The Gaussian sampling strategy follows some of the same motivation for sampling on the boundary. In this case, the goal is to obtain points near by using a Gaussian distribution that biases the samples to be closer to , but the bias is gentler, as prescribed by the variance parameter of the Gaussian. The samples are generated as follows. Generate one sample, , uniformly at random. Following this, generate another sample, , according to a Gaussian with mean ; the distribution must be adapted for any topological identifications and/or boundaries of . If one of or lies in and the other lies in , then the one that lies in is kept as a vertex in the roadmap. For some examples, this dramatically prunes the number of required vertices.

Steven M LaValle 2020-08-14