M. Lazarević,M.,and T.Latinović: Equations of motion of robotic system with piezo-modified viscoelastic and magnetorheological elements of fractional order,S.7.1,GAMM2013,Novi Sad,Serbia,(2013)
Chen, D. Xue, H. Dou:Fractional calculus and biomimetic control, in Proc. IEEE International Conference on Robotics and Biomimetics,Shenyang, China, Aug., pp. 901–906 (2004)
Čović, V., Lazarević, M.: Mechanics of robots, Faculty of Mechanical engineering, University of Belgrade, (in Serbian), (2009)
Edwards,C., Spurgeon,S.K.:Sliding mode control theory and applications, Taylor & Fran., NewYork, (1998)
Geng Fan Wu,Zhi-Yong:Coordinating control of multiple rigid bodies based on motion primi tives, Acta Mech. Sin., 28(2):482–489 (2012)
Gering,H., Guzzella,L., Hepener,S., Onder,C.: Time optimal motions of robots in assembly tasks, IEEE Transactions on Automatic Control, AC-31,(6):512–518 (1986)
Grinyagin,I.V., Biryukova,E.V., Maier,M.A.: Kinematic and Dynamic Synergies of Human Precision-Grip Movements, J Neurophysiol.,94: 2284–2294 (2004)
Hace,A., Jezernik,K.,: Robust position tracking control for direct drive motor, Industrial Electronics Society, 2000. IECON 2000. 26th Annual Confjerence of the IEEE, (2000)
Harkegard O, S. T. Glad:,Resolving actuator redundancy-optimal control vs. control allocation, Automatica 41, pp.137–144 (2005)
Hilfer R: Applications of Fractional Calculus in Physics,World Scientific, NJ, USA, (2000)
Karas and Baig: Robotic Neurosurgery,in Medical Robotics, ISBN: 978-3-902613-18-9, InTech Europe,(2008)
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
Klug,S.,Lens,T.,Von Stryk,O, Mohl,B.,Karguth,A.: Biologically Inspired Robot Manipulator for New Applications in Autom. Eng. Proc.of Robotik 2008,Munich,Germany,11–12 (2008)
Lathash,M.: Control of human movement, Human Kinetics Publishers (1994)
Latash,M.L.: Synergy, Oxford University Press US, pp.432 (2008)
Lazarević,M.P.: Finite time stability analysis of \( PD^{\alpha } \) fractional control of robotic time-delay systems, Mech. Resch.Commun., 33, pp.269–279 (2006)
Lazarević M.,A.Obradović,T. Latinović:Bio-Inspired Control of Redundant Robotic Systems Optimization Approach, Scientific Technical Review,Vol.62,No.3-4,pp.45–54 (2012)
Lazarević, M. :Fractional Order Control of a Robot System Driven by DC Motors, Scientific Technical Review,Vol.62,No.2,pp.20–29 (2012)
Lazarević P.M., Lj. Bucanović: Contribution to modeling and dynamical analysis of fractional order systems with basis of fractional calculus, Monograph (in Serbian) (Mechanical Engineering Faculty, University of Belgrade, Belgrade (2012).
Lazarević M., S.Batalov, T.Latinović, Fractional PID Controller Tuned by Genetic Algorithms for a Three DOF’s Robot System Driven by DC motors, 6th Workshop on Fractional Differentiation and Its Applications Part of 2013 IFAC Joint Conference SSSC Grenoble, France, February 4-6, pp.380–385 (2013)
Monje,C.A., et al.: Fractional-order Systems and Controls, Springer - Verlag, London, (2010)
Oldham K B and J. Spanier:The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press,New York, NY,USA (1974)
Podlubny, I.,: Fractional Differential Equations, Academic Press,San Diego,(1999)
Romanovas,M. Traechtler, M. L. Klingbeil and Y. Manoli: On fractional models for human motion tracking, Journal of Vibration and Control, DOI: 10.1177/1077546313479637,(2013)
Sabatier J., O.Agrawal, J.Atenreiro Machado: Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering,Springer (2007)
Schanzer,G, Callies,R.: Multiple constrained rivaling actuators in the optimal control of miniaturized manipulators, Multibody System Dynamics, 19:21–43 (2008)
Sehoon, Oh and Yoichi Hori: Fractional Order Impedance Control by Particle Swarm Optimization International Conference on Control, Automation and Systems,Oct. 14–17, 2008 in COEX, Seoul, Korea (2008)
Vepa,R.: Biomimetic Robotics-mechanisms and control, Cambridge University Press, (2009)
Webb,B.: Can robots make good models of biological behaviour? Behav. Brain Sci. 24, 24:1033–1094 (2001)
Acknowledgments
The support of the Ministry of Education, Science and Technological Development of the Republic of Serbia through projects TR 35006, 41006 is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lazarević, M. (2014). Some Applications of Biomimetics and Fractional Calculus in Control and Modeling of (Bio)robotic Systems. In: Rodić, A., Pisla, D., Bleuler, H. (eds) New Trends in Medical and Service Robots. Mechanisms and Machine Science, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-05431-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-05431-5_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05430-8
Online ISBN: 978-3-319-05431-5
eBook Packages: EngineeringEngineering (R0)