UPETrack: Unidirectional Position Estimation for Tracking Occluded Deformable Linear Objects

Real-time state tracking of Deformable Linear Objects (DLOs) is critical for enabling robotic manipulation of DLOs in industrial assembly, medical procedures, and daily-life applications. However, the high-dimensional configuration space, nonlinear dynamics, and frequent partial occlusions present fundamental barriers to robust real-time DLO tracking. To address these limitations, this study introduces UPETrack, a geometry-driven framework based on Unidirectional Position Estimation (UPE), which facilitates tracking without the requirement for physical modeling, virtual simulation, or visual markers. The framework operates in two phases: (1) visible segment tracking is based on a Gaussian Mixture Model (GMM) fitted via the Expectation Maximization (EM) algorithm, and (2) occlusion region prediction employing UPE algorithm we proposed. UPE leverages the geometric continuity inherent in DLO shapes and their temporal evolution patterns to derive a closed-form positional estimator through three principal mechanisms: (i) local linear combination displacement term, (ii) proximal linear constraint term, and (iii) historical curvature term. This analytical formulation allows efficient and stable estimation of occluded nodes through explicit linear combinations of geometric components, eliminating the need for additional iterative optimization. Experimental results demonstrate that UPETrack surpasses two state-of-the-art tracking algorithms, including TrackDLO and CDCPD2, in both positioning accuracy and computational efficiency.