Using Lie Group Symmetries of Fast Corrective Motion Planning. Seiler, K., Singh, S. P. N., , Sukkarieh, S., & Durrant-Whyte, H. The International Journal of Robotics Research, 31(2):151-166, 2012. doi abstract bibtex 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.
@ARTICLE{ijrr.fmc.2012,
author = {Konstantin Seiler and Surya P. N. Singh and and Salah Sukkarieh and
Hugh Durrant-Whyte},
title = {Using Lie Group Symmetries of Fast Corrective Motion Planning},
journal = {The International Journal of Robotics Research},
year = {2012},
volume = {31},
pages = {151-166},
number = {2},
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.},
doi = {10.1177/0278364911429977},
fauthor = {Konstantin Seiler and Surya P. N. Singh and Hugh Durrant-Whyte},
owner = {uqssing7},
pdf = {IJRR_2012_Seiler_151-66.pdf},
timestamp = {2012.02.16}
}
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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. 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These systems\r\n\t\r\n\toccur across the gamut of robotics, notably in locomotion, be it ground,\r\n\tunderwater, airborne, or surgical domains. Instead\r\n\t\r\n\tof reintegrating an entire trajectory, the method selectively alters\r\n\tsmall key segments of an initial trajectory in a consistent\r\n\t\r\n\tway so as to transform it via symmetry operations. The algorithm is\r\n\tformulated for arbitrary Lie groups and applied in\r\n\t\r\n\tthe context of the special Euclidean group and subgroups thereof.\r\n\tA sampling-based motion planner is developed that\r\n\t\r\n\tuses this method to create paths for underactuated systems with differential\r\n\tconstraints. It is also shown how the path\r\n\t\r\n\tcorrection method acts as a controller within a feedback control loop\r\n\tfor real-time path correction. These approaches are\r\n\t\r\n\tdemonstrated for ground vehicles in the plane and for flexible bevel\r\n\ttip needle steering in space. 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