Geometric and Force-Based Strategies for Dual-Mode Planar Manipulation of Deformable Linear Objects

This paper investigates the fundamental challenges in planar manipulation of deformable linear objects (DLOs), where conventional rigid-body pushing and rotation strategies are often inadequate due to complex deformation dynamics. While the robotic manipulation of rigid objects has been extensively explored, the inherent conflict between the infinite degree of freedom in DLOs and the limited control points available in a robotic system presents significant obstacles to effective shape maintenance and force regulation. To address these limitations, we proposed a unified systematic framework for two-dimensional DLO manipulation that integrates object shape modeling with constraint force derivation. By leveraging the principles of system energy minimization and Lagrangian mechanics, our method generates gripper trajectories that simultaneously satisfy the requirement of object shape deformation and force constraints. The efficacy of the framework is validated via a dual-mode manipulation of DLOs, comprising (1) pushing with a static contact point, followed by (2) rotation-based surface alignment through continuous changing contact points. Results demonstrate that our approach achieves integrated shape and force regulation within a single computational framework.