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G-TAMP is a subclass of task-and-motion planning in which the goal is to move multiple objects to target regions among movable obstacles. A standard graph search algorithm is not directly applicable, because G-TAMP problems involve hybrid search spaces and expensive action feasibility checks. To handle this, we introduce a novel planner that extends basic heuristic search with random sampling and a heuristic function that prioritizes feasibility checking on promising state\u2013action pairs. The main drawback of such pure planners is that they lack the ability to learn from planning experience to improve their efficiency. We propose two learning algorithms to address this. The first is an algorithm for learning a rank function that guides the discrete task-level search, and the second is an algorithm for learning a sampler that guides the continuous motion-level search. We propose design principles for designing data-efficient algorithms for learning from planning experience and representations for effective generalization. We evaluate our framework in challenging G-TAMP problems, and show that we can improve both planning and data efficiency.<\/jats:p>","DOI":"10.1177\/02783649211038280","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T05:09:08Z","timestamp":1631077748000},"page":"210-231","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":25,"title":["Representation, learning, and planning algorithms for geometric task and motion planning"],"prefix":"10.1177","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8888-7253","authenticated-orcid":false,"given":"Beomjoon","family":"Kim","sequence":"first","affiliation":[{"name":"Korea Advanced Institute of Science and Technology, Daejeon, Republic of 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