Computational complexity of motion planning of a robot through simple gadgets
Name
LIPIcs-FUN-2018-18.pdf
Description
Published version
Size
559.38 KB
Format
Adobe PDF
Checksum (MD5)
8b9f7c05cc35f07f0ab883aac2a28691
Author(s)
Demaine, Erik
Date Issued
2018
Citation
Demaine, Erik. 2018. "Computational complexity of motion planning of a robot through simple gadgets."
Version
Final published version
Abstract
© Erik D. Demaine, Isaac Grosof, Jayson Lynch, and Mikhail Rudoy; licensed under Creative Commons License CC-BY 9th International Conference on Fun with Algorithms (FUN 2018). We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change the state. This type of setup is common to many robot motion planning hardness proofs. We characterize the complexity for a natural simple case: each gadget connects up to four locations in a perfect matching (but each direction can be traversable or not in the current state), has one or two states, every gadget traversal is immediately undoable, and that gadget locations are connected by an always-traversable forest, possibly restricted to avoid crossings in the plane. Specifically, we show that any single nontrivial four-location two-state gadget type is enough for motion planning to become PSPACE-complete, while any set of simpler gadgets (effectively two-location or one-state) has a polynomial-time motion planning algorithm. As a sample application, our results show that motion planning games with "spinners" are PSPACE-complete, establishing a new hard aspect of Zelda: Oracle of Seasons.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.FUN.2018.18
