Motion Planning for Autonomous Vehicles using Optimization over Graphs of Convex Sets
This paper explores using optimization over Graphs of Convex Sets (GCS) to approximate solutions to nonlinear optimal control problems in autonomous driving. By representing free space as a union of convex regions in a directed graph and parameterizing motion with Bézier curves and polynomial time-scaling, the method maintains convex constraints under a simplified dynamic model. Experiments on CommonRoad scenarios show trajectories closely matching nonlinear programming approaches, with improved computational efficiency and reduced sensitivity to initialization.
[2605.14199] Motion Planning for Autonomous Vehicles using Optimization over Graphs of Convex Sets
[Submitted on 13 May 2026]
Title:Motion Planning for Autonomous Vehicles using Optimization over Graphs of Convex Sets
View a PDF of the paper titled Motion Planning for Autonomous Vehicles using Optimization over Graphs of Convex Sets, by Matheus Wagner and 1 other authors
View PDF HTML (experimental)
Abstract:Motion planning for autonomous vehicles requires generating collision-free and dynamically feasible trajectories in complex environments under real-time constraints. While nonlinear optimal control formulations provide high-fidelity solutions, they are computationally demanding and sensitive to initialization, whereas geometric planning methods scale well but often decouple path selection from trajectory optimization. This paper studies the extent to which optimization over Graphs of Convex Sets (GCS) can approximate solutions of nonlinear optimal control problems in the context of autonomous driving. The free space is represented as a finite union of convex regions organized as a directed graph, allowing nonconvex geometry to be handled through discrete connectivity decisions while maintaining convex trajectory constraints within each region. Vehicle motion is parameterized using Bezier curves for the spatial path and a polynomial time-scaling function for temporal evolution. Under small-slip and linear tire assumptions, a simplified dynamic bicycle model enables approximate enforcement of dynamic feasibility through convex constraints on trajectory derivatives. The approach is evaluated in CommonRoad scenarios involving static obstacle avoidance and lane-changing maneuvers, and is compared against a nonlinear discrete-time optimal control formulation. The results indicate that the GCS-based method generates collision-free and dynamically consistent trajectories that closely match those obtained from the nonlinear program, while exhibiting improved computational efficiency and reduced sensitivity to initialization. These findings suggest that GCS provides a structured approximation of nonlinear motion planning problems, capturing dominant geometric and dynamic effects while preserving convexity in the continuous relaxation.
Subjects:
Robotics (cs.RO); Systems and Control (eess.SY)
Cite as: arXiv:2605.14199 [cs.RO]
(or arXiv:2605.14199v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2605.14199
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Matheus Wagner [view email] [v1] Wed, 13 May 2026 23:29:54 UTC (3,149 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Motion Planning for Autonomous Vehicles using Optimization over Graphs of Convex Sets, by Matheus Wagner and 1 other authors
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.RO
new | recent | 2026-05
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?)