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sample points (consider just the line segmentp0p1in Fig. 6(a)), and we are consideringthe addition of a new sample pointp. We compute the closest pointqon the currentspanning tree top. Note thatqdoes not need to be a sampled point. It is allowed tolie within the interior of an edge of the spanning tree. If so, we add the pointqas anew vertex to the spanning tree.We then consider the line segment fromptoq.Ifthis line segment lies entirely within free space, we add it to the tree (see pointsp2andq2in Fig. 6(a) andp3andq3in Fig. 6(b)). If not (seeq4top4in Fig. 6(c)), we trimthe segment back to obtain the longest subsegment that lies within free space with oneendpoint atq. Letqp0denote this segment (seeq4p04in Fig. 6(d)). We add this segmentto the tree. The result is called arapidly-expanding random treeor (RRT).Next to PRMs, RRTs are perhaps the most widely used method for computing connec-tivity structures in configuration spaces. Notice that both PRMs and RRTs have theadvantage that they can be applied in configuration spaces of arbitrary dimensions.Lecture 177Spring 2018
CMSC 425Dave Mount & Roger Eastman(a)(b)(c)p2q2p0p1p3q3p2q2p0p1p2q2p0p1p3q3p4q4p04p2q2p0p1p3q3p4q4(d)Fig. 6: Generating a roadmap through the use of rapidly-expanding random trees (RRTs).Lecture 178Spring 2018