| Title:
|
Invariant subspaces for grasping internal forces and non-interacting force-motion control in robotic manipulation (English) |
| Author:
|
Mercorelli, Paolo |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
6 |
| Year:
|
2012 |
| Pages:
|
1229-1249 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper presents a parametrization of a feed-forward control based on structures of subspaces for a non-interacting regulation. With advances in technological development, robotics is increasingly being used in many industrial sectors, including medical applications (e. g., micro-manipulation of internal tissues or laparoscopy). Typical problems in robotics and general mechanisms may be mathematically formalized and analyzed, resulting in outcomes so general that it is possible to speak of structural properties in robotic manipulation and mechanisms. This work shows an explicit formula for the reachable internal contact forces of a general manipulation system. The main contribution of the paper consists of investigating the design of a feed-forward force-motion control which, together with a feedback structure, realizes a decoupling force-motion control. A generalized linear model is used to perform a careful analysis, resulting in the proposed general geometric structure for the study of mechanisms. In particular, a lemma and a theorem are presented which offer a parametrization of a feed-forward control for a task-oriented choice of input subspaces. The existence of these input subspaces is a necessary condition for the structural non-interaction property. A simulation example in which the subspaces and the control structure are explicitly calculated is shown and widely explicated. (English) |
| Keyword:
|
subspaces |
| Keyword:
|
matrices |
| Keyword:
|
manipulators |
| Keyword:
|
internal forces |
| MSC:
|
14L24 |
| MSC:
|
19L64 |
| MSC:
|
70Q05 |
| MSC:
|
93D09 |
| idMR:
|
MR3052883 |
| . |
| Date available:
|
2013-01-10T09:32:43Z |
| Last updated:
|
2013-09-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143128 |
| . |
| Reference:
|
[1] Basile, G., Marro, G.: Controlled and Conditioned Invariants in Linear System Theory..Prentice Hall, New Jersey 1992. Zbl 0758.93002, MR 1149379 |
| Reference:
|
[2] Basile, G., Marro, G.: A state space approach to non-interacting controls..Ricerche Automat. 1 (1970), 1, 68-77. |
| Reference:
|
[3] Basile, G., Marro, G.: Invarianza controllata e non interazione nello spazio degli stati..L'Elettrotecnica 56 (1969), 1. |
| Reference:
|
[4] Prattichizzo, A. Bicchi D., Mercorelli, P., Vicino, A.: Noninteracting force/motion control in general manipulation systems..In: Proc. 35th IEEE Conference on Decision and Control, CDC '96, Vol. 2, Kobe 1996, pp. 1952-1957. |
| Reference:
|
[5] Bicchi, A., Melchiorri, C., Balluchi, D.: On the mobility and manipulability of general multiple limb robots..IEEE Trans. Automat. Control 11 (1995), 2, 215-228. 10.1109/70.370503 |
| Reference:
|
[6] Bicchi, A.: Force distribution in multiple whole-limb manipulation..In: Proc. 1993 IEEE International Conference on Robotics and Automation, ICRA'03, Atlanta 1993, pp. 196-201. |
| Reference:
|
[7] Chu, D., Mehrmann, V.: Disturbance decoupling for linear time-invariant systems: A matrix pencil approach..IEEE Trans. Automat. Control 46 (2001), 5, 802-808. Zbl 1007.93011, MR 1833040, 10.1109/9.920805 |
| Reference:
|
[8] Chu, D., Mehrmann, V.: Disturbance decoupling for descriptor systems..SIAM J. Control Optim. 38 (2000), 1830-1850. Zbl 0963.93061, MR 1776658, 10.1137/S0363012900331891 |
| Reference:
|
[9] Cutkosky, M. R., Kao, I.: Computing and controlling the compliance of a robotic hand..IEEE Trans. Robotics Automat. 5 (1989), 2, 151-165. 10.1109/70.88036 |
| Reference:
|
[10] Marro, G., Barbagli, F.: The algebraic output feedback in the light of dual-lattice structures..Kybernetika 35 (1999), 6, 693-706. MR 1747970 |
| Reference:
|
[11] Mercorelli, P.: Robust decoupling through algebraic output feedback in manipulation systems..Kybernetika 46 (2010), 5, 850-869. Zbl 1205.93032, MR 2778924 |
| Reference:
|
[12] Mercorelli, P., Prattichizzo, D.: A geometric procedure for robust decoupling control of contact forces in robotic manipulation..Kybernetika 39 (2003), 4, 433-445. Zbl 1249.93046, MR 2024524 |
| Reference:
|
[13] Morse, A. S., Wonham, W. M.: Decoupling and pole assignment by dynamic compensation..SIAM J. Control 8 (1970), 1, 317-337. Zbl 0204.46401, MR 0272434, 10.1137/0308022 |
| Reference:
|
[14] Murray, R. M., Li, Z., Sastry, S. S.: A Mathematical Introduction to Robotic Manipulation..CRC Publisher (Taylor and Francis Group), Boca Raton 1994. Zbl 0858.70001, MR 1300410 |
| Reference:
|
[15] Prattichizzo, D., Mercorelli, P.: On some geometric control properties of active suspension systems..Kybernetika 36 (2000), 5, 549-570. MR 1882794 |
| Reference:
|
[16] Prattichizzo, D., Bicchi, A.: Dynamic analysis of mobility and graspability of general manipulation systems..IEEE Trans. Robotic Automat. 14 (1998), 2, 251-218. |
| Reference:
|
[17] Prattichizzo, D., Bicchi, A.: Consistent task specification for manipulation systems with general kinematics..ASME J. Dynamics Systems Measurements and Control 119 (1997), 760-767. Zbl 1026.70007, 10.1115/1.2802388 |
| Reference:
|
[18] Prattichizzo, D., Mercorelli, P., Bicchi, A., Vicino, A.: On the geometric control of internal forces in power grasps..In: Proc. 36th IEEE International Conference on Decision and Control, CDC'97, Vol. 2, San Diego 1997, pp. 1942-1947. |
| Reference:
|
[19] Salisbury, J. K., Roth, B.: Kinematic and force analysis of articulated mechanical hands..J. Mech. Transm. Automat. in Des. 105 1983, 35-41. 10.1115/1.3267342 |
| Reference:
|
[20] Wonham, W. M.: Linear Multivariable Control: A Geometric Approach..Springer-Verlag, New York 1979. Zbl 0609.93001, MR 0569358 |
| Reference:
|
[21] Wonham, W. M., Morse, A. S.: Decoupling and pole assignment in linear multivariable systems: a geometric approach..SIAM J. Control 8 (1970), 1, 1-18. Zbl 0206.16404, MR 0270771, 10.1137/0308001 |
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