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Mathematical model of a robotic golf player
Felix Gotti: email@example.com
In this project we would like to propose and evaluate a mathematical model for a golfing robot. An automatic golfer (AG) can be parametrized by the directions in which it can hit a golf ball as well as the possible levels of power of its swings. For the sake of modeling, it is reasonable to take the golf course to be the upper-half plane with holes located at some of its lattice points, and to model our AG using a set of defining lattice vectors specifying the directions (and levels of power) at which the AG can hit a ball. The locations a ball can reach while the AG is playing are precisely the lattice points of the monoid generated by the AG defining vectors. We would like to design an AG that, starting at the origin, is able to make a given hole and, more importantly, we would like to measure its efficiency. As our model is discrete (i.e., uses integer data), there are problems we will have to deal with, including the fact the AG will be unable to make a hole at certain locations. Using techniques from linear algebra and combinatorics, we would like to create a framework to answer the following questions: In how many ways an AG can make a given hole? What is the minimum number of tries a smart AG will need to make a reachable hole? What is the worst case scenario to make a reachable hole, i.e., the maximum number of tries an AG will need to make a reachable hole? In addition, probabilistic questions such as what is the expected number of tries a dumb AG will take to make a given hole will also be of interest.
This project will take place via Zoom (with regular virtual meetings). A suitable candidate is expected to be familiar with linear algebra, while having a basic knowledge of combinatorics and abstract algebra. Familiarity with probability and convex geometry may be helpful but not required. We expect to end up with a publishable result. However, the candidate is not required to have any previous research experience, but considerable enthusiasm with the idea of doing research.