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cs.RO updates on arXiv.org

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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Invariant Center Power and Elliptic Loci of Poncelet Triangles
Mark Helman, Dominique Laurain, Ronaldo Garcia, Dan Reznik · 2021-02-18 · via cs.RO updates on arXiv.org

We study center power with respect to circles derived from Poncelet 3-periodics (triangles) in a generic pair of ellipses as well as loci of their triangle centers. We show that (i) for any concentric pair, the power of the center with respect to either circumcircle or Euler's circle is invariant, and (ii) if a triangle center of a 3-periodic in a generic nested pair is a fixed affine combination of barycenter and circumcenter, its locus over the family is an ellipse.

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