Title: Geometric Constraints as General Interfaces for Robot Manipulation
Primary area: applications to robotics, autonomy, planning
Keywords: Embodied AI, Robotics, LLM

Abstract: We present GeoManip, a framework to enable generalist robots to leverage essential geometric constraints derived from object-part relations for robot manipulation. For example, cutting a carrot typically requires the knife’s blade to be perpendicular to the carrot’s medial axis. By capturing geometric constraints through symbolic language representations and translating them into low-level actions, GeoManip bridges the gap between natural language and robotic execution, boosting the generalizability across diverse, even unseen tasks, objects, and scenarios. Beyond vision-language-action models that require extensive training, GeoManip operates training-free by leveraging large foundational models: a constraint generator to predict stage-specific geometric constraints and a geometry parser to locate the involved object parts. A solver then optimizes trajectories for the inferred constraints from the task descriptions and scenes. Further, GeoManip learns in-context and provides five appealing human-robot interaction features: on-the-fly policy adaptation, learning from human demonstrations, learning from failure cases, long-horizon action planning, and efficient data collection for imitation learning. Extensive evaluations on both simulations and real-world scenarios demonstrate GeoManip’s state-of-the-art performance, with superior out-of-distribution generalization while avoiding costly model training.