A self-supervised learning and error compensation method for needle deflection prediction and control during insertion

OBJECTIVE: Flexible needles are prone to bending-induced deflection during insertion into soft tissue, which compromises targeting accuracy and increases the difficulty of closed-loop control. Existing physics-based models often exhibit limited generalization capability, whereas purely data-driven methods generally lack physical interpretability. This study aims to develop a flexible needle tip deflection prediction method that combines physical modeling and data-driven correction to improve prediction accuracy, robustness, and generalization performance. APPROACH: A mechanics-guided prediction framework integrating self-supervised consistency learning and supervised residual correction is proposed. First, a needle bending model is established using the Rayleigh-Ritz method to provide physically informed baseline predictions. Then, a self-supervised consistency constraint is introduced to capture the intrinsic relationships among samples at different insertion depths. In addition, a supervised residual branch is incorporated to compensate for system errors that are difficult to describe explicitly in complex insertion environments. MAIN RESULTS: Experimental results demonstrate that the proposed method remains stable across different network scales. Under the optimal configuration, it achieves a mean absolute error of 0.36 mm, a root mean square error of 0.51 mm, and a maximum error of 1.45 mm. The method also maintains favorable generalization performance in tests beyond the training depth range. In static target puncture experiments and straight-line trajectory tracking experiments, average errors of 0.95±0.16 mm and 0.28±0.22 mm are achieved, respectively. SIGNIFICANCE: The proposed method improves the prediction accuracy of flexible needle tip deflection while preserving physical interpretability through mechanics-based guidance. The resulting predictive framework provides stable and reliable prior information for autonomous closed-loop control and offers an effective route toward high-accuracy and robust needle insertion in soft tissue.