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Complete Title and Authors MAPRM : A Probabilistic Roadmap Planner with Sampling on the Medial Axis of the Free Space [ 2 ]
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wilmarth, Steven A. Amato, Nancy M. Stiller, Peter F. |
| Copyright Year | 2013 |
| Abstract | The method presented in this research paper takes advantage of the fact that the Medial Axis of the Configuration Space is a Strong Deformation Retract (SDR) of the whole Configuration Space, i.e., a path exists for two configurations if and only if there exists a homotopic path for their images in the Medial Axis. This research paper presents mathematical properties of the Medial Axis for a configuration space modeled as the closed union of disjoint polygons on a plane (2D). It also explains why there are some configurations (non-convex vertices) that cannot be mapped to the medial axis in a continuous way as to obtain an SDR of the original configuration space. The algorithm consists on using a Uniform Sampler to get initial configurations , and then retracts each of them to the Medial Axis of the C-Space. After generating the desired number of samples, it connects the different nodes, and then the Roadmap is ready for queries. The interesting part, however, is the retraction of a given configuration q to the medial axis. This is done by finding the closest configuration q c to q in the boundary set of the Free Space δ(Q f ree) and moving q away from the obstacle surface along the vector − → qq c until q c changes or is not unique anymore. At that point q will be on the medial axis. The mathematical results for this method show that this method does increase the number of samples in narrow passages in such a way that it does not depend on the size of the narrow passage, but the size and shape of the obstacles around it. More accurately, the probability might not increase as much for a given narrow passage, if the medial axis of the obstacle bounding it is very close to its surface. This happens because the probability changes from P r(A) = µ(N) µ(Q f ree) to P r(A) = µ(N)+µ(V N) µ(Q) , where A is the event of sampling the Narrow Passage N using PRM, A is the event of sampling N using MAPRM, µ is a function that maps a set to its volume, and V N is the set of points in the obstacle around N that are also mapped to the Medial Axis in N. This paper also presents an adaptation of the method to a free-flying rigid object in three dimensions. … |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://parasol.tamu.edu/people/aescalante/LiteratureSurvey.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
