Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Recent progress in motion planning has made it possible to determine homotopy inequivalent trajectories beten an initial and terminal configuration in a robot configuration space. Current approaches have hover either assumed the knowledge of differential one-forms related to a skeletonization of the collision space, or have relied on a simplicial representation of the free space. Both of these approaches are currently hover not yet practical for higher dimensional configuration spaces.  propose 2D topological task projections (TTPs): mappings from the configuration space to 2-dimensional spaces where simplicial complex filtrations and persistent homology can identify topological properties of the high-dimensional free configuration space. Our approach only requires the availability of collision free samples to identify winding centers that can be used to determine homotopy inequivalent trajectories.  propose the Winding Augmented RRT and RRT* (WA-RRT/RRT*) algorithms using which homotopy inequivalent trajectories can be found.  evaluate our approach in experiments with configuration spaces of planar linkages with 2–10 degrees of freedom. Results indicate that our approach can reliably identify suitable topological task projections and our proposed WA-RRT and WA-RRT* algorithms re able to identify a collection of homotopy inequivalent trajectories in each considered configuration space dimension.
['Florian T. Pokorny', 'Danica Kragic', 'Lydia E. Kavraki', 'Ken Goldberg']
I am writing a research paper on a idea High-dimensional Winding-Augmented Motion Planning with 2D topological task projections and persistent homology
[{"from": "human", "value": "I am writing a research paper on a idea High-dimensional Winding-Augmented Motion Planning with 2D topological task projections and persistent homology"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Recent progress in motion planning has made it possible to determine homotopy inequivalent trajectories beten an initial and terminal configuration in a robot configuration space. Current approaches have hover either assumed the knowledge of differential one-forms related to a skeletonization of the collision space, or have relied on a simplicial representation of the free space. Both of these approaches are currently hover not yet practical for higher dimensional configuration spaces.  propose 2D topological task projections (TTPs): mappings from the configuration space to 2-dimensional spaces where simplicial complex filtrations and persistent homology can identify topological properties of the high-dimensional free configuration space. Our approach only requires the availability of collision free samples to identify winding centers that can be used to determine homotopy inequivalent trajectories.  propose the Winding Augmented RRT and RRT* (WA-RRT/RRT*) algorithms using which homotopy inequivalent trajectories can be found.  evaluate our approach in experiments with configuration spaces of planar linkages with 2\u201310 degrees of freedom. Results indicate that our approach can reliably identify suitable topological task projections and our proposed WA-RRT and WA-RRT* algorithms re able to identify a collection of homotopy inequivalent trajectories in each considered configuration space dimension."}]