Geodesic path planning characteristics of the reconfigurable 1-S robot workspaces for hyperbolic, elliptical, and Euclidean geometries

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dc.contributor.authorŞahin, Haydar
dc.date.accessioned2025-01-23T05:29:18Z
dc.date.available2025-01-23T05:29:18Z
dc.date.issued2024
dc.departmentFakülteler, Mühendislik Fakültesi, Mekatronik Mühendisliği Bölümü
dc.description.abstractThe path-planning strategies are implemented by establishing the Riemann curvature tensor and geodesic equations of the 1-S robot workspace. This paper’s originality lies in formulation of the parametric 1-S robot workspace for path planning, which is based on the differential geometry of the geodesic and Riemann curvature equations. The novel results in defining the path plan with diffeomorphic and expandable trajectories with zero and negative sectional curvatures are encouraging, as shown in the research article’s result sections. The constant negative, constant positive, and zero sectional curvatures produce hyperbolic, elliptical, and Euclidean geometries. The workspace equation, derived using Lie algebra, defines the parameters of u12, u3, and u4 to obtain the shortest distances in path planning. The geodesic equations determine the shortest distances in the context of Riemann curvature tensor equations. These parameters from the workspace equation (α1, α2, θ1, r1) are used in the geodesic and Riemann curvature tensor equations. The results show that one needs to choose the most convenient parameters of the mechanism for path-planning capabilities. Both the topology of the mechanism, which is 1-S herein and the parameters of the workspaces should be selected for the pre-defined trajectories of the path planning, as shown in the results. The reconfigurable robots have many mechanism topologies to transform.
dc.identifier.doi10.24425/acs.2024.153102
dc.identifier.endpage803
dc.identifier.issn1230-2384
dc.identifier.issue4
dc.identifier.scopus2-s2.0-85214578219
dc.identifier.scopusqualityQ3
dc.identifier.startpage777
dc.identifier.urihttps://doi.org/10.24425/acs.2024.153102
dc.identifier.urihttps://hdl.handle.net/11501/1602
dc.identifier.volume34
dc.identifier.wosWOS:001398153800006
dc.identifier.wosqualityQ2
dc.indekslendigikaynakScopus
dc.indekslendigikaynakWeb of Science
dc.institutionauthorŞahin, Haydar
dc.institutionauthorid0000-0001-8435-9448
dc.language.isoen
dc.publisherPolska Akademia Nauk
dc.relation.ispartofArchives of Control Sciences
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectClifford Algebra
dc.subjectDirac Vector
dc.subjectGeodesic Equations
dc.subjectPath Planning
dc.subjectRiemann Curvature Tensor
dc.subjectRobot Workspace
dc.titleGeodesic path planning characteristics of the reconfigurable 1-S robot workspaces for hyperbolic, elliptical, and Euclidean geometries
dc.typeArticle

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