Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Tuesday 5
Combinatorics
Eric Fusy
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
The configuration space of a robotic arm in a tunnel of width 2
Federico Ardila  1, 2  , Hanner Bastidas  3  , Cesar Ceballos  4  , John Guo  2  
1 : Universidad de los Andes [Bogota]  -  Website
2 : Department of Mathematics [San Francisco=  -  Website
San Francisco State University Thornton Hall 937 1600 Holloway Ave San Francisco, CA 94132 -  États-Unis
3 : Univesidad del Valle [Cali] Colombia  (Univalle)  -  Website
Ciudad Universitaria MeléndezCalle 13 # 100-00Sede San FernandoCalle 4B # 36-00 -  Colombie
4 : Faculty of Mathematics [Vienna]  -  Website
Oskar-Morgenstern-Platz 1, 1090 Wien -  Autriche

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. 



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