A comprehensive path prediction model for robotic end-effectors considering multiple factors

Accurately predicting robotic end-effector path is the basis for industrial robot applications. However, existing studies are primarily limited to modeling single factors, resulting in a lack of generality and accuracy. Unlike previous studies that employed disparate methods for different factors, rendering integration impractical, this study introduces a comprehensive path model that systematically integrates reversal error, scaling error, joint stiffness, gravity, and the counterbalancing system into a unified kinematic and static framework. The model explicitly classifies joint angle deviations into reversal-induced, force-induced, and scaling-induced components, enabling targeted analytical formulations for each. In detail, the effects of reversal and scaling errors are revealed by establishing their relationship with the joint rotation direction and joint angle, respectively. The virtual work equation used in statics is now extended to characterize the effects of the gravity and counterbalancing system besides the joint stiffness. Based on this, a unified modeling framework is established to evaluate the effects of all the aforementioned factors on joint angles, and consequently, on the end-effector path. The model parameters, such as joint stiffness, hysteresis, and scaling coefficients, are calibrated through ballbar experiments under both loaded and unloaded conditions. Finally, the proposed path model is experimentally validated and shown to have higher accuracy for path prediction and error compensation, achieving up to 71.5% reduction in average path prediction error compared with the traditional model, and demonstrating significant improvements in compensated path accuracy during robotic milling tasks.