Hole in One: Using Qualitative Reasoning for Solving Hard Physical Puzzle Problems

The capability of determining the right sequence of physical actions to achieve a given task is essential for AI that interacts with the physical world. The great difficulty in developing this capability has two main causes: (1) the world is continuous and therefore the action space is infinite, (2) due to noisy perception, we do not know the exact physical properties of our environment and therefore cannot precisely simulate the consequences of a physical action. In this paper we define a realistic physical action selection problem that has many features common to these kind of problems, the minigolf hole-in-one problem: given a two-dimensional minigolf-like obstacle course, a ball and a hole, determine a single shot that hits the ball into the hole. We assume gravity as well as noisy perception of the environment. We present a method that solves this problem similar to how humans are approaching these problems, by using qualitative reasoning and mental simulation, combined with sampling of actions in the real environment and adjusting the internal knowledge based on observing the actual outcome of sampled actions. We evaluate our method using difficult minigolf levels that require the ball to bounce at several objects in order to hit the hole and compare with existing methods.