# Revisiting the Asymptotic Optimality of RRT^*

arXiv: https://arxiv.org/abs/1909.09688 · HTML: https://mlsanity.com/paper/1909.09688/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2019.

## Built on by (most cited first, 3 of 3)

- [Lazy Probabilistic Roadmaps Revisited](https://mlsanity.com/paper/2209.14471/) (2022)
- [Safe Path Planning and Observation Quality Enhancement Strategy for Unmanned Aerial Vehicles in Water Quality Monitoring Tasks](https://mlsanity.com/paper/2512.21375/) (2025)
- [Visual-RRT: Finding Paths toward Visual-Goals via Differentiable Rendering](https://mlsanity.com/paper/2604.16388/) (2026)

## Abstract (arXiv)

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 γ left(fraclog nnright)1/d to γ' left(fraclog nnright)1/(d+1) in order to account for the additional dimension of time that dictates the samples' ordering. Here γ, γ', are constants, and n, d, are the number of samples and the dimension of the problem, respectively.