Using Lie Group Symmetries for Fast Corrective Motion Planning

Using Lie Group Symmetries for Fast Corrective Motion Planning. Seiler, K., Singh, S. P. N., & Durrant-Whyte, H. In Algorithmic Foundations of Robotics IX, volume 68, of Springer Tracts in Advanced Robotics, pages 37-52. Springer, 2010.

Paper doi abstract bibtex

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 needle steering. Instead of re-integrating 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.

@INCOLLECTION{wafr2010.pathcorrection,
  author = {Konstantin Seiler and Surya P. N. Singh and Hugh Durrant-Whyte},
  title = {Using Lie Group Symmetries for Fast Corrective Motion Planning},
  booktitle = {Algorithmic Foundations of Robotics {IX}},
  publisher = {Springer},
  year = {2010},
  volume = {68},
  series = {Springer Tracts in Advanced Robotics},
  pages = {37-52},
  abstract = {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 needle steering. Instead of re-integrating 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.},
  doi = {10.1007/978-3-642-17452-0_3},
  pdf = {wafr2010_pathcorrecting.pdf},
  url = {http://bigbird.comp.nus.edu.sg/pmwiki/farm/wafr/uploads/Main/wafr2010_submission_30.pdf}
}

Downloads: 0