Learning to Place New Objects

The ability to place objects in the environment is an important skill for a personal robot. An object should not only be placed stably, but should also be placed in its preferred location/orientation. For instance, a plate is preferred to be inserted vertically into the slot of a dish-rack as compared to be placed horizontally in it. Unstructured environments such as homes have a large variety of object types as well as of placing areas. Therefore our algorithms should be able to handle placing new object types and new placing areas. These reasons make placing a challenging manipulation task. In this work, we propose a supervised learning algorithm for finding good placements given the point-clouds of the object and the placing area. It learns to combine the features that capture support, stability and preferred placements using a shared sparsity structure in the parameters. Even when neither the object nor the placing area is seen previously in the training set, our algorithm predicts good placements. In extensive experiments, our method enables the robot to stably place several new objects in several new placing areas with 98% success-rate; and it placed the objects in their preferred placements in 92% of the cases

VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method

Semi-analytical methods, such as rigorous coupled wave analysis, have been pivotal for numerical analysis of photonic structures. In comparison to other methods, they offer much faster computation, especially for structures with constant cross-sectional shapes (such as metasurface units). However, when the cross-sectional shape varies even mildly (such as a taper), existing semi-analytical methods suffer from high computational cost. We show that the existing methods can be viewed as a zeroth-order approximation with respect to the structure's cross-sectional variation. We instead derive a high-order perturbative expansion with respect to the cross-sectional variation. Based on this expansion, we propose a new semi-analytical method that is fast to compute even in presence of large cross-sectional shape variation. Furthermore, we design an algorithm that automatically discretizes the structure in a way that achieves a user specified accuracy level while at the same time reducing the computational cost

Learning to Generate 3D Shapes from a Single Example

Existing generative models for 3D shapes are typically trained on a large 3D dataset, often of a specific object category. In this paper, we investigate the deep generative model that learns from only a single reference 3D shape. Specifically, we present a multi-scale GAN-based model designed to capture the input shape's geometric features across a range of spatial scales. To avoid large memory and computational cost induced by operating on the 3D volume, we build our generator atop the tri-plane hybrid representation, which requires only 2D convolutions. We train our generative model on a voxel pyramid of the reference shape, without the need of any external supervision or manual annotation. Once trained, our model can generate diverse and high-quality 3D shapes possibly of different sizes and aspect ratios. The resulting shapes present variations across different scales, and at the same time retain the global structure of the reference shape. Through extensive evaluation, both qualitative and quantitative, we demonstrate that our model can generate 3D shapes of various types.Comment: SIGGRAPH Asia 2022; 19 pages (including 6 pages appendix), 17 figures. Project page: http://www.cs.columbia.edu/cg/SingleShapeGen