Motion Planning via Manifold Samples

Oren Salzman; Michael Hemmer; Barak Raveh; Dan Halperin

doi:10.1007/978-3-642-23719-5_42

European Symposium on Algorithms

ESA 2011: Algorithms – ESA 2011 pp 493-505

Motion Planning via Manifold Samples

Authors
Authors and affiliations

Oren Salzman
Michael Hemmer
Barak Raveh
Dan Halperin

Conference paper

DOI: 10.1007/978-3-642-23719-5_42

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

Cite this paper as:: Salzman O., Hemmer M., Raveh B., Halperin D. (2011) Motion Planning via Manifold Samples. In: Demetrescu C., Halldórsson M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg

Abstract

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with sampling-based approaches that are appropriate for higher dimensions. We suggest taking samples that are entire low-dimensional manifolds of the configuration space. These samples capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms then provide powerful primitive operations for complete analysis of the low-dimensional manifolds. We have implemented our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles. To this end, we have developed a primitive operation for the analysis of an appropriate set of manifolds using arrangements of curves of rational functions. This modular integration of several carefully engineered components has lead to a significant speedup over the PRM sampling-based algorithm, which represents an approach that is prevalent in practice.

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Authors and Affiliations

Oren Salzman
- 1
Michael Hemmer
- 1
Barak Raveh
- 1
- 2
Dan Halperin
- 1

1.Tel-Aviv UniversityIsrael
2.Hebrew UniversityIsrael

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Motion Planning via Manifold Samples

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