Deformable object manipulation (DOM) with point clouds has great potential as non-rigid 3D shapes can be measured without detecting and tracking image features. However, robotic shape control of deformable objects with point clouds is challenging due to: the unknown point-wise correspondences and the noisy partial observability of raw point clouds; the modeling difficulties of the relationship between point clouds and robot motions. To tackle these challenges, this paper introduces a novel modal-graph framework for the model-free shape servoing of deformable objects with raw point clouds. Unlike the existing works studying the object's geometry structure, our method builds a low-frequency deformation structure for the DOM system, which is robust to the measurement irregularities. The built modal representation and graph structure enable us to directly extract low-dimensional deformation features from raw point clouds. Such extraction requires no extra point processing of registrations, refinements, and occlusion removal. Moreover, to shape the object using the extracted features, we design an adaptive robust controller which is proved to be input-to-state stable (ISS) without offline learning or identifying both the physical and geometric object models. Extensive simulations and experiments are conducted to validate the effectiveness of our method for linear, planar, tubular, and solid objects under different settings.

翻译：原始点云测量非刚性三维形状时无需检测和跟踪图像特征，因此点云形变物体操作（DOM）具有巨大潜力。然而，基于点云的机器人形变物体形状控制面临三大挑战：原始点云中未知的点对应关系与噪声部分可观测性；点云与机器人运动之间关系建模的困难。针对这些挑战，本文提出了一种新颖的模态图框架，用于基于原始点云的无模型形变物体形状伺服。与现有研究物体几何结构的方法不同，我们的方法为DOM系统构建了低频形变结构，该结构对测量不规则性具有鲁棒性。所构建的模态表示和图结构使我们能够直接从原始点云中提取低维形变特征，这种提取无需额外的点云配准、精化及遮挡去除处理。此外，为了利用提取的特征塑造物体，我们设计了一种自适应鲁棒控制器，该控制器被证明具有输入-状态稳定性（ISS），且无需离线学习或辨识物体的物理与几何模型。通过大量仿真与实验，验证了本方法在线性、平面、管状及实体等不同设置下的有效性。