Deformable linear objects (DLOs), such as rods, cables, and ropes, play important roles in daily life. However, manipulation of DLOs is challenging as large geometrically nonlinear deformations may occur during the manipulation process. This problem is made even more difficult as the different deformation modes (e.g., stretching, bending, and twisting) may result in elastic instabilities during manipulation. In this paper, we formulate a physics-guided data-driven method to solve a challenging manipulation task -- accurately deploying a DLO (an elastic rod) onto a rigid substrate along various prescribed patterns. Our framework combines machine learning, scaling analysis, and physical simulations to develop a physics-based neural controller for deployment. We explore the complex interplay between the gravitational and elastic energies of the manipulated DLO and obtain a control method for DLO deployment that is robust against friction and material properties. Out of the numerous geometrical and material properties of the rod and substrate, we show that only three non-dimensional parameters are needed to describe the deployment process with physical analysis. Therefore, the essence of the controlling law for the manipulation task can be constructed with a low-dimensional model, drastically increasing the computation speed. The effectiveness of our optimal control scheme is shown through a comprehensive robotic case study comparing against a heuristic control method for deploying rods for a wide variety of patterns. In addition to this, we also showcase the practicality of our control scheme by having a robot accomplish challenging high-level tasks such as mimicking human handwriting, cable placement, and tying knots.

翻译：可变形线性物体（如杆、缆绳和绳索）在日常生活中扮演重要角色。然而，由于操控过程中可能发生大几何非线性变形，对这类物体的操控极具挑战性。更棘手的是，拉伸、弯曲和扭转等不同变形模式可能在操控中引发弹性失稳。本文提出一种物理引导的数据驱动方法，以解决一项高难度操控任务——将可变形线性物体（弹性杆）沿预设图案精确部署至刚性基底上。该框架融合机器学习、尺度分析与物理模拟，开发了一种基于物理学的神经控制器用于部署。我们探索了被操控可变形线性物体的重力能与弹性能之间的复杂相互作用，并提出一种对摩擦和材料属性具有鲁棒性的部署控制方法。通过分析杆与基底的众多几何及材料属性，我们证明仅需三个无量纲参数便可描述部署过程。因此，操控任务的控制律本质可通过低维模型构建，从而大幅提升计算速度。通过全面的机器人案例研究（与启发式控制方法进行图案部署对比），验证了最优控制方案的有效性。此外，我们通过让机器人完成模仿人类书写、电缆放置和打结等高阶挑战性任务，展示了该控制方案的实用性。