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arXiv · 2005.01242

Probabilistic Analysis of RRT Trees

Konrad Anand·Luc Devroye
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Abstract

This thesis presents analysis of the properties and run-time of the Rapidly-exploring Random Tree (RRT) algorithm. It is shown that the time for the RRT with stepsize $\epsilon$ to grow close to every point in the $d$-dimensional unit cube is $\Theta\left(\frac1{\epsilon^d} \log \left(\frac1\epsilon\right)\right)$. Also, the time it takes for the tree to reach a region of positive probability is $O\left(\epsilon^{-\frac32}\right)$. Finally, a relationship is shown to the Nearest Neighbour Tree (NNT). This relationship shows that the total Euclidean path length after $n$ steps is $O(\sqrt n)$ and the expected height of the tree is bounded above by $(e + o(1)) \log n$.

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Konrad Anand, Luc Devroye. 2020-05-04. Probabilistic Analysis of RRT Trees. https://arxiv.org/abs/2005.01242

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