A Geometric Approach to the Decoupling Control and to Speed up the Dynamics of a General Rigid Body Manipulation System

Abstract:

This contribution deals with a new analysis of a rigid body manipulation system. It is based on the well–knowngeometric control of system dynamics. In such a framework some typical problems in robotics are mathematicallyformalized and analyzed. The outcomes are so general that it is possible to speak of structural properties in roboticmanipulation. The problem of non-interacting force/motion control is investigated. A generalized linear model is usedand a careful analysis is made. The main result consists in proposing a task–oriented choice of the controlled outputs,for which the structural non-interaction property holds for a wide class of manipulation systems. Moreover, a decoupledlinear model predictive control is proposed which uses a pre-selecting matrix to speed up the dynamics of the mechanisms.The pre-selecting matrix enables to considers subspaces which correspond to the eigenvectors of decoupled system tospeed up the dynamic of the considered mechanism.

• Periodical: Applied Mechanics and Materials (Volume 534)
• Pages: 93-103
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.534.93
• Online since: February 2014
• Authors: Paolo Mercorelli
• Keywords: Decoupling, Force/Motion Control, Geometric Approach, Manipulator, Model Predictive Control

References

[1] G. Basile and G. Marro. A state space approach to non-interacting controls. Ricerche di Automatica, 1(1): 68-77, (1970).

[2] G. Basile and G. Marro. Controlled and conditioned invariants in linear system theory. Prentice Hall, New Jersey, (1992).

[3] A. Bicchi. Force distribution in multiple whole-limb manipulation. In IEEE International Conference on Robotics and Automation, ICRA, volume 2, pages 196-201, Atlanta, Georgia, USA, (1993).

DOI: 10.1109/robot.1993.292146

[4] A. Bicchi, C. Melchiorri, and D. Balluchi. On the mobility and manipulability of general multiple limb robots. IEEE Transactions on Automatic Control, 11(2): 215-228, (1995).

DOI: 10.1109/70.370503

[5] A. Bicchi D. Prattichizzo, P. Mercorelli and A. Vicino. Noninteracting force/motion control in general manipulation systems. In Proceedings of the 35th IEEE Conference on Decision Control, CDC '96, Kobe (Japan), December (1996).

DOI: 10.1109/cdc.1996.572865

[6] P. Mercorelli. Geometric structures for the parameterization of non-interacting dynamics for multi-body mechanisms. International Journal of Pure and Applied Mathematics - IJPAM, 59(3): 257-273, (2010).

[7] P. Mercorelli. A switching kalman filter for sensorless control of a hybrid hydraulic piezo actuator using mpc for camless internal combustion engines. In Proceedings of the 2012 IEEE International Conference on Control Applications, pages 980-985, Dubrovnik, 3-5 October (2012).

DOI: 10.1109/cca.2012.6402717

[8] P. Mercorelli and D. Prattichizzo. A geometric procedure for robust decoupling control of contact forces in robotic manipulation. Kybernetika, 39(4): 433-445, (2003).

[9] A.S. Morse and W.M. Wonham. Decoupling and pole assignment by dynamic compensation. SIAM Journal on Control, 8(1): 317-337, (1970).

DOI: 10.1137/0308022

[10] R.M. Murray, Z. Li, and S.S. Sastry. A mathematical introduction to robotic manipulation. CRC Press, Boca Raton, Florida, (1994).

[11] D. Prattichizzo and A. Bicchi. Consistent task specification for manipulation systems with general kinematics. ASME Journal of Dynamics Systems Measurements and Control, 119: 760-767, (1997).

DOI: 10.1115/1.2802388

[12] D. Prattichizzo and A. Bicchi. Dynamic analysis of mobility and graspability of general manipulation systems. Transactions on Robotic and Automation, 14(2): 251-218, (1998).

DOI: 10.1109/70.681243

[13] D. Prattichizzo and P. Mercorelli. On some geometric control properties of active suspension systems. Kybernetika, 36(5): 549-570, (2000).

[14] D. Prattichizzo, P. Mercorelli, A. Bicchi, and A. Vicino. On the geometric control of internal forces in power grasps. In Proceedings of the 36th IEEE Conference of Decirsion and Control, CDC'97, San Diego (CA), (1997).

DOI: 10.1109/cdc.1997.657879

[15] J.K. Salisbury and B. Roth. Kinematic and force analysis of articulated mechanical hands. Journal of Mechanisms, Transmissions and Actuation in Design, 105, (1983).

DOI: 10.1115/1.3267342

[16] H. Sunan, T.K. Kiong, and L.T. Heng. Applied Predictive Control. Springer-Verlag London, Printed in Great Britain, (2002).

[17] W.M. Wonham. Linear multivariable control: a geometric approach. Springer-Verlag, New York, (1979).

[18] W.M. Wonham and A.S. Morse. Decoupling and pole assignment in linear multivariable systems: a geometric approach. SIAM Journal on Control, 8(1): 1-18, (1970).

DOI: 10.1137/0308001