Discovering empirical equations from robot-collected data

Abstract

Discovery of multidimensional empirical equations has been a task of systems such as BACON and FAHRENHEIT. When confronted with data collected in a robotic experiment, BACON-like generalization mechanism of FAHRENHEIT reached an impasse because it found many acceptable equations for some datasets while none for others. We describe an improved generalization mechanism that handles both problems. We apply that mechanism to a robot arm experiment similar to Galileo's experiments with the inclined plane. The system collected data, determined empirical error and eventually found empirical equations acceptable within error. By confronting empirical equations developed by FAHRENHEIT with theoretical models based on classical mechanics, we have shown that empirical equations provide superior fit to data. Systematic deviations between data and a theoretical model hint at processes not captured by the model but accounted for in empirical equations.