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Topological Complexity and Its Applications in Rational Configuration Spaces

This work delves into the topological complexity of rational configuration spaces, focusing on implications in robot motion planning. Key contributions include the definition of topological complexity, foundational properties, and computational methods presented throughout various academic contributions. The synergy between topological robotics and motion planning is highlighted, alongside significant results such as theorems regarding the detection of spaces where topological complexity is minimized. Insights from notable researchers like Michael Farber, Daniel Quillen, and Dennis Sullivan enrich the discourse on rational homotopy theory and its applications in robotics.

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Topological Complexity and Its Applications in Rational Configuration Spaces

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  1. Topological complexity of rational configuration spaces and applications EACAT4 2011

  2. Configuration space Robot motion planning

  3. Jean Claude Latombe, Kluwer 1991 Topological robotics in motion plannings

  4. Definition

  5. Topological complexity Remark Michael Farber, 2003

  6. A. Schwarz Firstproperties

  7. Computing thetopologicalcomplexity M. Farber, J. González, S. Tabachnikov, S. Yuzvinsky,… y

  8. Corollary M. Farber, S. Tabachnikov, S. Yuzvinsky, 2003 J. Adem, S. Gitler, I. James, 1972

  9. Problem Michael Farber, 2005

  10. Rationalhomotopytheory: thebasics Dennis Sullivan 1977 Daniel Quillen 1969

  11. Theorem Problem’ Theorem L. Lechuga, A. M.

  12. Theanswer… B. Jessup , A. M., P.E. Parent Theorem

  13. Someapplications… Corollary 1. Topologicalcomplexity of formal spaces

  14. Examples…

  15. 2. Detection of spacesforwhich TC equalscat B. Jessup , A. M., P.E. Parent Theorem

  16. 3. Reducedtopologicalcomplexity Theorem

  17. 4. A robot withan extra arm Remark Theorem B. Jessup , A. M., P.E. Parent

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