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（DLOs），如杆、电缆和绳索，在日常生活中扮演着重要角色。然而，由于操作过程中可能发生巨大的几何非线性变形，DLOs的操控极具挑战性。这一问题因不同变形模式（如拉伸、弯曲和扭转）在操控中可能引发弹性失稳而变得更加复杂。本文提出了一种物理引导的数据驱动方法，用于解决一项具有挑战性的操控任务——将弹性杆精确地沿各种预设图案部署到刚性基底上。我们的框架结合了机器学习、缩放分析和物理仿真，开发了基于物理的神经控制器用于部署。我们探究了被操控DLO的重力能与弹性能之间的复杂相互作用，并提出了一种对摩擦和材料特性具有鲁棒性的DLO部署控制方法。通过物理分析，我们从杆和基底的众多几何与材料特性中证明，仅需三个无量纲参数即可描述部署过程。因此，操控任务的控制规律本质可通过低维模型构建，从而极大提升计算速度。通过与启发式控制方法在多种杆部署图案上的综合机器人案例对比，我们展示了最优控制方案的有效性。此外，我们还通过让机器人完成模仿人类手写、电缆放置和打结等高阶挑战性任务，验证了控制方案的实用性。