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[Submitted on 25 Jul 2026] Title:RMRRT: Riemannian Barrier Metric RRT for Inequality-Aware Steering on Equality Manifolds View a PDF of the paper titled RMRRT: Riemannian Barrier Metric RRT for Inequality-Aware Steering on Equality Manifolds, by Minhyeong Kang and Sanghyun Kim View PDF HTML (experimental) Abstract:This paper presents a motion planning framework that unifies equality and inequality constraints within a single geometric formulation for sampling-based planning in high-dimensional robotic systems. In conventional sampling-based planners, equality constraints are typically enforced through projection, whereas inequality constraints are handled separately through binary validity checks such as collision testing, often leading to inefficient exploration. To address this limitation, we propose Riemannian Barrier Metric RRT (RMRRT), which constructs a unified local geometry for planning on equality-constrained manifolds. RMRRT first builds an ambient barrier metric from inequality-sensitive barrier terms and then induces a tangent-space metric via a (G)-orthogonal projection associated with the equality constraints. The resulting tangent-space metric is used consistently in both steering and nearest-neighbor selection, biasing exploration away from nearby inequality boundaries while preserving first-order equality consistency. In this work, the metric is instantiated from signed-distance-based geometric proxy inequalities to provide collision-informative tangent-space directions; hard feasibility is enforced separately through standard validity checks. Experimental results show that RMRRT achieves a 100% success rate across diverse constrained manipulation tasks in both simulation and real-world settings, while reducing planning time relative to representative constrained planning baselines. Ablation studies further demonstrate that the proposed metric improves exploration quality by reducing rejected samples and shortening path length. Experiment videos and source code are available at: this https URL Subjects: Robotics (cs.RO) Cite as: arXiv:2610.06863 [cs.RO] (or arXiv:2610.06863v1 [cs.RO] for this version) https://doi.org/10.48550/arXiv.2610.06863 arXiv-issued DOI via DataCite Submission history From: Sanghyun Kim [view email] [v1] Sat, 25 Jul 2026 20:36:18 UTC (1,853 KB) Full-text links: Access Paper: View a PDF of the paper titled RMRRT: Riemannian Barrier Metric RRT for Inequality-Aware Steering on Equality Manifolds, by Minhyeong Kang and Sanghyun Kim 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?)