Advertisement

Guaranteed Detection of the Singularities of 3R Robotic Manipulators

  • Romain BenoitEmail author
  • Nicolas Delanoue
  • Sébastien Lagrange
  • Philippe Wenger
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 24)

Abstract

The design of new manipulators requires the knowledge of their kinematic behaviour. Important kinematic properties can be characterized by the determination of certain points of interest. Important points of interest are cusps and nodes, which are special singular points responsible for the non-singular posture changing ability and for the existence of voids in the workspace, respectively. In practice, numerical errors should be properly tackled when calculating these points. This paper proposes an interval analysis based approach for the design of a numerical algorithm that finds enclosures of points of interest in the workspace and joint space of the studied robot. The algorithm is applied on 3R manipulators with mutually orthogonal joint axes.

Keywords

Interval analysis Singular points 3R Robot Cusp Node 

References

  1. 1.
    Baili M, Wenger P, Chablat D (2004) A classification of 3R orthogonal manipulators by the topology of their workspace. IEEE international conference on robotics and automation, pp 1933–1938Google Scholar
  2. 2.
    Bohigas O, Manubens M, Ros L (2013) Singularities of non-redundant manipulators: a short account and a method for their computation in the planar case. Mech Mach Theory 68:1–17CrossRefGoogle Scholar
  3. 3.
    Bohigas O, Zlatanov D, Ros L, Manubens M, Porta JM (2012) Numerical computation of manipulator singularities. In: Robot Autom (ICRA), 2012 IEEE international conference on, pp 1351–1358. IEEEGoogle Scholar
  4. 4.
    Corvez S, Rouillier F (2004) Automated deduction in geometry, lecture notes in computer science. In: Chapter using computer algebra tools to classify serial manipulators, vol 2930. Springer, Berlin, pp 31–43Google Scholar
  5. 5.
    Husty M, Ottaviano E, Ceccarelli M (2008) Advances in robot kinematics, analysis and design. In: Chapter a geometrical characterization of workspace singularities in 3R manipulators. Springer, pp 411–418Google Scholar
  6. 6.
    Jaulin L, Kieffer M, Didrit O, Walter E (2001) Applied interval analysis with examples in parameter and state estimation. Springer-Verlag, Robust Control and RoboticsCrossRefzbMATHGoogle Scholar
  7. 7.
    Merlet JP (2011) Interval analysis and robotics. In: Robotics Research. Springer, pp 147–156Google Scholar
  8. 8.
    Moore RE (1996) Interval Analysis. Prentice-Hall, Englewood CliffsGoogle Scholar
  9. 9.
    Neumaier A (1990) Interval methods for systems of equations, encyclopedia of mathematics and its applications, vol 37. Cambridge University Press, CambridgeGoogle Scholar
  10. 10.
    Wenger P (2007) Cuspidal and noncuspidal robot manipulators. Robotica 25, pp 677–689. doi: 10.1017/S0263574707003761. URL http://journals.cambridge.org/article_S0263574707003761

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Romain Benoit
    • 1
    Email author
  • Nicolas Delanoue
    • 1
  • Sébastien Lagrange
    • 1
  • Philippe Wenger
    • 2
  1. 1.LARISAngersFrance
  2. 2.Institut de Recherche en Communications et Cybernétique de NantesNantes cedex 03France

Personalised recommendations