Design and implementation of math-solving robot: Rank analysis for solving magic square puzzle

Abstract

This paper presents the design of a math-solving robot which has many potential applications in service, entertainment, and educational robotics. We design a robot scanning and recognizing a printed math problem on a paper and then writing an answer on it. We specifically attempt to solve magic square puzzles and compute simple calculation. Controlling motors and recognizing targets from low-cost sensors are very challenging; however, we address the design of our robot to generate stable and effective motions, built with a Lego Mindstorms EV3 in addition to robust sensing ability through its color sensor in our software design. We also present a linear system method and rank analysis in order to decide if the given puzzle has a unique solution, more than one solution, or no solution. Through real robot experiments with quantitative and qualitative analysis regarding scanning, matching, and algorithm, we demonstrate our robot solves given magic square problems and simple calculations.