A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms

Paolo Mercorelli

Kybernetika (2012)

  • Volume: 48, Issue: 6, page 1266-1288
  • ISSN: 0023-5954

Abstract

top
In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined for decoupling these outputs and for their perfect trajectory tracking. The control of robotic manipulation is investigated. These are mechanical structures more complex than conventional serial-linkage arms. The robotic hand with possible inner contacts is a paradigm of general manipulation systems. Unilateral contacts between mechanical parts make the control of manipulation system quite involved. In fact, contacts can be considered as unactuated (passive) joints. The main goal of dexterous manipulation consists of controlling the motion of the manipulated object along with the grasping forces exerted on the object. In the robotics literature, the general problem of force/motion control is known as ``hybrid control". This paper is focused on the decoupling and functional controllability of contact forces and object motions. The goal is to synthesize a control law such that each output vector, namely the grasping force and the object motion, can be independently controlled by a corresponding set of generalized input forces. The functional force/motion controllability is investigated. It consists of achieving force and motion tracking with no error on variables transients. The framework used in this paper is the geometric approach to the structural synthesis of multivariable systems.

How to cite

top

Mercorelli, Paolo. "A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms." Kybernetika 48.6 (2012): 1266-1288. <http://eudml.org/doc/251361>.

@article{Mercorelli2012,
abstract = {In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined for decoupling these outputs and for their perfect trajectory tracking. The control of robotic manipulation is investigated. These are mechanical structures more complex than conventional serial-linkage arms. The robotic hand with possible inner contacts is a paradigm of general manipulation systems. Unilateral contacts between mechanical parts make the control of manipulation system quite involved. In fact, contacts can be considered as unactuated (passive) joints. The main goal of dexterous manipulation consists of controlling the motion of the manipulated object along with the grasping forces exerted on the object. In the robotics literature, the general problem of force/motion control is known as ``hybrid control". This paper is focused on the decoupling and functional controllability of contact forces and object motions. The goal is to synthesize a control law such that each output vector, namely the grasping force and the object motion, can be independently controlled by a corresponding set of generalized input forces. The functional force/motion controllability is investigated. It consists of achieving force and motion tracking with no error on variables transients. The framework used in this paper is the geometric approach to the structural synthesis of multivariable systems.},
author = {Mercorelli, Paolo},
journal = {Kybernetika},
keywords = {geometric approach; manipulators; functional controllability; geometric approach; manipulators; functional controllability; geometric multivariable control theory; goal of dexterous manipulation; synthesis of multivariable systems; reachable internal forces; conventional serial-linkage arms; perfect trajectory tracking; rigid-body object motions; Manipulation system analysis; hybrid control; motion tracking},
language = {eng},
number = {6},
pages = {1266-1288},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms},
url = {http://eudml.org/doc/251361},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Mercorelli, Paolo
TI - A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 6
SP - 1266
EP - 1288
AB - In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined for decoupling these outputs and for their perfect trajectory tracking. The control of robotic manipulation is investigated. These are mechanical structures more complex than conventional serial-linkage arms. The robotic hand with possible inner contacts is a paradigm of general manipulation systems. Unilateral contacts between mechanical parts make the control of manipulation system quite involved. In fact, contacts can be considered as unactuated (passive) joints. The main goal of dexterous manipulation consists of controlling the motion of the manipulated object along with the grasping forces exerted on the object. In the robotics literature, the general problem of force/motion control is known as ``hybrid control". This paper is focused on the decoupling and functional controllability of contact forces and object motions. The goal is to synthesize a control law such that each output vector, namely the grasping force and the object motion, can be independently controlled by a corresponding set of generalized input forces. The functional force/motion controllability is investigated. It consists of achieving force and motion tracking with no error on variables transients. The framework used in this paper is the geometric approach to the structural synthesis of multivariable systems.
LA - eng
KW - geometric approach; manipulators; functional controllability; geometric approach; manipulators; functional controllability; geometric multivariable control theory; goal of dexterous manipulation; synthesis of multivariable systems; reachable internal forces; conventional serial-linkage arms; perfect trajectory tracking; rigid-body object motions; Manipulation system analysis; hybrid control; motion tracking
UR - http://eudml.org/doc/251361
ER -

References

top
  1. Basile, G., Marro, G., A state space approach to non-interacting controls., Ricerche Automat. 1 (1970), 1, 68-77. 
  2. Basile, G., Marro, G., On the perfect output controllability of linear dynamic systems., Ricerche Automat. 2 (1971), 1-10. 
  3. Basile, G., Marro, G., Controlled and Conditioned Invariants in Linear System Theory., Prentice Hall, New Jersey 1992. Zbl0758.93002MR1149379
  4. Bicchi, A., Melchiorri, C., Balluchi, D., 10.1109/70.370503, IEEE Trans. Automat. Control 11 (1995), 2, 215-228. DOI10.1109/70.370503
  5. Bicchi, A., Prattichizzo, D., A standard form for the dynamics of general manipulation systems., In: International Conference on Robotics and Automation (ICRA), 1995. 
  6. Bicchi, A., Prattichizzo, D., S., Sastry, S., Planning motions of rolling surfaces., In: Proc. 34th Conference on Decision and Control (CDC), 1995. 
  7. Prattichizzo, A. Bicchi D., Mercorelli, P., Vicino, A., Noninteracting force/motion control in general manipulation systems., In: Proc. 35th IEEE Conf. on Decision Control, CDC '96, Kobe 1996. 
  8. Marro, G., Barbagli, F., The algebraic output feedback in the light of dual-lattice structures., Kybernetika 35 (1999), 6, 693-706. MR1747970
  9. Mercorelli, P., Geometric Control Tools for Mechanical Systems., Ph.D. Thesis, University of Bologna 1998. 
  10. Mercorelli, P., Robust decoupling through algebraic output feedback in manipulation systems., Kybernetika 46 (2010), 5, 850-869. Zbl1205.93032MR2778924
  11. Mercorelli, P., Prattichizzo, D., A geometric procedure for robust decoupling control of contact forces in robotic manipulation., Kybernetika 39 (2003), 4, 433-445. Zbl1249.93046MR2024524
  12. Murray, R. M., Li, Z., Sastry, S. S., A Mathematical Introduction to Robotic Manipulation., CRC Publisher, Boca Raton 1994. Zbl0858.70001MR1300410
  13. Prattichizzo, D., Structural Properties and Control of Robotics Manipulation., Ph.D. Thesis, University of Pisa 1995. 
  14. Prattichizzo, D., Bicchi, A., Specifying consistent control goals for kinematically defective manipulation systems., In: ICRA, 1996. 
  15. Prattichizzo, D., Bicchi, A., Dynamic analysis of mobility and graspability of general manipulation systems., Trans. Robotic Automat. 14 (1998), 2, 251-218. 
  16. Prattichizzo, D., Mercorelli, P., On some geometric control properties of active suspension systems., Kybernetika 36 (2000), 5, 549-570. MR1882794
  17. Salisbury, J. K., Whole-arm manipulation., In: Proc. 4th International Symposium of Robotics Research, 1987. 
  18. Siciliano, B., Parallel Force/Position Control of Robotic Manipulatio., Springer-Verlag, London 1996. 
  19. Wonham, W. M., Linear Multivariable Control: A Geometric Approach., Springer-Verlag, New York 1979. Zbl0609.93001MR0569358
  20. Yamamoto, Y., Yun, X., 10.1109/70.538986, IEEE Trans. Robotics Automat. 12 (1996), 5, 816-824. DOI10.1109/70.538986

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.