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FineCog-Nav: Integrating Fine-grained Cognitive Modules for Zero-shot Multimodal UAV Navigation DENALI: A Dataset Enabling Non-Line-of-Sight Spatial Reasoning with Low-Cost LiDARs SENSE: Stereo OpEN Vocabulary SEmantic Segmentation Continual Hand-Eye Calibration for Open-world Robotic Manipulation PLAF: Pixel-wise Language-Aligned Feature Extraction for Efficient 3D Scene Understanding GaussianFlow SLAM: Monocular Gaussian Splatting SLAM Guided by GaussianFlow GIST: Multimodal Knowledge Extraction and Spatial Grounding via Intelligent Semantic Topology $π_{0.7}$: a Steerable Generalist Robotic Foundation Model with Emergent Capabilities R3D: Revisiting 3D Policy Learning Vision-Based Safe Human-Robot Collaboration with Uncertainty Guarantees Benchmarking Classical Coverage Path Planning Heuristics on Irregular Hexagonal Grids for Maritime Coverage Scenarios NEAT-NC: NEAT guided Navigation Cells for Robot Path Planning HRDexDB: A Large-Scale Dataset of Dexterous Human and Robotic Hand 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Feedback-Based Mobile Robot Navigation in 3-D Environments Using Artificial Potential Functions Technical Report
Ro'i Lang, Elon Rimon · 2026-01-14 · via cs.RO updates on arXiv.org

This technical report presents the construction and analysis of polynomial navigation functions for motion planning in 3-D workspaces populated by spherical and cylindrical obstacles. The workspace is modeled as a bounded spherical region, and obstacles are encoded using smooth polynomial implicit functions. We establish conditions under which the proposed navigation functions admit a unique non-degenerate minimum at the target while avoiding local minima, including in the presence of pairwise intersecting obstacles. Gradient and Hessian analyses are provided, and the theoretical results are validated through numerical simulations in obstacle rich 3-D environments.

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