We consider the problem of grasp and manipulation planning when the state of the world is only partially observable. Specifically, we address the task of picking up unknown objects from a table top. The proposed approach to object shape prediction aims at closing the knowledge gaps in the robot's understanding of the world. A completed state estimate of the environment can then be provided to a simulator in which stable grasps and collision-free movements are planned.The proposed approach is based on the observation that many objects commonly in use in a service robotic scenario possess symmetries. We search for the optimal parameters of these symmetries given visibility constraints. Once found, the point cloud is completed and a surface mesh reconstructed.Quantitative experiments show that the predictions are valid approximations of the real object shape. By demonstrating the approach on two very different robotic platforms its generality is emphasized.

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