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

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

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

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

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

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

NUS CS52477 The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS52478 The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS52479 The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs  Algorithm

NUS CS The Gaussian Sampling Strategy for PRMs

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.

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

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.

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.

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.

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.

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.

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

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

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 ~