Hybrid statistical modelling of the frequency response function of industrial robots

Models that predict the Frequency Response Function (FRF) of six degree-of-freedom (6-dof) industrial robots used for machining operations such as milling are usually built using Experimental Modal Analysis (EMA) of vibration data obtained from modal impact hammer tests performed at a finite number of points in the robot?s workspace corresponding to specific arm configurations. While modal impact hammer tests are not constrained by the operating conditions of the robot, such as specific arm configurations allowed by part fixturing, they are limited by the number of workspace points that can be practically sampled and the associated robot downtime. Alternatively, the process of determining robot FRFs from on-line machining process data (e.g., forces and vibration) through Operational Modal Analysis (OMA) enables a denser sampling of the robot?s workspace without requiring robot downtime. However, OMA may require several long tool paths and one or more complex part setups to enable sampling of a sufficiently large number of locations/arm configurations. This paper presents an efficient hybrid statistical modelling methodology that combines the two approaches, thus enabling possible optimization of sampling density and robot downtime, to efficiently determine the robot FRFs as a function arm configuration. The approach consists of first calibrating a Gaussian Process Regression (GPR) model with FRF data derived from EMA conducted at a small number of discrete locations in the robot?s workspace. Then, FRFs calculated from OMA of milling forces and tool tip vibration data derived from robotic milling tests are used to update the initial GPR model using Bayesian inference and efficient hyperparameter updating. The proposed hybrid robot FRF modelling method is experimentally validated and shown to yield accurate predictions of the robot FRF while being computationally efficient.