A Physics-Informed Neural Network Framework for Real-Time Model Predictive Shape Manipulation of Deformable Linear Objects

Shape control of deformable linear objects (DLOs) is a major challenge in robotics due to their high-dimensional, nonlinear dynamics and sensitivity to boundary conditions. Existing data-driven and physics-based models either require large datasets or suffer from excessive computational cost for real-time control. This paper presents a Cosserat-based Physics-Informed Neural Network (C-PINN) framework for efficient, real-time DLO modeling and automatic shape control. By embedding Cosserat rod theory directly into the PINN loss, C-PINN achieves accurate, physically consistent predictions of the DLO while dramatically reducing the requirement for large-scale training data and is robust to unseen scenarios. To enhance generalization and training stability, we introduce a curriculum learning strategy and propose an online sim-to-real residual adaptation module to bridge the gap between simulation and real-world deployment. The learned surrogate model is integrated into a gradient-based model predictive controller (MPC), enabling real-time, closed-loop shape control. Extensive experiments demonstrate that our approach generalizes well to various DLO materials and configurations in both 2D and 3D scenarios, and adapts robustly to interactive, human-in-the-loop manipulation. Both simulation and real-world experiments show that our method consistently attains significantly lower RMSE, as confirmed by comprehensive comparisons with various baselines. These results highlight the effectiveness and versatility of C-PINN for practical, high-precision DLO manipulation in diverse robotic scenarios. Compared to traditional analytical solvers, C-PINN achieves up to a 228-fold improvement in computational speed. Note to Practitioners—This work is motivated by the need for fast and accurate shape control of flexible objects such as cables, wires, and ropes, which is a common challenge in fields like electronics assembly, robotics, and medical devices. Existing solutions based on physics simulation are often too computationally intensive for real-time use, while purely data-driven methods require large datasets and may struggle with new or changing conditions. Our approach integrates physical modeling directly into a neural network, allowing for quick and reliable prediction and control of deformable linear objects using much less training data. In practice, this means engineers can achieve high-precision manipulation and adapt to different object types or tasks without the need for massive data collection or extensive parameter tuning. Our framework also supports real-time feedback and online adaptation to real-world conditions, making it robust to variations in material properties and external disturbances. We also show how the physics-embedded model can be effectively integrated with model predictive control. A key limitation is that our method currently assumes slow or quasi-static motion and does not account for rapid dynamics or complex environmental contacts, which may affect accuracy in certain scenarios. Future work will focus on handling dynamic effects and environmental interactions. This approach could also be extended to other flexible material handling tasks, such as textile automation or surgical tool positioning. © 2025 IEEE.