翻訳待ち：Dual Park-Ravani Interpolation of Rigid Motions: Acceleration-Field Continuity and Holonomic Hermite Repair
AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。ソース概要：arXiv:2608.28826v1 Announce Type: new Abstract: The Park-Ravani construction generates a twice continuously differentiable, frame-invariant spline on SO(3) by exponentiating cubic canonical-coordinate polynomials. We show that the construction transfers, without changing form, to the group of orthogonal dual tensors, a representation of rigid displacements. The transferred recurrence is stated compactly through the dual extension of the right Jacobian of the exponential map and its first Fr\'echet derivative. This yields interpolation of prescribed rigid poses and continuity of the body dual twist and its first derivative. Using the higher-order rigid-body kinematics of dual spatial twists, we then prove that the resulting curve has a continuous physical acceleration field, not merely a continuous quantity obtained by formally differentiating the dual part of a twist. We also distinguish algebraic dual transfer from temporal differential prolongation: their simultaneous first-order use takes place in a hyper-dual algebra, and interpolation of arbitrary prolonged nodal data need not be holonomic. A noncommuting three-pose example verifies the recurrence, all knot continuity statements, and dimensional covariance under a change from meters to millimeters. We define and analyze the first-order holonomy defect of a generic hyper-dual interpolant, exhibit an exact counterexample, and remove the defect by cubic or quintic Hermite interpolation in dual logarithmic coordinates.
AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。
--> [Submitted on 28 Aug 2026] Title:Dual Park-Ravani Interpolation of Rigid Motions: Acceleration-Field Continuity and Holonomic Hermite Repair View a PDF of the paper titled Dual Park-Ravani Interpolation of Rigid Motions: Acceleration-Field Continuity and Holonomic Hermite Repair, by Daniel Condurache View PDF HTML (experimental) Abstract:The Park-Ravani construction generates a twice continuously differentiable, frame-invariant spline on SO(3) by exponentiating cubic canonical-coordinate polynomials. We show that the construction transfers, without changing form, to the group of orthogonal dual tensors, a representation of rigid displacements. The transferred recurrence is stated compactly through the dual extension of the right Jacobian of the exponential map and its first Fréchet derivative. This yields interpolation of prescribed rigid poses and continuity of the body dual twist and its first derivative. Using the higher-order rigid-body kinematics of dual spatial twists, we then prove that the resulting curve has a continuous physical acceleration field, not merely a continuous quantity obtained by formally differentiating the dual part of a twist. We also distinguish algebraic dual transfer from temporal differential prolongation: their simultaneous first-order use takes place in a hyper-dual algebra, and interpolation of arbitrary prolonged nodal data need not be holonomic. A noncommuting three-pose example verifies the recurrence, all knot continuity statements, and dimensional covariance under a change from meters to millimeters. We define and analyze the first-order holonomy defect of a generic hyper-dual interpolant, exhibit an exact counterexample, and remove the defect by cubic or quintic Hermite interpolation in dual logarithmic coordinates. Comments: 12 pages. Ancillary Python programs reproduce the numerical verification Subjects: Robotics (cs.RO) MSC classes: 65D05, 65D17, 70B10, 22E70 Cite as: arXiv:2608.28826 [cs.RO] (or arXiv:2608.28826v1 [cs.RO] for this version) https://doi.org/10.48550/arXiv.2608.28826 arXiv-issued DOI via DataCite (pending registration) Submission history From: Daniel Condurache [view email] [v1] Fri, 28 Aug 2026 19:54:39 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled Dual Park-Ravani Interpolation of Rigid Motions: Acceleration-Field Continuity and Holonomic Hermite Repair, by Daniel Condurache View PDF HTML (experimental) TeX Source view license Current browse context: cs.RO new | recent | 2026-08 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?)