Modeling and Control of Robotic Manipulators Based on Symbolic Regression

Model-based design is an important method of addressing problems associated with designing complex control systems. For complex dynamic systems in the presence of uncertainties, the modeling process from the first principles becomes extremely tedious and simplification in mechanism and parameter measurement may result in model inaccuracy. On the contrary, machine learning has the characteristic of fitting complicated equations, which makes it widely used in the research of model identification. However, it only brings a black-box model where the design schemes based on an analytical model cannot be applied. In this article, a simple and novel scheme for modeling and control of robotic manipulators is proposed; without prior knowledge, a dynamic model in an analytical form is obtained from artificially excited training data using the symbolic regression technique, and then, a controller is designed based on the dynamic model. Due to the ingenious experimental design, on one hand, the amount of training data is far less than the system identification method by machine learning. On the other hand, a decoupling feature is used in the model that greatly simplifies controller design. The experimental results on two-degree of freedom (DOF) and 6-DOF robotic manipulator simulators verify that the scheme is feasible and effective.

I. Introduction

The dynamic model of a robotic manipulator is to characterize the relationship between its motion state and the applied torques, which plays an important role in addressing controller design problems [1]. In particular, accurate dynamic equations of a manipulator are critical for its high-precision operation. Two main methods of deriving the dynamic equations are the first principle modeling and the data-driven modeling. The former is to use physical principles to derive a dynamic model under the condition that the structural parameters of the manipulator are known. In the latter, the motion and force data of the manipulator are collected through experiments, and hence, the dynamic model is obtained by data mining.