Using Lie Group Symmetries for Fast Corrective Motion Planning

  • Konstantin Seiler
  • Surya P. N. Singh
  • Hugh Durrant-Whyte
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 68)


For a mechanical system it often arises that its planned motion will need to be corrected either to refine an approximate plan or to deal with disturbances. This paper develops an algorithmic framework allowing for fast and elegant path correction for nonholonomic underactuated systems with Lie group symmetries, which operates without the explicit need for control strategies. These systems occur frequently in robotics, particularly in locomotion, be it ground, underwater, airborne, or surgical domains. Instead of reintegrating an entire trajectory, the method alters small segments of an initial trajectory in a consistent way so as to transform it via symmetry operations. This approach is demonstrated for the cases of a kinematic car and for flexible bevel tip needle steering, showing a prudent and simple, yet computationally tractable, trajectory correction.


Control Input Base Space Algorithmic Framework Rapidly Explore Random Tree Initial Path 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Konstantin Seiler
    • 1
  • Surya P. N. Singh
    • 1
  • Hugh Durrant-Whyte
    • 1
  1. 1.Australian Centre for Field RoboticsUniversity of SydneyAustralia

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