Document Type
Conference Proceeding
Publication Date
8-2020
Abstract
This paper investigates a restricted version of robot motion planning, in which particles on a board uniformly respond to global signals that cause them to move one unit distance in a particular direction. We look at the problem of assembling patterns within this model. We first derive upper and lower bounds on the worst-case number of steps needed to reconfigure a general purpose board into a target pattern. We then show that the construction of k-colored patterns of size-n requires Ω(n log k) steps in general, and Ω(n log k + √ k) steps if the constructed shape must always be placed in a designated output location. We then design algorithms to approach these lower bounds: We show how to construct k-colored 1 × n lines in O(n log k + k) steps with unique output locations. For general colored shapes within a w×h bounding box, we achieve O(wh log k+hk) steps.
Recommended Citation
Caballero, David, Angel A. Cantu, Timothy Gomez, Austin Luchsinger, Robert Schweller, and Tim Wylie. 2020. “Building Patterned Shapes in Robot Swarms with Uniform Control Signals.” Canadian Conference on Computational Geometry, October. https://par.nsf.gov/biblio/10262148-building-patterned-shapes-robot-swarms-uniform-control-signals.
Publication Title
CCCG 2020, Saskatoon, Canada, August 5-7, 2020