Cloth manipulation is a category of deformable object manipulation of great interest to the robotics community, from applications of automated laundry-folding and home organizing and cleaning to textiles and flexible manufacturing. Despite the desire for automated cloth manipulation, the thin-shell dynamics and under-actuation nature of cloth present significant challenges for robots to effectively interact with them. Many recent works omit explicit modeling in favor of learning-based methods that may yield control policies directly. However, these methods require large training sets that must be collected and curated. In this regard, we create a framework for differentiable modeling of cloth dynamics leveraging an Extended Position-based Dynamics (XPBD) algorithm. Together with the desired control objective, physics-aware regularization terms are designed for better results, including trajectory smoothness and elastic potential energy. In addition, safety constraints, such as avoiding obstacles, can be specified using signed distance functions (SDFs). We formulate the cloth manipulation task with safety constraints as a constrained optimization problem, which can be effectively solved by mainstream gradient-based optimizers thanks to the end-to-end differentiability of our framework. Finally, we assess the proposed framework for manipulation tasks with various safety thresholds and demonstrate the feasibility of result trajectories on a surgical robot. The effects of the regularization terms are analyzed in an additional ablation study.

翻译：布料操控是变形物体操控中的一个重要类别，在机器人领域具有广泛应用，包括自动叠衣、家庭整理清洁以及纺织品与柔性制造等。尽管自动化布料操控需求迫切，但布料薄壳动力学与欠驱动特性使机器人难以有效与其交互。近期许多研究摒弃显式建模，转而采用基于学习的方法直接生成控制策略。然而，这些方法需要收集并整理大规模训练数据集。为此，我们提出一种基于扩展位置动力学（XPBD）算法的布料动力学可微建模框架。结合期望控制目标，我们设计了包括轨迹平滑度和弹性势能在内的物理感知正则化项以提升操控效果。此外，可利用符号距离函数（SDF）指定安全约束（如避障）。我们将带安全约束的布料操控任务建模为约束优化问题，得益于框架的端到端可微性，主流梯度优化器可高效求解该问题。最后，我们评估了所提框架在不同安全阈值下的操控任务性能，并在手术机器人上验证了轨迹结果的可行性。通过消融实验进一步分析了正则化项的影响。