Robotic Approaches at the Crossroads of Chaos, Fractals and Percolation Theory

  • Burak H. Kaygisiz
  • Murat Karahan
  • Aydan M. ErkmenEmail author
  • Ismet Erkmen
Part of the Understanding Complex Systems book series (UCS)


Nonlinear dynamics and chaos in robots have been extensively studied in the fields of service robots, humanoids and biologically inspired systems such as swarms, mobile sensor networks and bio-robots. This chapter surveys chaos in robots while introducing novel approaches to overcome the uncertainty in robotic systems stemming from chaotic dynamics and environments. The chapter begins with chaotic motions in feedback controlled two-and three-degree-of-freedom robots and continues in expending into higher degrees of freedom spanning the fields of biologically inspired robotics. Chaos arising through bifurcations under parametric changes in robotic devices is overviewed including detailed phase plane analyses. This chapter also provides the detailed overview of our works in the relevant topic of chaotic analyses of robotic systems dealing with the identification of the chaotic boundaries in nonlinear robotic systems, using cell mapping equipped with measures of fractal dimension and rough sets. Moreover, fractal structures that motivated roboticists to generate scale invariant modular robots are explained throughout the chapter. Lastly, percolation guided prioritized exploration technique for a search and rescue robot in chaotic environment is presented.


Fractal Dimension Mobile Robot Lyapunov Exponent Strange Attractor Percolation Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Burak H. Kaygisiz
    • 1
  • Murat Karahan
    • 2
  • Aydan M. Erkmen
    • 3
    Email author
  • Ismet Erkmen
    • 4
  1. 1.KAREL-ARGEAnkaraTurkey
  2. 2.TUBITAK-UZAY ODTU YerleskesiAnkaraTurkey
  3. 3.Department of Electrical and Electronics EngineeringMiddle East Technical UniversityAnkaraTurkey
  4. 4.Electrical Engineering DepartmentMiddle East Technical UniversityAnkaraTurkey

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