Geodesic path planning characteristics of the reconfigurable 1-S robot workspaces for hyperbolic, elliptical, and Euclidean geometries
The 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 robotworkspace for path planning, which is based on the differential geometry of the geodesi...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Polish Academy of Sciences
2024-12-01
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| Series: | Archives of Control Sciences |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/133807/art06.pdf |
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| Summary: | The 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 robotworkspace 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 ��1, ��2, ��3, and ��4 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 (��1, ��2, ��1, ��1) 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. |
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| ISSN: | 1230-2384 |