Class #5: Sampling-Based Motion Planning: Probabilistic Roadmaps
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The figure on the left illustrates the concept of a probabilistic roadmap. The figure in the middle shows the milestones of a roadmap created for a virtual camera in a home. The figure on the right shows a probabilistic roadmap tree for docking a spacecraft against a space station (from Jeff Phillips).

• Topics
  - Principle, rationale, and requirements of probabilistic roadmaps
  - Multi- and Single-query PRM planners
  - Narrow passage issue and expansiveness of free space
  - Probabilistic completeness and convergence of PRM planners
• Required Readings:
• Basic paper on probabilistic roadmaps:
  L.E. Kavraki, P. Svestka, J.C. Latombe, and M. Overmars. Probabilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces. IEEE Transactions on Robotics and Automation, 12(4):566-580, 1996 [pdf]
• Analysis of probabilistic-roadmap planner:
  D. Hsu, J.C. Latombe, and H. Kurniawati. On the Probabilistic Foundations of Probabilistic Roadmap Planning. Int. J. of Robotics Research, 25(7):627-643, July 2006 [pdf]
• Other Readings:
• Computation of neearest neighbors in configuration space:
  Plaku, E. and Kavraki, L. E. . Quantitative Analysis of Nearest Neighbors Search in High-Dimensional Sampling-based Motion Planning. In Workshop on Algorithmic Foundations of Robotics (WAFR), New York City, NY, July 2006. [pdf]
• Deterministic vs. random sampling:
  S. M. LaValle, M. S. Branicky, and S. R. Lindemann. On the relationship between classical grid search and probabilistic roadmaps. International Journal of Robotics Research, 23(7/8):673-692, July/August 2004. [pdf]
• A number of papers on probabilistic roadmaps and related methods can be found at the websites of:
  - Lydia Kavraki
  - Nancy Amato
  - Mark Overmars
  - David Hsu
  - James Kuffner
  - Steve LaValle
  - MOLOG project
  
  
• Slides