Romansy 16 pp 147-154 | Cite as

Nonlinearity detection and reduction based on unnormalized quasi-velocities

  • Przemyslaw Herman
  • Krzysztof Kozlowski
Part of the CISM Courses and Lectures book series (CISM, volume 487)


In this paper an analysis concerning dynamical couplings between manipulator links is proposed. In order to detect nonlinearities we utilize equations of motion in terms of unnormalized quasi-velocities (UQV) introduced originally by Jain and Rodriguez (1995). Based on the equations some observations which are helpful for nonlinearity investigation and reduction were made. The presented strategy was tested by simulation on a 3 d.o.f. spatial manipulator.


Manipulator Link Joint Velocity Spatial Manipulator Joint Axis Kinematic Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. M. Bergerman, M. Lee, and Y.S. Xu. A Dynamic Coupling Index for Underactuated Manipulators. J. Robotic Systems, 10:693–707, 1995.CrossRefGoogle Scholar
  2. T.A.H. Coelho, L. Yong, and V.F.A. Alves. Decoupling of dynamic equations by means of adaptive balancing of 2-dof open-loop mechanisms. Mechanism and Machine Theory, 39:871–881, 2004.MATHCrossRefMathSciNetGoogle Scholar
  3. M. Cotsaftis, J. Robert, M. Rouff, and C. Vibet. Applications and prospect of the nonlinear decoupling method. Comput. Methods Appl. Engrg., 154:163–178, 1998.MATHCrossRefMathSciNetGoogle Scholar
  4. A. Jain and G. Rodriguez. Diagonalized Lagrangian Robot Dynamics. IEEE Transactions on Robotics and Automation, 11:571–584, 1995.CrossRefGoogle Scholar
  5. D. Koditschek. Natural Motion for Robot Arms. In Proceedings of the 23rd IEEE Conference on Decision and Control, pages 733–735, 1984.Google Scholar
  6. D. Koditschek. Robot Kinematics and Coordinate Transformations. In Proceedings of the 24th IEEE Conference on Decision and Control, pages 1–4, 1985.Google Scholar
  7. K. Kozlowski. Mathematical Dynamic Robot Models and Identification of Their Parameters. Technical University of Poznan Press, Poznan, 1992 (in Polish).Google Scholar
  8. J.L. Pons, R. Ceres, A.R. Jimenez, L. Calderon, and J.M. Martin. Nonlinear Performance Index (npi): A tool for Manipulator Dynamics Improvement. Journal of Intelligent and Robotic Systems, 18:277–287, 1997.MATHCrossRefGoogle Scholar
  9. L. Sciavicco and B. Siciliano. Modeling and Control of Robot Manipulators. The McGraw-Hill Companies, Inc., New York, 1996.Google Scholar
  10. J.J. Slotine and W. Li. Applied Nonlinear Control. Prentice Hall, New Jersey, 1991.MATHGoogle Scholar

Copyright information

© CISM, Udine 2006

Authors and Affiliations

  • Przemyslaw Herman
    • 1
  • Krzysztof Kozlowski
    • 1
  1. 1.Chair of Control and Systems EngineeringPoznan University of TechnologyPoznanPoland

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