We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the computational domain. Our approach is based on the combination of two neural networks (NNs). The first NN, conditioned on a latent code, provides an implicit representation of geometry variability through signed distance functions. This automated shape encoding technique generates compact, low-dimensional representations of geometries within a latent space, without requiring the explicit construction of an encoder. The second NN reconstructs the output physical fields independently for each spatial point, thus avoiding the computational burden typically associated with high-dimensional discretizations like computational meshes. Furthermore, we show that accuracy in geometrical characterization can be further enhanced by employing Fourier feature mapping as input feature of the NN. The meshless nature of the proposed method, combined with the dimensionality reduction achieved through automatic feature extraction in latent space, makes it highly flexible and computationally efficient. This strategy eliminates the need for manual intervention in extracting geometric parameters, and can even be applied in cases where geometries undergo changes in their topology. Numerical tests in the field of fluid dynamics and solid mechanics demonstrate the effectiveness of the proposed method in accurately predict the solution of PDEs in domains of arbitrary shape. Remarkably, the results show that it achieves accuracy comparable to the best-case scenarios where an explicit parametrization of the computational domain is available.

Precisely grasping and reconstructing articulated objects is key to enabling general robotic manipulation. In this paper, we propose CenterArt, a novel approach for simultaneous 3D shape reconstruction and 6-DoF grasp estimation of articulated objects. CenterArt takes RGB-D images of the scene as input and first predicts the shape and joint codes through an encoder. The decoder then leverages these codes to reconstruct 3D shapes and estimate 6-DoF grasp poses of the objects. We further develop a mechanism for generating a dataset of 6-DoF grasp ground truth poses for articulated objects. CenterArt is trained on realistic scenes containing multiple articulated objects with randomized designs, textures, lighting conditions, and realistic depths. We perform extensive experiments demonstrating that CenterArt outperforms existing methods in accuracy and robustness.

Multi-objective optimization problems are ubiquitous in robotics, e.g., the optimization of a robot manipulation task requires a joint consideration of grasp pose configurations, collisions and joint limits. While some demands can be easily hand-designed, e.g., the smoothness of a trajectory, several task-specific objectives need to be learned from data. This work introduces a method for learning data-driven SE(3) cost functions as diffusion models. Diffusion models can represent highly-expressive multimodal distributions and exhibit proper gradients over the entire space due to their score-matching training objective. Learning costs as diffusion models allows their seamless integration with other costs into a single differentiable objective function, enabling joint gradient-based motion optimization. In this work, we focus on learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel framework for joint grasp and motion optimization without needing to decouple grasp selection from trajectory generation. We evaluate the representation power of our SE(3) diffusion models w.r.t. classical generative models, and we showcase the superior performance of our proposed optimization framework in a series of simulated and real-world robotic manipulation tasks against representative baselines.

We present CARTO, a novel approach for reconstructing multiple articulated objects from a single stereo RGB observation. We use implicit object-centric representations and learn a single geometry and articulation decoder for multiple object categories. Despite training on multiple categories, our decoder achieves a comparable reconstruction accuracy to methods that train bespoke decoders separately for each category. Combined with our stereo image encoder we infer the 3D shape, 6D pose, size, joint type, and the joint state of multiple unknown objects in a single forward pass. Our method achieves a 20.4% absolute improvement in mAP 3D IOU50 for novel instances when compared to a two-stage pipeline. Inference time is fast and can run on a NVIDIA TITAN XP GPU at 1 HZ for eight or less objects present. While only trained on simulated data, CARTO transfers to real-world object instances. Code and evaluation data is available at: http://carto.cs.uni-freiburg.de

The ability to reason about changes in the environment is crucial for robots operating over extended periods of time. Agents are expected to capture changes during operation so that actions can be followed to ensure a smooth progression of the working session. However, varying viewing angles and accumulated localization errors make it easy for robots to falsely detect changes in the surrounding world due to low observation overlap and drifted object associations. In this paper, based on the recently proposed category-level Neural Descriptor Fields (NDFs), we develop an object-level online change detection approach that is robust to partially overlapping observations and noisy localization results. Utilizing the shape completion capability and SE(3)-equivariance of NDFs, we represent objects with compact shape codes encoding full object shapes from partial observations. The objects are then organized in a spatial tree structure based on object centers recovered from NDFs for fast queries of object neighborhoods. By associating objects via shape code similarity and comparing local object-neighbor spatial layout, our proposed approach demonstrates robustness to low observation overlap and localization noises. We conduct experiments on both synthetic and real-world sequences and achieve improved change detection results compared to multiple baseline methods. Project webpage: https://yilundu.github.io/ndf_change