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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Criterion for the Existence of a Separated Coordinate Representation for Underactuated Mechanical Systems
 Institute of Electrical and Electronics Engineers IEEE; IEEE Industrial Electronics Society IES; Thüringer Innovationszentrum Mobilität; Technische Universität Ilmenau: IEEE International Conference on Mechatronics, ICM 2019. Proceedings : Ilmenau, Germany, 1820 March 2019 Piscataway, NJ: IEEE, 2019 ISBN: 9781538669594 ISBN: 9781538669587 ISBN: 9781538669600 pp.1924 
 International Conference on Mechatronics (ICM) <2019, Ilmenau> 
 Deutsche Forschungsgemeinschaft DFG RO 2427/21 

 English 
 Conference Paper 
 Fraunhofer IIS, Institutsteil Entwurfsautomatisierung (EAS) () 
Abstract
Mechanical rigid body systems typically are modeled by a system of coupled second order nonlinear differential equations, where the right hand side describes the effect of the system's input, i. e., the external generalized forces. The components of the input are assigned to the scalar differential equations via a matrix which in general depends on the configuration. On the other hand, in the literature predominates the assumption that a separated coordinate representation exists such that a decomposition of the equations of motion into a nonactuated and a fully actuated subsystem is possible. This decomposition disburdens the systems analysis and the controller design but the conditions of its existence have not yet obtained much attention. The present contribution proposes a criterion, whether or not such a choice of separated coordinates is possible. The criterion is an application of the famous Frobenius theorem and will be discussed both in differential form and in vector field formulation. Its application is shown by three simple examples.