This research addresses the challenge of large/complex deformation in the shape control tasks of Deformable Linear Objects (DLO). We propose a collaborative approach using two manipulators to achieve shape control of a DLO in 2D workspace. The proposed methodology introduces an innovative Intermediary Shapes Generation (ISG) algorithm which outputs a series of intermediary shapes to guide the DLO towards the desired shape. The robot controller is formulated as an optimization problem, where the main objective is to minimize the error between the current shape and the desired shape, while ensuring the diminishing rigidity property of the DLO as a constraint. We conduct extensive simulations and real-life experiments to evaluate the effectiveness of our approach. We consider various scenarios of basic shapes, as well as complex deformations with opposite concavities between initial and final shapes. The outcomes demonstrate the robustness and high accuracy of the proposed system in achieving complex deformations. This capability represents the primary contribution of our research. The optimization-based control framework, coupled with the ISG algorithm, enables effective shape control without the need for extensive modeling nor training, and offers a promising solution for practical applications requiring precise shape control of DLOs. Moreover, we carry out a thorough review and comparative analysis encompassing the latest literature in DLO shape control, and the techniques for DLO modeling.

中文翻译：

---

用于大变形任务的可变形线性物体的机器人协同操作

这项研究解决了可变形线性物体（DLO）形状控制任务中大/复杂变形的挑战。我们提出了一种协作方法，使用两个操纵器来实现 2D 工作空间中 DLO 的形状控制。所提出的方法引入了一种创新的中间形状生成 (ISG) 算法，该算法输出一系列中间形状以引导 DLO 达到所需的形状。机器人控制器被表述为一个优化问题，其主要目标是最小化当前形状和期望形状之间的误差，同时确保 DLO 的刚性递减特性作为约束。我们进行了广泛的模拟和现实实验来评估我们方法的有效性。我们考虑基本形状的各种场景，以及初始形状和最终形状之间具有相反凹度的复杂变形。结果证明了所提出的系统在实现复杂变形方面的鲁棒性和高精度。这种能力代表了我们研究的主要贡献。基于优化的控制框架与 ISG 算法相结合，无需进行大量建模或训练即可实现有效的形状控制，并为需要 DLO 精确形状控制的实际应用提供了一种有前途的解决方案。此外，我们对 DLO 形状控制的最新文献以及 DLO 建模技术进行了彻底的回顾和比较分析。