The Gaussian Sampling Strategy for Probalistic Roadmap Planners

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

Sampling a Point Uniformly at Random – A Recap repeat sample a configuration q with a suitable sampling strategy ifq is collision-free then add q to the roadmap R connect q to existing milestones returnR NUS CS5247

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 CS5247

The Gaussian Sampling Strategy for PRMs • Random Sampler (about 13000 samples) • Gaussian Sampler (about 150 samples) NUS CS5247

The Gaussian Sampling Strategy for PRMs • Adopts the idea of Gaussian Blurring in image processing. NUS CS5247

The Gaussian Sampling Strategy for PRMs • Algorithm NUS CS5247

The Gaussian Sampling Strategy for PRMs NUS CS5247

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 CS5247

The Gaussian Sampling Strategy for PRMs • Extension • Use 3 samples instead of 2 • Gaussian Sampler (using pairs) • Gaussian Sampler (using triples) NUS CS5247

The Gaussian Sampling Strategy for PRMs – Experimental Results • Random sampler required about 13000 nodes. • Gaussian sampler required 150 nodes. • Random sampler took about 60 times longer than the Gaussian sampler. NUS CS5247

The Gaussian Sampling Strategy for PRMs – Experimental Results • A scene requiring a difficult twist of the robot. • Random sampler required about 10000 nodes. • Gaussian sampler required 750 nodes. • Random sampler took about 13 times longer than the Gaussian sampler. NUS CS5247

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 CS5247

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 CS5247

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 CS5247

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 CS5247

Comparison between Gaussian Sampling and Bridge Test Gaussian Sampling Bridge Test NUS CS5247

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 ~ NUS CS5247

The Gaussian Sampling Strategy for Probalistic Roadmap Planners