Learning Sequential Acquisition Policies for Robot-Assisted Feeding

A robot providing mealtime assistance must perform specialized maneuvers with various utensils in order to pick up and feed a range of food items. Beyond these dexterous low-level skills, an assistive robot must also plan these strategies in sequence over a long horizon to clear a plate and complete a meal. Previous methods in robot-assisted feeding introduce highly specialized primitives for food handling without a means to compose them together. Meanwhile, existing approaches to long-horizon manipulation lack the flexibility to embed highly specialized primitives into their frameworks. We propose Visual Action Planning OveR Sequences (VAPORS), a framework for long-horizon food acquisition. VAPORS learns a policy for high-level action selection by leveraging learned latent plate dynamics in simulation. To carry out sequential plans in the real world, VAPORS delegates action execution to visually parameterized primitives. We validate our approach on complex real-world acquisition trials involving noodle acquisition and bimanual scooping of jelly beans. Across 38 plates, VAPORS acquires much more efficiently than baselines, generalizes across realistic plate variations such as toppings and sauces, and qualitatively appeals to user feeding preferences in a survey conducted across 49 individuals. Code, datasets, videos, and supplementary materials can be found on our website: https://sites.google.com/view/vaporsbot

Texture Generation on 3D Meshes with Point-UV Diffusion

In this work, we focus on synthesizing high-quality textures on 3D meshes. We present Point-UV diffusion, a coarse-to-fine pipeline that marries the denoising diffusion model with UV mapping to generate 3D consistent and high-quality texture images in UV space. We start with introducing a point diffusion model to synthesize low-frequency texture components with our tailored style guidance to tackle the biased color distribution. The derived coarse texture offers global consistency and serves as a condition for the subsequent UV diffusion stage, aiding in regularizing the model to generate a 3D consistent UV texture image. Then, a UV diffusion model with hybrid conditions is developed to enhance the texture fidelity in the 2D UV space. Our method can process meshes of any genus, generating diversified, geometry-compatible, and high-fidelity textures. Code is available at https://cvmi-lab.github.io/Point-UV-DiffusionComment: Accepted to ICCV 2023, Ora

The Decomposition Theorem and the topology of algebraic maps

We give a motivated introduction to the theory of perverse sheaves, culminating in the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties. While most proofs are omitted, we discuss several approaches to the Decomposition Theorem, indicate some important applications and examples.Comment: 117 pages. New title. Major structure changes. Final version of a survey to appear in the Bulletin of the AM

Period Integrals of CY and General Type Complete Intersections

We develop a global Poincar\'e residue formula to study period integrals of families of complex manifolds. For any compact complex manifold $X$ equipped with a linear system $V^*$ of generically smooth CY hypersurfaces, the formula expresses period integrals in terms of a canonical global meromorphic top form on $X$. Two important ingredients of our construction are the notion of a CY principal bundle, and a classification of such rank one bundles. We also generalize our construction to CY and general type complete intersections. When $X$ is an algebraic manifold having a sufficiently large automorphism group $G$ and $V^*$ is a linear representation of $G$, we construct a holonomic D-module that governs the period integrals. The construction is based in part on the theory of tautological systems we have developed in the paper \cite{LSY1}, joint with R. Song. The approach allows us to explicitly describe a Picard-Fuchs type system for complete intersection varieties of general types, as well as CY, in any Fano variety, and in a homogeneous space in particular. In addition, the approach provides a new perspective of old examples such as CY complete intersections in a toric variety or partial flag variety.Comment: An erratum is included to correct Theorem 3.12 (Uniqueness of CY structure