O(n) Algorithm for Elastic Link/Joint Robots with End-Effector Contact

  • Hubert Gattringer
  • Andreas Müller
  • Florian Pucher
  • Alexander Reiter
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 33)


This paper deals with the dynamical modeling of flexible multibody systems like elastic robots that go in contact with the environment. Models for elastic systems have a large degree of freedom leading to longer calculation times for solving the equations of motion (EOM). Conventionally, this includes the inversion of the mass matrix with a cubic run time complexity O(n3). By using a subsystem formulation and the Projection Equation an O(n) algorithm can be formulated that significantly reduces the simulation time. Additional contacts with the environment can be included in the equations of motion by the corresponding constraint Jacobian and the contact forces. For the explicit calculation of these forces, normally the inverse of the mass matrix is needed again. A novel algorithm to avoid this inversion is presented. Therein, the contact forces are calculated by additional runs of the same O(n) algorithm that is used without contact. The transition phase between different contact states is treated with the help of Newton’s impact law, again avoiding the inversion of the mass matrix. Simulation results for an elastic robot show the effectiveness of the proposed algorithms.


Dynamical modeling Elastic multibody systems Ritz approximation O(n) algorithm Contact 



This work has been supported by the Austrian COMET-K2 program of the Linz Center of Mechatronics (LCM).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Hubert Gattringer
    • 1
  • Andreas Müller
    • 1
  • Florian Pucher
    • 1
  • Alexander Reiter
    • 1
  1. 1.Institute of RoboticsJohannes Kepler University LinzLinzAustria

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