RRT*の漸近最適性の再検討
Revisiting the Asymptotic Optimality of RRT$^*$
RRT*の最適性証明の論理的なギャップを指摘し、時間次元を考慮して接続半径を大きくすべきとする厳密な代替証明を与えた論文。
著者: Kiril Solovey, Lucas Janson, Edward Schmerling, Emilio Frazzoli, Marco Pavone
分類: cs.RO, math.OC
原文アブストラクト
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.
