Using Lie group symmetries for fast corrective motion planning

Seiler, Konstantin M., Singh, Surya P. N., Sukkarieh, Salah and Durrant-Whyte, Hugh (2012) Using Lie group symmetries for fast corrective motion planning. International Journal of Robotics Research, 31 2: 151-166. doi:10.1177/0278364911429977

Author Seiler, Konstantin M.
Singh, Surya P. N.
Sukkarieh, Salah
Durrant-Whyte, Hugh
Title Using Lie group symmetries for fast corrective motion planning
Journal name International Journal of Robotics Research   Check publisher's open access policy
ISSN 0278-3649
Publication date 2012-02
Year available 2011
Sub-type Article (original research)
DOI 10.1177/0278364911429977
Volume 31
Issue 2
Start page 151
End page 166
Total pages 16
Editor David Hsu
Volkan Isler
Jean-Claude Latombe
Ming C. Lin
Place of publication London, United Kingdom
Publisher Sage Publications
Collection year 2013
Language eng
Abstract In this paper we develop an algorithmic framework allowing for fast and elegant path correction exploiting Lie group symmetries and operating without the need for explicit control strategies such as cross-track regulation. These systems occur across the gamut of robotics, notably in locomotion, be it ground, underwater, airborne, or surgical domains. Instead of reintegrating an entire trajectory, the method selectively alters small key segments of an initial trajectory in a consistent way so as to transform it via symmetry operations. The algorithm is formulated for arbitrary Lie groups and applied in the context of the special Euclidean group and subgroups thereof. A sampling-based motion planner is developed that uses this method to create paths for underactuated systems with differential constraints. It is also shown how the path correction method acts as a controller within a feedback control loop for real-time path correction. These approaches are demonstrated for ground vehicles in the plane and for flexible bevel tip needle steering in space. The results show that using symmetry-based path correction for motion planning provides a prudent and simple, yet computationally tractable, integrated planning and control strategy.
Keyword Nonholonomic planning
Lie group symmetry
Path correction
Online systems
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online before print December 22, 2011. Special Issue on the Ninth International Workshop on Algorithmic Foundations of Robotics (WAFR).

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2013 Collection
School of Information Technology and Electrical Engineering Publications
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