# The Provable Virtue of Laziness in Motion Planning

arXiv: https://arxiv.org/abs/1710.04101 · HTML: https://mlsanity.com/paper/1710.04101/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2017.

## Built on by (most cited first, 6 of 6)

- [Reducing Collision Checking for Sampling-Based Motion Planning Using Graph Neural Networks](https://mlsanity.com/paper/2210.08864/) (2022)
- [Active Learning of Abstract Plan Feasibility](https://mlsanity.com/paper/2107.00683/) (2021)
- [Policy-Guided Lazy Search with Feedback for Task and Motion Planning](https://mlsanity.com/paper/2210.14055/) (2022)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Leveraging Experience in Lazy Search](https://mlsanity.com/paper/2110.04669/) (2021)
- [T*varepsilon -- Bounded-Suboptimal Efficient Motion Planning for Minimum-Time Planar Curvature-Constrained Systems](https://mlsanity.com/paper/2204.01673/) (2022)

## Abstract (arXiv)

The Lazy Shortest Path (LazySP) class consists of motion-planning algorithms that only evaluate edges along shortest paths between the source and target. These algorithms were designed to minimize the number of edge evaluations in settings where edge evaluation dominates the running time of the algorithm; but how close to optimal are LazySP algorithms in terms of this objective? Our main result is an analytical upper bound, in a probabilistic model, on the number of edge evaluations required by LazySP algorithms; a matching lower bound shows that these algorithms are asymptotically optimal in the worst case.