TY - GEN
T1 - On the power of manifold samples in exploring configuration spaces and the dimensionality of narrow passages
AU - Salzman, Oren
AU - Halperin, Dan
N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2013.
PY - 2013
Y1 - 2013
N2 - We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a sixdimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.
AB - We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a sixdimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.
UR - http://www.scopus.com/inward/record.url?scp=85009499754&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-36279-8_19
DO - 10.1007/978-3-642-36279-8_19
M3 - منشور من مؤتمر
SN - 9783642362781
T3 - Springer Tracts in Advanced Robotics
SP - 313
EP - 329
BT - Springer Tracts in Advanced Robotics
A2 - Frazzoli, Emilio
A2 - Roy, Nicholas
A2 - Lozano-Perez, Tomas
A2 - Rus, Daniela
T2 - 10th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2012
Y2 - 13 June 2012 through 15 June 2012
ER -