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Quantitative Analysis of Nearest-Neighbors Search in High-Dimensional Sampling-Based Motion Planning

  • Erion Plaku
  • Lydia E. Kavraki
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 47)

Abstract

We quantitatively analyze the performance of exact and approximate nearest-neighbors algorithms on increasingly high-dimensional problems in the context of sampling-based motion planning. We study the impact of the dimension, number of samples, distance metrics, and sampling schemes on the efficiency and accuracy of nearest-neighbors algorithms. Efficiency measures computation time and accuracy indicates similarity between exact and approximate nearest neighbors.

Our analysis indicates that after a critical dimension, which varies between 15 and 30, exact nearest-neighbors algorithms examine almost all the samples. As a result, exact nearest-neighbors algorithms become impractical for sampling-based motion planners when a considerably large number of samples needs to be generated. The impracticality of exact nearest-neighbors algorithms motivates the use of approximate algorithms, which trade off accuracy for efficiency. We propose a simple algorithm, termed Distance-based Projection onto Euclidean Space (DPES), which computes approximate nearest neighbors by using a distance-based projection of high-dimensional metric spaces onto low-dimensional Euclidean spaces. Our results indicate DPES achieves high efficiency and only a negligible loss in accuracy.

Keywords

Motion Planning Critical Dimension Geodesic Distance Distance Metrics Motion Planner 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Erion Plaku
    • 1
  • Lydia E. Kavraki
    • 1
  1. 1.Department of Computer ScienceRice University 

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