A preliminary case study of planning with complex transitions: Plotting

Plotting is a tile-matching puzzle video game published by Taito in 1989. Its objective is to reduce a given grid of coloured blocks down to a goal number or fewer. This is achieved by the avatar character repeatedly shooting the block it holds into the grid. Plotting is an example of a planning problem: given a model of the environment, a planning problem asks us to find a sequence of actions that can lead from an initial state of the environment to a given goal state while respecting some constraints. The key difficulty in modelling Plotting is in capturing the way the puzzle state changes after each shot. A single shot can affect multiple tiles directly, and the grid is affected by gravity so numerous other tiles can be affected indirectly. We present and evaluate a constraint model of the Plotting problem that captures this complexity. We also discuss the difficulties and inefficiencies of modelling Plotting in PDDL, the standard language used for input to specialised AI planners. We conclude by arguing that AI planning could benefit from a richer modelling language.