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[Submitted on 14 Oct 2026] Title:BubbleCBF: Constructive Safety for Second-Order Systems and Application to Autonomous Robot Navigation in Unknown Environments View a PDF of the paper titled BubbleCBF: Constructive Safety for Second-Order Systems and Application to Autonomous Robot Navigation in Unknown Environments, by Mani Amani and 5 other authors View PDF HTML (experimental) Abstract:Satisfying safety constraints for systems with second-order dynamics is challenging because a position constraint may require infeasible deceleration. Higher-order control barrier functions (CBFs) provide an approach for expressing safety conditions for such systems but feasibility depends on the system dynamics and available control authority. We develop a constructive approach for designing feasible safety constraints for second-order control-affine systems. Starting from a signed distance function (SDF), we construct collision-free spheres, i.e., bubbles, in position space, and use their quadratic geometry and overlap to construct a velocity-dependent safety constraint. The associated safe set is represented as a union of intersections and enforced through a quadratic-program safety filter. Under mild assumptions on the dynamics, bubble overlap, and design parameters, we prove that the quadratic-program-based controller is well defined, continuous in the system state, and renders the set forward invariant. We also derive sufficient conditions for feasibility under bounded inputs. We demonstrate that our BubbleCBF, applied to a differential-drive robot, achieves safe autonomous navigation in unknown environments. Videos and results are available at: this https URL. Subjects: Robotics (cs.RO) Cite as: arXiv:2610.20895 [cs.RO] (or arXiv:2610.20895v1 [cs.RO] for this version) https://doi.org/10.48550/arXiv.2610.20895 arXiv-issued DOI via DataCite (pending registration) Submission history From: Mani Amani [view email] [v1] Wed, 14 Oct 2026 20:24:47 UTC (6,088 KB) Full-text links: Access Paper: View a PDF of the paper titled BubbleCBF: Constructive Safety for Second-Order Systems and Application to Autonomous Robot Navigation in Unknown Environments, by Mani Amani and 5 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.RO new | recent | 2026-10 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?)