| Publications |
Anna Yershova and Steven M. LaValle, 2004 IEEE International Conference on Robotics and Automation (ICRA 2004) Stephen R. Lindemann, Anna Yershova, and Steven M. LaValle, Sixth International Workshop on the Algorithmic Foundations of Robotics (WAFR 2004) |
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| Presentations |
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Software
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sampling.tar.gz | This software provides several uniform sequences over the three-dimensional rotation group, SO(3). These sequences are: layered Sukharev grid sequence, Sukharev grid sequence and random uniform sequence. The first two sequences are deterministic. The output is parameterized using the set of unit quaternions. The code is written using C++. The advantages of the deterministic sequences provided by this software are: uniformity (good covering of SO(3) is obtained, this can be formulated in terms of spherical dispersion and discrepancy), incremental quality (samples are added one by one maintaining the uniformity of the resulting distribution), explicit neighborhood structure (the samples are organized in a grid fashion, allowing efficient nearest neighbor calculations). It is important to note that the resulting sequence is infinite, that is, infinitely many samples can be generated retaining all of the above properties. Deterministic sequences were tested in sampling-based motion planning algorithms and compared to the performance of random sequences. While the performance efficiency is usually comparable, deterministic sequences provide important resolution completeness guarantees to motion planning methods. |