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NUS CS5247 The Gaussian Sampling Strategy for Probalistic Roadmap Planners Valdrie Boor, Mark H. Overmars, A. Frank van der Stappen, 1999 Wai Kok Hoong

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NUS CS52472 Sampling a Point Uniformly at Random – A Recap repeat sample a configuration q with a suitable sampling strategy if q is collision-free then add q to the roadmap R connect q to existing milestones return R

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NUS CS52473 Sampling a Point Uniformly at Random – A Recap repeat sample a configuration q with a suitable sampling strategy if q is collision-free then add q to the roadmap R connect q to existing milestones return R

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NUS CS52474 The Gaussian Sampling Strategy for PRMs Obstacle-sensitive strategy Idea: Sample near the boundaries of the C- space obstacles with higher probability. Rationale: The connectivity of free space is more difficult to capture near narrow passages than in wide-open area

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NUS CS52475 The Gaussian Sampling Strategy for PRMs Random Sampler (about samples) Gaussian Sampler (about 150 samples)

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NUS CS52476 The Gaussian Sampling Strategy for PRMs Adopts the idea of Gaussian Blurring in image processing.

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NUS CS52477 The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS52478 The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS52479 The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs Algorithm

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NUS CS The Gaussian Sampling Strategy for PRMs

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NUS CS The Gaussian Sampling Strategy for PRMs Pros May lead to discovery of narrow passages or openings to narrow passages. Cons The algorithm dose not distinguish between open space boundaries and narrow passage boundaries.

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NUS CS The Gaussian Sampling Strategy for PRMs Extension Use 3 samples instead of 2 Gaussian Sampler (using pairs) Gaussian Sampler (using triples)

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NUS CS The Gaussian Sampling Strategy for PRMs – Experimental Results Random sampler required about nodes. Gaussian sampler required 150 nodes. Random sampler took about 60 times longer than the Gaussian sampler.

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NUS CS The Gaussian Sampling Strategy for PRMs – Experimental Results A scene requiring a difficult twist of the robot. Random sampler required about nodes. Gaussian sampler required 750 nodes. Random sampler took about 13 times longer than the Gaussian sampler.

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NUS CS The Gaussian Sampling Strategy for PRMs – Experimental Results A scene with 5000 obstacles. Random sampler required over 450 nodes. Gaussian sampler required about 85 nodes. Random sampler took about 4 times longer than the Gaussian sampler.

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NUS CS The Gaussian Sampling Strategy for PRMs – Experimental Results Running time of algorithm increases when sigma is chosen to be very small because hard to find a pair of nodes that generates a successful sample, thus performance deterioration. When sigma is chosen to be very large, output of sampler started to approximate random sampling, thus performance also deteriorated. Choose sigma such that most configurations lie at a distance of at most the length of the robot from the obstacles.

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NUS CS The Bridge Test for Sampling Narrow Passages with PRMs Narrow-passage strategy Rationale: Finding the connectivity of the free space through narrow passage is the only hard problem.

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NUS CS The Bridge Test for Sampling Narrow Passages with PRMs The bridge test most likely yields a high rejection rate of configurations It generally results in a smaller number of milestones, hence fewer connections to be tested Since testing connections is costly, there can be significant computational gain

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NUS CS Comparison between Gaussian Sampling and Bridge Test Gaussian SamplingBridge Test

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NUS CS Summary Sample near the boundaries of the C-space obstacles The connectivity of free space is more difficult to capture near its narrow passages than in wide-open area Random Sampler is faster in scenes where the obstacles are reasonably distributed with wide corridors. Gaussian Sampler is faster in scenes where there is varying obstacle density, resulting in large open areas and small passages. ~ The End ~

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