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.

Predicting the cross-sectional profile of the whole bending segment for metal tube bending is essential to achieve high-precision bending, yet still remains challenging. The existing prediction methods mainly base on theoretical derivation under certain assumptions and approximations, which do not fully characterize the whole bending segment profile neither do they fully utilize the information in the bending process. In this study, a Bo-LSTM-based progressive prediction method for the cross-sectional profile sequence is proposed, which comprehensively utilizes the profile information during the bending process and achieves an accurate prediction of the cross-sectional profile of the whole bending segment in the subsequent bending process. Firstly, the method of describing the cross-sectional profile in polar radial vector and the cross-sections of the bending segment in discrete sequences are proposed, which cover the information of cross-sectional distortion and wall thickness variation (viz. cross-sectional defects) for the whole bending segment. Secondly, an LSTM network is constructed integrating Bayesian-optimization-based hyper-parameters selection approach to progressively predict the tube cross-sectional profile sequence. Finally, the proposed methods are verified on simulated datasets as well as experimental data, and the accuracy is compared with networks of different structures. The results show that Bo-LSTM has better prediction accuracy. Meanwhile, the progressive prediction pattern has better robustness compared to chain prediction pattern.