Machine-learning a perfect bending soccer goal shot

Abstract

The objective of this work is to ascertain the optimal bending kick velocity and spin that a player should impart to exactly hit a target within a soccer goal, using machine-learning optimization. Specifically, the work develops a model of a kicking player producing a high-velocity spinning soccer ball which interacts with the surrounding air that induces drag forces and the Magnus effect, both of which are functions of the Reynolds number. This yields a set of highly nonlinear, coupled, differential equations. The framework is designed to enable digital-twin type technologies, i.e. digital replicas that run in real time with the physical system on laptops or other mobile systems for rapid feedback. The overall guiding motivation is to provide a useful tool to assist coaches and to rapidly train players. Numerical examples are provided to illustrate the process.