Manipulating three-dimensional (3D) deformable objects presents significant challenges for robotic systems due to their infinite-dimensional state space and complex deformable dynamics. This paper proposes a novel model-free approach for shape control with constraints imposed on key points. Unlike existing methods that rely on feature dimensionality reduction, the proposed controller leverages the coordinates of key points as the feature vector, which are extracted from the deformable object's point cloud using deep learning methods. This approach not only reduces the dimensionality of the feature space but also retains the spatial information of the object. By extracting key points, the manipulation of deformable objects is simplified into a visual servoing problem, where the shape dynamics are described using a deformation Jacobian matrix. To enhance control accuracy, a prescribed performance control method is developed by integrating barrier Lyapunov functions (BLF) to enforce constraints on the key points. The stability of the closed-loop system is rigorously analyzed and verified using the Lyapunov method. Experimental results further demonstrate the effectiveness and robustness of the proposed method.

翻译：三维变形物体的操纵因其无限维状态空间和复杂的变形动力学而对机器人系统提出了重大挑战。本文提出了一种新颖的无模型方法，用于在关键点上施加约束的形状控制。与现有依赖特征降维的方法不同，所提出的控制器利用关键点的坐标作为特征向量，这些关键点是通过深度学习方法从变形物体的点云中提取的。该方法不仅降低了特征空间的维度，还保留了物体的空间信息。通过提取关键点，变形物体的操纵被简化为一个视觉伺服问题，其中形状动力学使用变形雅可比矩阵进行描述。为了提高控制精度，通过集成障碍李雅普诺夫函数（BLF）来对关键点施加约束，从而开发了一种预定性能控制方法。闭环系统的稳定性通过李雅普诺夫方法进行了严格的分析和验证。实验结果进一步证明了所提方法的有效性和鲁棒性。