[Submitted on 3 Sep 2026]
Title:Achieving Asymptotic Near-Optimality Without $δ$-Similarity
View a PDF of the paper titled Achieving Asymptotic Near-Optimality Without $\delta$-Similarity, by Michael Moncton and Eric Frew
View PDF HTML (experimental)
Abstract:Sampling-based motion planning algorithms are a popular class of trajectory planning algorithm due to their speed in complex, high-dimensional environments and ability to handle kinodynamic constraints, specifically through the use of forward dynamics propagation. Many such planners claim to achieve asymptotic near-optimality by proving the almost sure sampling of trajectories that are close to an optimal trajectory in the state space, known as $\delta$-similar trajectories. This paper shows that the proof behind asymptotic $\delta$-similarity relies on an unstated assumption that $\delta$-similar trajectory segments will always be kept once sampled. This assumption does not hold in general. A problematic case, referred to as ``crowding out,'' is described, where locally low-cost paths prevent trajectories that are $\delta$-similar to the optimal trajectory from being added to the tree. It is shown, however, that asymptotic near-optimality guarantees can still be achieved without guarantees of $\delta$-similar solution trajectories when crowding out is properly accounted for. An example environment and system are provided where crowding out is shown to occur, demonstrating a scenario where inductively sampling a $\delta$-similar solution trajectory is impossible.
Comments: Submitted to IEEE RA-L
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2609.04464 [cs.RO]
(or arXiv:2609.04464v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2609.04464
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Michael Moncton [view email] [v1] Thu, 3 Sep 2026 20:46:08 UTC (277 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Achieving Asymptotic Near-Optimality Without $\delta$-Similarity, by Michael Moncton and Eric Frew
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.RO
new | recent | 2026-09
Change to browse by:
cs
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
Author
Venue
Institution
Topic
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)