NDLI: The Configuration Space of a Robotic Arm in a Tunnel

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bastidas, Hanner Guo, John Ardila, Federico Ceballos, Cesar
Copyright Year	2017
Abstract	We study the motion of a robotic arm inside a rectangular tunnel. We prove that the configuration space of all possible positions of the robot is a ${CAT}(0)$ cubical complex. This allows us to use techniques from geometric group theory to find the optimal way of moving the arm from one position to another. We also compute the diameter of the configuration space, that is, the longest distance between two positions of the robot.
Sponsorship	York University. Austrian Science Fund. Banting Research Foundation. National Science Foundation
Starting Page	2675
Ending Page	2702
Page Count	28
File Format	PDF
ISSN	08954801
DOI	10.1137/16M1089411
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	31
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2017-12-06
Access Restriction	Subscribed
Subject Keyword	robot tableau motion planning CAT(0) Exact enumeration problems, generating functions lattice path Distance in graphs Computer graphics; computational geometry cubical complex poset with inconsistent pairs distributive lattice Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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The Configuration Space of a Robotic Arm in a Tunnel