Physics-informed LSTM-Transformer vision-enhanced system: Real-time axis prediction in tube free-bending manufacturing

• A high-precision visual system enables real-time 3D tracking of tube-end trajectory during bending. • Physics-Informed LSTM-Transformer integrates displacement constraints into its loss function. • Data-physics driven mechanism achieves accurate real-time prediction of the springback tube axis. The free-bending technique, distinguished by its exceptional flexibility in axis control, is emerging as a transformative paradigm for manufacturing complex tubular structures, overcoming geometric limitations inherent to conventional tube bending manufacturing processes. However, the high flexibility in multi-axis free-bending systems introduces nonlinear control complexities that critically compromise the tube forming accuracy. Real-time machine vision approaches enable in-process tracking of tubular geometric deviations, providing a fast method for axis prediction. To this end, this paper presents a real-time vision-enhanced prediction system that integrates with an LSTM-Transformer framework. A high-precision visual sensing system is developed to capture tube-end trajectory, integrating 3D-printed markers, depth camera, kinematic decoupling, and instance segmentation for accurate motion tracking and process parameter inversion. Subsequently, a physics-informed hybrid LSTM-Transformer architecture is proposed for dynamic bend axis springback prediction, incorporating trajectory-derived physical constraints and multi-objective optimization for spatio-temporal springback prediction during dynamic forming. Additionally, an online differential geometry mapping method for real-time curvature parameter estimation is introduced, eliminating the need for post-scanning and additional equipment, enabling closed-loop process parameter compensation during bending. Experimental results show that the proposed method reduces the mean absolute error of axial springback prediction by more than 60% compared to traditional theoretical models, with the mean absolute error for all groups remaining below 12 mm.