Articulated objects like cabinets and doors are widespread in daily life. However, directly manipulating 3D articulated objects is challenging because they have diverse geometrical shapes, semantic categories, and kinetic constraints. Prior works mostly focused on recognizing and manipulating articulated objects with specific joint types. They can either estimate the joint parameters or distinguish suitable grasp poses to facilitate trajectory planning. Although these approaches have succeeded in certain types of articulated objects, they lack generalizability to unseen objects, which significantly impedes their application in broader scenarios. In this paper, we propose a novel framework of Generalizable Articulation Modeling and Manipulating for Articulated Objects (GAMMA), which learns both articulation modeling and grasp pose affordance from diverse articulated objects with different categories. In addition, GAMMA adopts adaptive manipulation to iteratively reduce the modeling errors and enhance manipulation performance. We train GAMMA with the PartNet-Mobility dataset and evaluate with comprehensive experiments in SAPIEN simulation and real-world Franka robot. Results show that GAMMA significantly outperforms SOTA articulation modeling and manipulation algorithms in unseen and cross-category articulated objects. We will open-source all codes and datasets in both simulation and real robots for reproduction in the final version. Images and videos are published on the project website at: http://sites.google.com/view/gamma-articulation
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