The Robotics Institute

Carnegie Mellon Robotics Institute

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Abstract

Flexible manipulators can be characterized by a dynamic model with a large number of vibration modes, and the use of the model in the model-based control schemes requires reduction of model order. Balanced truncation is an effective method for model reduction of asymptotically stable systems by transforming the states to a coordinate system in which the controllability and observability Gramians are equal and diagonal, and eliminating the states which contribute weakly to the input-output map. An elastic flexible manipulator, however, is a marginally stable system and thus the balanced truncation method can not be directly applied. In this report, we present a method of reducing the order of a marginally stable system based on the fact that translation transformations in the frequency domain preserve input-output properties of the system. We address the successful application of the method to model reduction of flexible manipulators with infinite-dimensional or finite-dimensional model. The method is also applicable for any other marginally stable model, such as elastic space trusswork and multi-dimensional space vehicle structure.

Notes

Grant ID: NAGW-2998

Number of pages: 18

Text Reference

Jie Yang, Yangsheng Xu, and Mei Chen, "Model Reduction of Flexible Manipulators," tech. report CMU-RI-TR-92-08, Robotics Institute, Carnegie Mellon University, June, 1992

BibTeX Reference

@techreport{Yang_1992_284,
   author = "Jie Yang and Yangsheng Xu and Mei Chen",
   title = "Model Reduction of Flexible Manipulators",
   booktitle = "",
   institution = "Robotics Institute",
   month = "June",
   year = "1992",
   number= "CMU-RI-TR-92-08",
   address= "Pittsburgh, PA",
}

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