IJPAM: Volume 79, No. 2 (2012)

INTERNAL FORCES IN ROBOTIC MANIPULATION AND
IN GENERAL MECHANISMS USING
A GEOMETRIC APPROACH

Paolo Mercorelli
Leuphana University of Lueneburg
Institute of Product and Process Innovation (PPI)
Volgershall 1, D-21339 Lueneburg, GERMANY


Abstract. Robotic devices with high performance in precision and speed are required in many industrial sectors and even in applications such as medical ones (micro manipulation of internal tissues or laparoscopy) or in entertainment. This paper presents some constructive geometric structures which can be used to design force controllers for robotic manipulators and general mechanisms. The approach is based on the well-known geometric control of system dynamics. In such a framework which uses elements of the invariant subspace theory, some typical problems in robotics can be mathematically formalized and analyzed. A generalized linear model is used and a careful analysis is made. The main result of the paper consists of proposing an explicit new subspace structure for grasping internal forces in robotic manipulations and general mechanisms.

Received: April 14, 2012

AMS Subject Classification: 19L64, 70Q05, 14L24

Key Words and Phrases: subspaces, matrices, manipulators, internal forces

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 2