Fourier Features Let Agents Learn High Precision Policies with Imitation Learning
Authors: Balázs Gyenes, Emiliyan Gospodinov, Jan Frieling, Enrico Krohmer, Nicolas Schreiber, Xiaogang Jia, Niklas Freymuth, Gerhard Neumann
Abstract
High-precision robotic manipulation requires fine-grained spatial reasoning that is often difficult to achieve with RGB-only policies due to depth ambiguity and perspective scale issues. Policies that leverage 3D information directly, such as those based on point clouds, offer a stronger geometric prior over purely image-based ones, yet their performance remains highly task-dependent. We hypothesize that this discrepancy may be due to the spectral bias of neural networks towards learning low frequency functions, which especially affects architectures conditioned on slow-moving Cartesian features. We thus propose to map point clouds from Cartesian space into high-dimensional Fourier space, effectively equipping the point cloud encoder with direct access to high-frequency features. We experimentally validate the use of Fourier features on challenging manipulation tasks from the RoboCasa and ManiSkill3 benchmarks and on a real robot setup. Despite their simplicity, we find that Fourier features provide significant benefits across diverse encoder architectures and benchmarks and are robust across hyperparameters. Our results indicate that Fourier features let policies leverage geometric details more effectively than Cartesian features, showing their potential as a general-purpose tool for point cloud-based imitation learning. We provide source code and videos on our project page: https://fourier-il.github.io/fourier-il
3D policy learning promises superior generalization and cross-embodiment transfer, but progress has been hindered by training instabilities and severe overfitting, precluding the adoption of powerful 3D perception models. In this work, we systematically diagnose these failures, identifying the omission of 3D data augmentation and the adverse effects of Batch Normalization as primary causes. We propose a new architecture coupling a scalable transformer-based 3D encoder with a diffusion decoder, engineered specifically for stability at scale and designed to leverage large-scale pre-training. Our approach significantly outperforms state-of-the-art 3D baselines on challenging manipulation benchmarks, establishing a new and robust foundation for scalable 3D imitation learning. Project Page: https://r3d-policy.github.io/
Generalizable robot manipulation requires stable 3D understanding of functional object parts, such as handles, tool heads, openings, and graspable regions. Raw point clouds provide geometry but lack explicit part semantics, and their sampled points vary with viewpoint, sensor configuration, and object instance. Existing 2D feature lifting and discrete 3D point-wise features enrich point clouds with semantics, but the resulting features remain attached to observation-dependent samples. We propose an object-centric continuous semantic field that conditions on an object point cloud and reads part-aware semantic embeddings at explicit 3D query locations. The field is trained from part-annotated object models and then frozen to generate semantic point clouds as object-level conditioning for manipulation policies. Experiments on RoboTwin simulation tasks and real-world bimanual object manipulation show that our representation provides more stable functional-part cues and improves policy performance over raw point-cloud, 2D feature lifting, and 3D point-wise feature baselines. Project Page: \href{https://zainzh.github.io/beyond-point-attached-semantics}{https://zainzh.github.io/beyond-point-attached-semantics}.
Imitation learning is a prominent paradigm for robotic manipulation. However, existing visual imitation methods map 2D image observations directly to 3D action outputs, imposing a 2D-3D mismatch that hinders spatial reasoning and degrades robustness. We present VolumeDP, a policy architecture that restores spatial alignment by explicitly reasoning in 3D. VolumeDP first lifts image features into a Volumetric Representation via cross-attention. It then selects task-relevant voxels with a learnable module and converts them into a compact set of spatial tokens, markedly reducing computation while preserving action-critical geometry. Finally, a multi-token decoder conditions on the entire token set to predict actions, thereby avoiding lossy aggregation that collapses multiple spatial tokens into a single descriptor. VolumeDP achieves a state-of-the-art average success rate of 88.8% on the LIBERO simulation benchmark, outperforming the strongest baseline by a substantial 14.8% improvement. It also delivers large performance gains over prior methods on the ManiSkill and LIBERO-Plus benchmarks. Real-world experiments further demonstrate higher success rates and robust generalization to novel spatial layouts, camera viewpoints, and environment backgrounds. Code and videos are available on the project page: https://yzc0731.github.io/VolumeDP/