Fractional Control of Coordinated Manipulators
N. M. Fonseca Ferreira* and J. A. Tenreiro Machado**
*Dept. of Electrical Engineering, Institute of Engineering of Coimbra, Rua Pedro Nunes, 3031-601 Coimbra, Portugal
**Dept. of Electrical Engineering, Institute of Engineering of Porto, Rua Dr António Bernardino de Almeida, 4200-072 Porto, Portugal
When two robots execute a coordinated motion it is required specification not only of the desired trajectory of each robot, but also of the forces exerted by the end effectors. This article discusses the fractional-order position and force control of two co-operative robots handling one object. The system robustness and performance is analyzed and compared with other control approaches. The experiments reveal that fractional algorithms lead to performances superior to classical integer-order controllers.
-  Y. C. Tsai and A. H. Soni, “Accessible Region and Synthesis of Robot Arms,” ASME J. Mech. Design, Vol.103, pp. 803-811, 1981.
-  T. Yoshikawa, “Manipulability of Robotic Mechanisms,” The Int. J. Robotics Research, Vol.4, pp. 3-9, 1985.
-  H. Asada, “A Geometrical Representation of Manipulator Dynamics and its Application to Arm Design,” ASME J. Dynamic Syst. Meas., Contr., Vol.105, pp. 131-142, 1983.
-  J. A. T. Machado and A. M. Galhano, “A Statistical and Harmonic Model for Robot Manipulators,” IEEE Int. Conf. on Robotics and Automation, New Mexico, USA, 1997.
-  Y. Nakamura, K. Nagai, and T. Yoshikawa, “Dynamics and Stability in Coordination of Multiple Robotic Mechanisms,” Int. Journal of Robotics Research, Vol.8, pp. 44-61, 1989.
-  A. K. Bejczy and T. Jonhg Tarn, “Redundancy in Robotics Connected Robots Arms as Redundant Systems,” 4th IEEE Int. Conf. on Intelligent Engineering Systems, Portoroz, Slovenia, 2000.
-  M. H. Raibert and J. J. Craig, “Hybrid Position/Force Control of Manipulators,” ASME J. Dynamic Syst. Meas., Contr., Vol.2, No.2, pp. 126-133, 1981.
-  N. M. Fonseca Ferreira and J. T. Machado, “Fractional-Order Hybrid Control of Robotic Manipulator,” 11th IEEE Int. Conf. on Advanced Robotics, Coimbra, Portugal, 2003.
-  N. Hogan, “Impedance control: An Approach to Manipulation, Parts I-Theory, II-Implementation, III-Applications,” ASME J. Dynamic Syst. Meas., Contr., Vol.107, No.1, pp. 1-24, 1985.
-  N. M. Fonseca Ferreira, J. T. Machado, and J. Boaventura Cunha, “Fractional-Order Position/Force Robot Control,” 2nd IEEE Int. Conf. on Computational Cybernetics, Vienna, Austria, pp. 126-133, 2004.
-  A. Oustaloup, “La Dérivation Non Entière: Théorie, Synthese et Applications,” Hermes, Paris, 1995.
-  J. T. Machado, “Analysis and Design of Fractional-Order Digital Control Systems,” Journal of Systems Analysis, Modelling and Simulation, Vol.27, pp. 107-122, 1997.
-  I. Podlubny, “Fractional-Order Systems and PIαDμ -controllers,” IEEE Trans. on Automatic Control, Vol.44, No.1, pp. 208-213, 1999.