Kybernetika 46 no. 5, 850-869, 2010

Robust decoupling through algebraic output feedback in manipulation systems

Paolo Mercorelli

Abstract:

This paper investigates the geometric and structural characteristics involved in the control of general mechanisms and manipulation systems. These systems consist of multiple cooperating linkages that interact with a reference member of the mechanism (the "object") by means of contacts on any available part of their links. Grasp and manipulation of an object by the human hand is taken as a paradigmatic example for this class of manipulators. Special attention is devoted to the output specification and its controllability. An example design of a force controller using algebraic output feedback is presented at the end of this paper. In this example, a matrix representing a static output feedback is designed. The coefficients of this matrix are the weights for the sensed outputs. With the approach proposed in this paper, a robust decoupling is obtained between the output feedback and the contact forces and joint positions.

Keywords:

geometric approach, manipulators, force/motion control

Classification:

93D09, 19L64, 70Q05, 14L24

paper.pdf

References:

  1. G. Basile and G. Marro: Controlled and Conditioned Invariants in Linear System Theory. Prentice Hall, New Jersey, 1992.   CrossRef
  2. S. P. Bhattacharyya: Generalized controllability, controlled invariant subspace and parameter invariant control. SIAM J. Algebraic Discrete Methods 4 (1983), 4, 529-533.   CrossRef
  3. A. Bicchi, C. Melchiorri and D. Balluchi: On the mobility and manipulability of general multiple limb robots. IEEE Trans. Automat. Control 11 (1995), 2, 215-228.   CrossRef
  4. A. Bicchi and D. Prattichizzo: Manipulability of cooperating robots with unactuated joints and closed-chain mechanisms. IEEE Trans. Robotics and Automation 16 (2000), 4, 336-345.   CrossRef
  5. A. Bicchi, D. Prattichizzo, P. Mercorelli and A. Vicino: Noninteracting force/motion control in general manipulation systems. In: Proc. 35th IEEE Conf. on Decision Control, CDC '96, Kobe 1996.   CrossRef
  6. A. Isidori: Nonlinear Control Systems: An Introduction. Springler-Verlag, Berlin 1989.   CrossRef
  7. G. Marro and F. Barbagli: The algebraic output feedback in the light of dual lattice structures. Kybernetika 35 (1999), 6, 693-706.   CrossRef
  8. M. T. Mason and J. K. Salisbury: Robot Hands and the Mechanics of Manipulation. The MIT Press, Cambridge 1985.   CrossRef
  9. L. Meirovitch: Analytical Methods in Vibrations. Macmillan Pub. Co., Inc., New York 1967.   CrossRef
  10. P. Mercorelli: A subspace to describe grasping internal forces in robotic manipulation systems. J. Math. Control Sci. Appl. 1 (2007), 1, 209-216.   CrossRef
  11. P. Mercorelli: Geometric structures for the parameterization of non-interacting dynamics for multi-body mechanisms. Internat. J. Pure Appl. Math. 59 (2010), 3, 257-273.   CrossRef
  12. P. Mercorelli and D. Prattichizzo: A geometric procedure for robust decoupling control of contact forces in robotic manipulation. Kybernetika 39 (2003), 4, 433-445.   CrossRef
  13. D. Prattichizzo and A. Bicchi: Consistent task specification for manipulation systems with general kinematics. Amer. Soc. Mech. Engrg. 119 (1997), 760-767.   CrossRef
  14. D. Prattichizzo and A. Bicchi: Dynamic analysis of mobility and graspability of general manipulation systems. Trans. Robotic Automat. 14 (1998), 2, 251-218.   CrossRef
  15. D. Prattichizzo and P. Mercorelli: Motion-decoupled internal force control in grasping with visco-elastic contacts. In: Proc. IEEE Conf. in Robotic and Automation, ICRA 2000, San Francisco 2000.   CrossRef
  16. D. Prattichizzo and P. Mercorelli: On some geometric control properties of active suspension systems. Kybernetika 36 (2000), 5, 549-570.   CrossRef
  17. W. M. Wonham: Linear Multivariable Control: A Geometric Approach. Springer Verlag, New York 1979.   CrossRef
  18. Y. Yamamoto and X. Yun: Effect of the dynamic interaction on coordinated control of mobile manipulators. IEEE Trans. Robotics Automat. 12 (1996), 5, 816-824.   CrossRef