Recreational Formal Methods: Designing Vacuum Cleaning Trajectories

F.W. Vaandrager and F. Verbeek. Recreational Formal Methods: Designing Vacuum Cleaning Trajectories. In Bulletin of the EATCS 113:100-109, June 2014.


We study an example due to Wooldridge of a small robotic agent that will vacuum clean a room. The room is an nxn grid and at any point the robot can move forward one step or turn right 90 degrees. The problem is to find a deterministic strategy for the robot in which (1) its next action only depends on its current square and orientation (one of north, west, south, east), and (2) all squares are visited infinitely often. We use a model checker and a SAT solver to find such strategies, and a proof assistant to exhibit certain symmetries in the problem.

Published version
Local copy (pdf)
Slides (pdf) used in presentation at the Dutch Model Checking Day
Uppaal model: vacuumcleaner.xml, vacuumcleaner.q
zChaff and Isabelle sources: