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Deformable object manipulation (DOM) for robots has a wide range ofapplications in various fields such as industrial, service and health caresectors. However, compared to manipulation of rigid objects, DOM posessignificant challenges for robotic perception, modeling and manipulation, dueto the infinite dimensionality of the state space of deformable objects (DOs)and the complexity of their dynamics. The development of computer graphics andmachine learning has enabled novel techniques for DOM. These techniques, basedon data-driven paradigms, can address some of the challenges that analyticalapproaches of DOM face. However, some existing reviews do not include allaspects of DOM, and some previous reviews do not summarize data-drivenapproaches adequately. In this article, we survey more than 150 relevantstudies (data-driven approaches mainly) and summarize recent advances, openchallenges, and new frontiers for aspects of perception, modeling andmanipulation for DOs. Particularly, we summarize initial progress made by LargeLanguage Models (LLMs) in robotic manipulation, and indicates some valuabledirections for further research. We believe that integrating data-drivenapproaches and analytical approaches can provide viable solutions to openchallenges of DOM.

A Survey on Robotic Manipulation of Deformable Objects: Recent Advances, Open Challenges and New Frontiers