UPETrack: Unidirectional Position Estimation for Tracking Occluded Deformable Linear Objects

TL;DR

This work tackles real-time tracking of deformable linear objects under partial occlusion without relying on physical models or visual markers. It introduces UPETrack, a two-phase method that combines GMM-EM-based visible-segment estimation with Unidirectional Position Estimation to infer occluded node positions via closed-form geometric relations, complemented by geodesic-distance based uniformization to maintain spacing. Experiments against state-of-the-art methods show superior accuracy and computational efficiency under static and dynamic occlusions, suggesting strong potential for real-time robotic manipulation of DLOs. The approach offers a practical, marker-free solution with implications for industrial, medical, and service robotics tasks that require robust DLO perception and control.

Abstract

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.

Figures (10)

• Figure 1: (a) The robotic manipulation of a DLO usually involves transforming the DLO from its current configuration into a goal shape. However, local occlusions can compromise the completeness of the perceived shape of the DLO, severely hampering robotic decision-making. (b) Therefore, it is necessary to establish tracking algorithms for real-time state estimation of DLOs, enabling the reconstruction of their complete geometric configuration based on the tracking results.
• Figure 2: UPETrack integrates the current DLO point cloud with prior temporal nodes to obtain visible segments. It then employs Unidirectional Position Estimation (UPE) for occluded node localization, followed by uniform resampling to generate final state estimates.
• Figure 3: The algorithm determines node visibility by checking whether the number of neighboring points ($q$) within radius $r_{vis}$ around $\textbf{y}_{m}^{t-1}$ exceeds threshold $V_{lim}$, marking $\textbf{y}_{m}^{t}$ as visible if $q\geq V_{lim}$ or occluded otherwise.
• Figure 4: For tip occlusion scenarios, UPE traverses from the occluded end until locating a sequence of continuous visible nodes. The algorithm then reverses direction, leveraging the continuous visible nodes to iteratively estimate the nearest occluded node. Each estimated node is reclassified as visible, propagating estimations until full occlusion resolution.
• Figure 5: The local linear combination displacement represents the displacement $\boldsymbol{\varDelta} _{m}$ of the occluded nodes $\textbf{y}_m^{t-1}$ as a distance-weighted sum of visible node displacements from the continuous visible nodes.