Learning Motion Feasibility from Point Clouds in Cluttered Environments

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

Learning motion latents for robotic manipulation heavily relies on extracting motion patterns from visual sequences, yet effective action abstractions require understanding three-dimensional geometric transformations. Here, we introduce GeoMoLa (Geometry-Aware Motion Latents), which learns discrete motion latent codes by predicting how point clouds evolve during manipulation rather than reconstructing visual observations. This four-dimensional objective -- spatial geometry changing through time -- forces latent representations to encode actual physical motion rather than appearance patterns. GeoMoLa achieves state-of-the-art performance using only single-view RGB-D input, while existing methods require multi-view reconstruction, succeeding across diverse manipulation benchmarks. Our ablations reveal that geometric prediction is the key to driving performance, quantitatively validating that manipulation depends on spatial understanding. Furthermore, the learned codes exhibit effective motion abstraction: applying them to novel scenes produces physically consistent transformations regardless of visual context. Our real-world experiments also confirm this robustness capability, achieving robust manipulation with minimal demonstrations in cluttered environments where geometric reasoning determines success. Thus, we demonstrate that effective motion latents for robot control can better emerge from understanding motion through its three-dimensional effects rather than pixel-level patterns.

Task-oriented grasping (TOG) requires robots to grasp functional parts of objects (e.g., the handle of a mug for pouring), yet these affordance regions are frequently occluded in cluttered scenes. Active perception via next-best-view (NBV) planning can resolve such occlusions by moving the camera for more informative observations. However, existing NBV methods typically optimize viewpoints for grasping the target object as a whole without distinguishing which part is task-relevant. A naive adaptation, fully scanning the target object before predicting the affordance, wastes most of the viewpoint budget on task-irrelevant surfaces (e.g., the mug body for pouring). To address this, we propose ATAP, an Affordance-Targeted Active Perception framework that shifts viewpoint planning from exhaustive target scanning to targeted affordance verification. ATAP hypothesizes the occluded target geometry via a generative shape prior and predicts the affordance distribution over the imagined complete surface. In cluttered scenes, severe occlusion can make the location of the hidden affordance ambiguous, leaving multiple locations plausible given the partial observation. ATAP therefore introduces an uncertainty-aware viewpoint planner that jointly optimizes expected entropy reduction over these competing hypotheses and expected affordance verification gain from real observations. This process iterates until the affordance is sufficiently verified for grasp execution. Experiments in simulation and real-world cluttered scenes show that ATAP substantially improves the functional grasp success rate over fixed-view TOG baselines, and outperforms reconstruction-based active perception with over 57% fewer NBV steps.