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A Dynamic Model for a Hybrid Articulated Robot
Author(s) -
Höbarth Wolfgang,
Gattringer Hubert,
Bremer Hartmut
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810123
Subject(s) - control theory (sociology) , holonomic constraints , mathematics , partial differential equation , ordinary differential equation , deflection (physics) , degrees of freedom (physics and chemistry) , differential equation , computer science , mathematical analysis , physics , classical mechanics , control (management) , quantum mechanics , artificial intelligence
The dynamic modeling of hybrid systems, consisting of flexible and rigid parts results in large partial differential equation systems (PDE). With the assumption of small deflections and the Ritz expansion the PDE can be approximated by an ordinary differential equation system (ODE) but the number of degrees of freedom is generally high. In this paper a hybrid articulated robot with 2 flexible links and 6 joints is under consideration. The joints are equipped with Harmonic Drive gears with high gear ratio but relative low stiffness. Therefore additionally degrees of freedom are introduced for the elastic deflection of the gears. The links are modeled with flexibility in two bending directions and in torsional sense. To be able to achieve structured equations the projection equation in subsystem representation is used. The projection equation is based on the momentum and the angular momentum equations of each single finite or infinitesimal body which are projected into the space of minimal coordinates and subsequently are summed up. Groups of bodies are collected to the so called subsystems with separated describing velocities. These subsystems are linked together with the kinematical chain. Because the robot is tree structured it is possible to obtain an explicit expression for the second derivatives of the minimal coordinates with a recursive scheme (O(n) efficiency). The robot is controlled with a feed forward controller and a linear PD joint controller. Simulation results and measured data are presented and compared. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)