Multi-step manipulation in dynamic environments remains challenging. Two major families of methods fail in distinct ways: (i) imitation learning (IL) is reactive but lacks compositional generalization, as monolithic policies do not decide which skill to reuse when scenes change; (ii) classical task-and-motion planning (TAMP) offers compositionality but has prohibitive planning latency, preventing real-time failure recovery. We introduce SymSkill, a unified learning framework that combines the benefits of IL and TAMP, allowing compositional generalization and failure recovery in real-time. Offline, SymSkill jointly learns predicates, operators, and skills directly from unlabeled and unsegmented demonstrations. At execution time, upon specifying a conjunction of one or more learned predicates, SymSkill uses a symbolic planner to compose and reorder learned skills to achieve the symbolic goals, while performing recovery at both the motion and symbolic levels in real time. Coupled with a compliant controller, SymSkill enables safe and uninterrupted execution under human and environmental disturbances. In RoboCasa simulation, SymSkill can execute 12 single-step tasks with 85% success rate. Without additional data, it composes these skills into multi-step plans requiring up to 6 skill recompositions, recovering robustly from execution failures. On a real Franka robot, we demonstrate SymSkill, learning from 5 minutes of unsegmented and unlabeled play data, is capable of performing multiple tasks simply by goal specifications. The source code and additional analysis can be found on https://sites.google.com/view/symskill.
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