Biconvex Optimization for Smooth Minimum-Time Trajectories around Convex Obstacles
arXiv:2608.02834v1 Announce Type: new Abstract: We present a biconvex approach for minimum-time motion planning around convex obstacles that is guaranteed to converge, is anytime, and supports derivative constraints to arbitrary order. We jointly convexify the minimum-time objective and all derivative constraints through a change of variables, and handle collision avoidance via time-varying separating planes, reducing the problem to a biconvex program. This program is solved by alternating between computing maximum-margin separating planes and optimizing the trajectory. By only adding planes for obstacles that the current iterate collides with, the trajectory can jump around obstacles and escape local minima. The method is guaranteed to converge starting from a simple collision-free polygonal curve. In our experiments on drone navigation and dual-arm bin unloading, we find that the proposed method reliably produces high-quality trajectories with computation times comparable to state-of-the-art decomposition-based motion planners, while handling a larger class of problems and being substantially more robust to bad initialization. Project page:https://wernerpe.github.io/bmtp-website/
-->
[Submitted on 3 Aug 2026]
Title:Biconvex Optimization for Smooth Minimum-Time Trajectories around Convex Obstacles
View a PDF of the paper titled Biconvex Optimization for Smooth Minimum-Time Trajectories around Convex Obstacles, by Peter Werner and 2 other authors
View PDF HTML (experimental)
Abstract:We present a biconvex approach for minimum-time motion planning around convex obstacles that is guaranteed to converge, is anytime, and supports derivative constraints to arbitrary order. We jointly convexify the minimum-time objective and all derivative constraints through a change of variables, and handle collision avoidance via time-varying separating planes, reducing the problem to a biconvex program. This program is solved by alternating between computing maximum-margin separating planes and optimizing the trajectory. By only adding planes for obstacles that the current iterate collides with, the trajectory can jump around obstacles and escape local minima. The method is guaranteed to converge starting from a simple collision-free polygonal curve. In our experiments on drone navigation and dual-arm bin unloading, we find that the proposed method reliably produces high-quality trajectories with computation times comparable to state-of-the-art decomposition-based motion planners, while handling a larger class of problems and being substantially more robust to bad initialization. Project page:this https URL
Comments: 18 pages, 9 figures, 4 tables. Submitted to IEEE Transactions on Robotics. Project page: this https URL Code: this https URL
Subjects:
Robotics (cs.RO); Systems and Control (eess.SY)
Cite as: arXiv:2608.02834 [cs.RO]
(or arXiv:2608.02834v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2608.02834
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Peter Werner [view email] [v1] Mon, 3 Aug 2026 19:48:24 UTC (15,467 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Biconvex Optimization for Smooth Minimum-Time Trajectories around Convex Obstacles, by Peter Werner and 2 other authors
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.RO
new | recent | 2026-08
Change to browse by:
cs cs.SY eess eess.SY
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?)