3D-Force Estimation for Dual-arm Manipulation of Deformable Linear Objects via Factor Graphs

Continuum robots offer key advantages in navigating unstructured environments, but their safe operation requires accurate estimation of the external contact forces acting anywhere along the robot body. Estimating these forces at unknown locations is an ill-conditioned problem, particularly for multiple contacts. We propose a unified shape and force estimation framework formulated on a factor graph. By incorporating a Gaussian mixture force parameterization into a discretized probabilistic Cosserat rod model, we reduce the dimensionality of the unknown external forces and mitigate the ill-conditioning of node-wise force estimation. The framework fuses strain, tendon tension, and pose measurements to simultaneously estimate the robot's shape and external forces while accounting for modeling and sensor uncertainties. Numerical simulations demonstrate that the proposed method outperforms existing methods in terms of force location and magnitude estimation for both single and multi-contact scenarios. We further present a progressive variant that introduces basis functions on demand to estimate contact forces sequentially during a simulated confined-navigation task.

Most research on the manipulation of deformable objects focuses on lightweight systems with negligible mechanical response, effectively restricting attention to quasi-static regimes. This assumption excludes a broad class of practically relevant objects, such as hoses, pipes, and wiring harnesses, whose dynamics cannot be ignored during manipulation. In this work, we address this limitation by introducing a closed-loop control architecture that explicitly accounts for object dynamics and recasts manipulation as a shape-regulation problem. Control is achieved by modulating forces and torques applied at multiple fixed points along the object. This approach builds on three methodological contributions: a fully dynamic model of linear deformable objects based on discrete strain parameterizations; an extension of the notion of actuation coordinates to SE(3), yielding a structured and inherently underactuated control architecture; and nonlinear feedback strategies providing explicit conditions for steady-state convergence to desired configurations. Extensive simulations on representative manipulation tasks demonstrate the performance gains enabled by the proposed modelbased formulation. We finally validate the approach experimentally through a real-time closed-loop implementation with online shape estimation, confirming its practical feasibility and effectiveness

Deformable linear objects (DLO) pose a coupled perception and control challenge: their slender geometry makes precise localization difficult, while their deformations depend on object-specific physical properties. To address this challenge, we propose PS-DLO, a property- and spatially aware DLO manipulation policy. First, contrastive image-text learning maps the initial observation to categorical descriptions of DLO properties, providing explicit physical and structural priors for action generation. Second, SAM3 extracts mask-guided features from future observations, which are distilled into the policy's action expert to encode task-relevant DLO regions and their subsequent configurations. We evaluate PS-DLO on nine real-world tasks across single-arm and bimanual platforms, training a shared multi-task policy for each embodiment. PS-DLO achieves an average success rate of 68.9%, exceeding the strongest baseline by 20.0 percentage points. In generalization experiments, PS-DLO achieves higher success rates than the baseline in six of seven visual-shift conditions on butterfly-knot untying. These results demonstrate that combining object-property priors with future spatial supervision improves multi-task DLO manipulation and robustness to visual variation.