TY - JOUR

T1 - Geometric structures for the parameterization of non-interacting dynamics for multi-body mechanisms

AU - Mercorelli, Paolo

N1 - Cited By (since 1996): 1 Export Date: 22 May 2012 Source: Scopus Language of Original Document: English Correspondence Address: Mercorelli, P.; Faculty of Automotive Engineering, University of Applied Sciences - Wolfsburg, 12, Robert-Koch-Platz, Wolfsburg, 38440, Germany; email: p.mercorelli@ostfalia.de References: Basile, G., Marro, G., Invarianza controllata e non interazione nello spazio degli stati (1969) L'Elettrotecnica, 56 (1); Basile, G., Marro, G., A state space approach to non-interacting controls (1970) Ricerche di Automática, 1 (1), pp. 68-77; Basile, G., Marro, G., (1992) Controlled and Conditioned Invariants in Linear System Theory, , Prentice Hall, New Jersey; Bicchi, A., Melchiorri, C., Balluchi, D., On the mobility and manipulability of general multiple limb robots (1995) IEEE Trans, on Automat. Contr., 11 (2), pp. 215-228; Bicchi, A., Prattichizzo, D., Mercorelli, P., Vicino, A., Noninteracting force/motion control in general manipulation systems (1996) Proc 35-th IEEE Conf on Decision Control, CDC'96, , Kobe (Japan), December; Chu, D., Mehrmann, V., Disturbance decoupling for descriptor systems (2000) SIAM J. Control and Optim., 38, pp. 1830-1858; Chu, D., Mehrmann, V., Disturbance decoupling for linear timeinvariant systems: A matrix pencil approach (2001) IEEE Transactions on Automatic Control, 46 (5), pp. 802-808; Cutkosky, M.R., Kao, I., Computing and controlling the compliance of a robotic hand (1989) IEEE Trans. Robotics Automat, 5 (2), pp. 151-165; Mercorelli, P., Prattichizzo, D., A geometric procedure for robust decoupling control of contact forces in robotic manipulation (2003) Kybernetika, 39 (4), pp. 433-445; Mercorelli, P., A subspace to describe grasping internal forces in robotic manipulation systems (2007) Journal of Mathematical Control Science and Applications (JMCSA), 1 (1), pp. 209-216; Morse, A.S., Wonham, W.M., Decoupling and pole assignment by dynamic compensation (1970) SIAM J. Control, 1, pp. 317-337; Murray, R.M., Li, Z., Sastry, S.S., (1994) A Mathematical Introduction to Robotic Manipulation, , CRC, Boca Raton, Florida; Prattichizzo, D., Bicchi, A., Consistent task specification for manipulation systems with general kinematics (1997) ASME Journal of Dynamics Systems Measurements and Control, 119, pp. 760-767; Prattichizzo, D., Bicchi, A., Dynamic analysis of mobility and graspability of general manipulation systems (1980) Transaction on Robotic and Automation, 14 (2), pp. 251-1218; Prattichizzo, D., Mercorelli, P., On some geometric control properties of active suspension systems (2000) Kybernetika, 36 (5), pp. 549-570; Prattichizzo, D., Mercorelli, P., Bicchi, A., Vicino, A., On the geometric control of internal forces in power grasps (1997) Proc 36-th IEEE CDC'97, , San Diego (CA); Salisbury, J.K., Roth, B., Kinematic and force analysis of articulated mechanical hands (1983) J. Mech. Transm. Automat, in Des., 105; Wonham, W.M., (1979) Linear Multivariable Control: A Geometric Approach, , Springer-Verlag, New York; Wonham, W.M., Morse, A.S., Decoupling and pole assignment in linear multivariable systems: A geometric approach (1970) SIAM J. Control, 8 (1), pp. 1-18

PY - 2010

Y1 - 2010

N2 - This paper presents a totally general geometric approach to the study of robotics manipulators and the dynamics of general mechanisms. In particular, a parametrization of a pre-compensator based on structures of subspaces for a non-interacting controller is presented. 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 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 investigates the design of a force/motion controller. 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 pre-compensator for a taskoriented choice of input subspaces. The existence of these input subspaces is a necessary condition for the structural non-interaction property.

AB - This paper presents a totally general geometric approach to the study of robotics manipulators and the dynamics of general mechanisms. In particular, a parametrization of a pre-compensator based on structures of subspaces for a non-interacting controller is presented. 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 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 investigates the design of a force/motion controller. 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 pre-compensator for a taskoriented choice of input subspaces. The existence of these input subspaces is a necessary condition for the structural non-interaction property.

KW - Engineering

KW - Decoupling

KW - Force/motion control

KW - Geometric approach

KW - Invariant subspaces

KW - Manipulators

KW - Matrices

UR - http://www.scopus.com/inward/record.url?scp=78649774643&partnerID=8YFLogxK

M3 - Journal articles

VL - 59

SP - 257

EP - 273

JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

SN - 1311-8080

IS - 3

ER -