A hybrid model in a nonlinear disturbance observer for improving compliance error compensation of robotic machining

The joint deflection of robots in machining degrades product accuracy. Compliance error compensation has been investigated to reduce the static deflection of robotic machining. The challenge in compliance error compensation is accurately measuring the deflection or cutting force. External sensors have been used to measure them in robotic machining, but it is not practical. The authors proposed a nonlinear disturbance observer to indirectly measure the cutting force online in robotic machining in the previous study. The observer, however, needs to utilize the robot model that includes characteristics of high nonlinearity, uncertainty, and high dynamic variation for different robot postures. After investigating these challenges of modeling, this paper proposes a hybrid modeling approach combining a physics-based model with a new empirical friction model, and a data-driven model to accurately estimate the cutting force while minimizing the error of the robot's mathematical model. The joint torque calculated from the hybrid model can cover the effect of joints' postures and speeds on the varying dynamic in its workspace. Real-time optimization just before cutting is also proposed to adapt to the real-time joint's motion conditions. The experimental results from aluminum multi-axis cutting show that the estimated cutting force via the nonlinear disturbance observer based on the proposed hybrid modeling approach can improve its accuracy up to 45% and 74% in the x and y directions respectively, compared to the physics-based modeling approach. The deflection of the tool center point can be compensated by using a compliance error compensation method up to 79.1% and 75.4% in the x and y directions, respectively, at 0.5 mm/s feed rate, and up to 77.2% and 78.9% at 3 mm/s feed rate. Consequently, the approaches developed in this paper can solve the problems of conventional robot modeling and improve the accuracy of robot machining.