Shape control of deformable objects is a challenging and important robotic problem. This paper proposes a model-free controller using novel 3D global deformation features based on modal analysis. Unlike most existing controllers using geometric features, our controller employs a physically-based deformation feature by decoupling 3D global deformation into low-frequency mode shapes. Although modal analysis is widely adopted in computer vision and simulation, it has not been used in robotic deformation control. We develop a new model-free framework for modal-based deformation control under robot manipulation. Physical interpretation of mode shapes enables us to formulate an analytical deformation Jacobian matrix mapping the robot manipulation onto changes of the modal features. In the Jacobian matrix, unknown geometry and physical properties of the object are treated as low-dimensional modal parameters which can be used to linearly parameterize the closed-loop system. Thus, an adaptive controller with proven stability can be designed to deform the object while online estimating the modal parameters. Simulations and experiments are conducted using linear, planar, and solid objects under different settings. The results not only confirm the superior performance of our controller but also demonstrate its advantages over the baseline method.

翻译：可变形物体的形状控制是一个具有挑战性的重要机器人问题。本文提出了一种基于模态分析的创新型三维全局变形特征的无模型控制器。与大多数使用几何特征的现有控制器不同，我们的控制器通过将三维全局变形解耦为低频模态形状，采用了基于物理的变形特征。尽管模态分析在计算机视觉和仿真领域被广泛采用，但尚未被用于机器人变形控制。我们开发了一种新的无模型框架，用于机器人操作下的模态变形控制。模态形状的物理解释使我们能够构建一个分析性的变形雅可比矩阵，将机器人操作映射到模态特征的变化上。在该雅可比矩阵中，物体的未知几何和物理属性被视为低维模态参数，这些参数可用于线性参数化闭环系统。因此，可以设计一个具有稳定性保证的自适应控制器，在在线估计模态参数的同时对物体进行变形。我们使用不同设置下的线性、平面和实体物体进行了仿真和实验。结果不仅证实了我们控制器的优越性能，还展示了其相对于基线方法的优势。