Certifiably Safe Manipulation of Deformable Linear Objects via Joint Shape and Tension Prediction

Manipulating deformable linear objects (DLOs) is challenging due to their complex dynamics and the need for safe interaction in contact-rich environments. Most existing models focus on shape prediction alone and fail to account for contact and tension constraints, which can lead to damage to both the DLO and the robot. In this work, we propose a certifiably safe motion planning and control framework for DLO manipulation. At the core of our method is a predictive model that jointly estimates the DLO's future shape and tension. These predictions are integrated into a real-time trajectory optimizer based on polynomial zonotopes, allowing us to enforce safety constraints throughout the execution. We evaluate our framework on a simulated wire harness assembly task using a 7-DOF robotic arm. Compared to state-of-the-art methods, our approach achieves a higher task success rate while avoiding all safety violations. The results demonstrate that our method enables robust and safe DLO manipulation in contact-rich environments.