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- W2974656257 abstract "RRT* is one of the most widely used sampling-based algorithms for asymptotically-optimal motion planning. This algorithm laid the foundations for optimality in motion planning as a whole, and inspired the development of numerous new algorithms in the field, many of which build upon RRT* itself. In this paper, we first identify a logical gap in the optimality proof of RRT*, which was developed in Karaman and Frazzoli (2011). Then, we present an alternative and mathematically-rigorous proof for asymptotic optimality. Our proof suggests that the connection radius used by RRT* should be increased from $gamma left(frac{log n}{n}right)^{1/d}$ to $gamma' left(frac{log n}{n}right)^{1/(d+1)}$ in order to account for the additional dimension of time that dictates the samples' ordering. Here $gamma$, $gamma'$, are constants, and $n$, $d$, are the number of samples and the dimension of the problem, respectively." @default.
- W2974656257 created "2019-09-26" @default.
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- W2974656257 date "2019-09-20" @default.
- W2974656257 modified "2023-09-23" @default.
- W2974656257 title "Revisiting the Asymptotic Optimality of RRT" @default.
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