Multibody System Dynamics

, Volume 36, Issue 3, pp 295–321 | Cite as

Index reduction by minimal extension for the inverse dynamics simulation of cranes

  • Robert Altmann
  • Peter Betsch
  • Yinping Yang


The present work deals with the inverse dynamics simulation of underactuated mechanical systems relying on servo constraints. The servo-constraint problem of discrete mechanical systems is governed by differential–algebraic equations (DAEs) with high index. We propose a new index reduction approach, which makes possible the stable numerical integration of the DAEs. The new method is developed in the framework of a specific crane formulation and facilitates a reduction from index five to index three and even to index one. Particular attention is placed on the special case in which the reduced index-1 formulation is purely algebraic. In this case the system at hand can be classified as differentially flat system. Both redundant coordinates and minimal coordinates can be employed within the newly developed approach. The success of the proposed method is demonstrated with two representative numerical examples.


Underactuated mechanical systems Servo constraints Feedforward control Differentially flat systems 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Institut für MechanikKarlsruher Institut für TechnologieKarlsruheGermany

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