A Neural Network Separation Approach for the Inclusion of Static Friction in Nonlinear Static Models of Industrial Robots

Static friction modeling is a critical task to have the accurate robot model. In this article, a neural network separation approach to include nonlinear static friction in models of industrial robots is proposed. For this purpose, the terms corresponding to static friction within the overall robot mathematical model are separable terms treated independently from the rest of the model. The separation modeling process is accomplished by first determining the mathematical model for the system by excluding the friction terms and estimating its parameter values. This part of the model corresponds to gravitational terms only. Because persistency of excitation is required to maintain high accuracy and avoid singularity in the estimations, data with large variations across multiple joint angles are gathered for estimation purposes and a weighted least squares approach is used. This estimation results in a highly accurate static mathematical model for industrial robots. Results from the weighted least squares estimation are compared with the original least squares estimation, ridge regression, a least absolute shrinkage and selection operator, and an elastic net to show superior performance. After modeling the gravitational terms of the model, a multilayer perceptron neural network is used to identify static friction forces in the model from the experimental data. This is required in the case of a robot with multiple degrees of freedom because the friction of each joint is a function of several other joint angles acting upon it; making the solution complex and difficult to be obtained through other friction modeling methods. The experimental results obtained from a Universal Robots-UR5 demonstrate the high accuracy of the proposed modeling methodology under static conditions, and future work will consider the implementation of dynamic terms to integrate friction forces during movement.