id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_3ojj6euqpffpffdnts5x737t7a	Federico Ardila-Mantilla	CAT(0) Geometry, Robots, and Society	2020	11	.pdf	application/pdf	7066	649	71	powerful idea is the root of a very useful approach to Problem 1: We build and understand the "map of possibilities," down robotic arm in a rectangular tunnel is a CAT(0) cubical To answer this question, let us build the "map of possibilities" of the robot. In our specific example, Figure 6 shows the configuration space of the robot 𝑅2,6 of length 6 in a tunnel of height Thus a robot with a CAT(0) configuration space is easier Theorem 5 provides algorithms to move optimally between any two points in a CAT(0) cubical complex in the our first hope is that the corresponding map of possibilities is a CAT(0) cubical complex. map is CAT(0), and it allows us to use 𝑇𝑛 as a remote control to move the robot optimally. This coral PIP serves as a witness that the map of possibilities of the robotic arm 𝑅𝑚,𝑛 is a CAT(0) cubical complex.	./cache/work_3ojj6euqpffpffdnts5x737t7a.pdf	./txt/work_3ojj6euqpffpffdnts5x737t7a.txt