# Informed Sampling for Asymptotically Optimal Path Planning (Consolidated Version)

arXiv: https://arxiv.org/abs/1706.06454 · HTML: https://mlsanity.com/paper/1706.06454/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2017.

## Built on by (most cited first, 5 of 5)

- [Parallelised Diffeomorphic Sampling-based Motion Planning](https://mlsanity.com/paper/2108.11775/) (2021)
- [Optimal task and motion planning and execution for human-robot multi-agent systems in dynamic environments](https://mlsanity.com/paper/2303.14874/) (2023)
- [Speeding up deep neural network-based planning of local car maneuvers via efficient B-spline path construction](https://mlsanity.com/paper/2203.06963/) (2022)
- [Informed Steiner Trees: Sampling and Pruning for Multi-Goal Path Finding in High Dimensions](https://mlsanity.com/paper/2205.04548/) (2022)
- [Unified Linear Parametric Map Modeling and Perception-aware Trajectory Planning for Mobile Robotics](https://mlsanity.com/paper/2507.09340/) (2025)

## Abstract (arXiv)

Anytime almost-surely asymptotically optimal planners, such as RRT*, incrementally find paths to every state in the search domain. This is inefficient once an initial solution is found as then only states that can provide a better solution need to be considered. Exact knowledge of these states requires solving the problem but can be approximated with heuristics. This paper formally defines these sets of states and demonstrates how they can be used to analyze arbitrary planning problems. It uses the well-known L2 norm (i.e., Euclidean distance) to analyze minimum-path-length problems and shows that existing approaches decrease in effectiveness factorially (i.e., faster than exponentially) with state dimension. It presents a method to address this curse of dimensionality by directly sampling the prolate hyperspheroids (i.e., symmetric n-dimensional ellipses) that define the L2 informed set. The importance of this direct informed sampling technique is demonstrated with Informed RRT*. This extension of RRT* has less theoretical dependence on state dimension and problem size than existing techniques and allows for linear convergence on some problems. It is shown experimentally to find better solutions faster than existing techniques on both abstract planning problems and HERB, a two-arm manipulation robot.