Federico Ardila ; Hanner Bastidas ; Cesar Ceballos ; John Guo - The configuration space of a robotic arm in a tunnel of width 2

dmtcs:6402 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6402
The configuration space of a robotic arm in a tunnel of width 2

Authors: Federico Ardila 1,2; Hanner Bastidas 3; Cesar Ceballos 4; John Guo 2

  • 1 Universidad de los Andes [Bogota]
  • 2 Department of Mathematics [San Francisco]
  • 3 Universidad del Valle [Cali]
  • 4 Faculty of Mathematics [Vienna]

We study the motion of a robotic arm inside a rectangular tunnel of width 2. We prove that the configuration space S of all possible positions of the robot is a CAT(0) cubical complex. Before this work, very few families of robots were known to have CAT(0) configuration spaces. This property allows us to move the arm optimally from one position to another.

https://doi.org/10.46298/dmtcs.6402
Source: HAL:hal-02173755v1
Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • CAREER: Matroids, polytopes, and their valuations in algebra and geometry; Funder: National Science Foundation; Code: 0956178

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Source : ScholeXplorer IsRelatedTo DOI 10.1112/plms/s3-71.3.585
  • 10.1112/plms/s3-71.3.585
Ends of Group Pairs and Non-Positively Curved Cube Complexes

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