Action Map Policy: Learning 3D Closed-loop Manipulation via Pixel Classification
Authors: Haojie Huang, Zhang Ye, Linfeng Zhao, Boce Hu, Mingxi Jia, Yu Qi, Ahmed Agha, Dian Wang, +2 more
Organizations: Northeastern University · Stanford University · Brown University
Abstract
The action space poses a major challenge in robot learning, since it is often high-dimensional, can span long time horizons, and frequently admits multi-modal optimal solutions. A good choice of action representation and loss function can help to address these concerns, but there are often trade offs. We propose Action Map Policy (AMP), which casts 3D closed-loop manipulation policy learning as a classification problem in image space. While classification has been an effective formulation in generative language models, applying it to robot action learning is difficult because naively discretizing high-dimensional continuous actions explodes the token vocabulary. Our key idea is to project 3D actions onto the camera image planes and treat each pixel location as a discrete class, thus controlling dimensionality while retaining multi-modality. This method supports millimeter-level precision for high-dimensional actions without requiring a prohibitively large vocabulary, while preserving fine-grained pixel-wise visual signals. Furthermore, it can predict the entire action chunk in a single forward pass, avoiding complex noise scheduling and iterative denoising while achieving substantially faster inference than diffusion policies. Experiments on various manipulation tasks show that AMP outperforms strong baselines, achieving higher success rates, faster inference, and enhanced spatial reasoning.
Vision-language-action (VLA) models have advanced rapidly across backbones, training recipes, and data scale, yet the action decoder, which converts the backbone's hidden state into a continuous control signal, has barely changed and remains a single-point predictor across the majority of current VLAs. Whether implemented via autoregressive token bins, L1 regression, or flow-matching denoising, the resulting decoder treats the action space as unstructured, leaving the geometric proximity of neighboring actions unexploited during training. To advance this, we introduce ActionMap, a voxel heatmap action head that drops into an existing VLA in place of its native action decoder. For each new action, the head predicts a voxel heatmap over the action space, where each voxel directly stores the probability of the corresponding action. Across LIBERO simulation and real-world Franka manipulation, our heatmap head surpasses two architecturally distinct backbones at matched training steps (e.g., +8.2% over OpenVLA-OFT's L1 regression head on the LIBERO four-suite average), converges at comparable or faster rates on both backbones, and remains markedly more data-efficient at low training data. The cross-backbone consistency indicates that action representation is a real lever for VLA performance, distinct from further backbone or recipe scaling. Project Page: https://showlab.github.io/ActionMap/.
Representing manipulation actions as 2D trajectories in the camera plane provides a compact and interpretable basis for learning complex 3D manipulation policies. However, it also creates challenges from out-of-frame trajectories and limited precision. We propose Pix2Act, an imitation learning method that addresses these challenges by generating continuous image-space keypoint trajectories in each camera plane and losslessly recovering end-effector poses via triangulation. This reformulates high-dimensional 3D control as a simpler, more learnable 2D prediction problem. Crucially, it aligns observations and actions in the same coordinate space, enabling equivariant transformations to jointly rotate individual camera images together with their image-space actions. We analyze the symmetry properties of this augmentation and design a network architecture that can fuse multiple camera views while respecting their per-view rotations. As a result, Pix2Act implicitly enlarges the support of the data distribution and learns invariant action structures across transformations, yielding improved generalization and overall performance. Across diverse simulated and real-world manipulation tasks, Pix2Act outperforms state-of-the-art baselines and remains robust under camera perturbations.
We present AEM, an Action-Effect Memory pretraining framework for robot manipulation that learns compact temporal representations from vision-action history. Unlike prior robot representation pretraining methods that mainly focus on single-frame visual encoding, AEM targets the temporal nature of manipulation, where the current observation alone is often insufficient under partial observability. AEM models manipulation as an action-driven interaction process by interleaving visual and action features and applying masked modeling to recover missing content from incomplete histories, thereby learning action-conditioned state evolution. The Mamba-encoded output of the final vision token is used as a compact history representation, serving as the global context for decoding and downstream control. This design preserves a single-vector temporal bottleneck while keeping inference efficient. We evaluate AEM with Diffusion Policy and Flow Policy. AEM consistently improves manipulation performance in both simulation and real-world settings, outperforming baselines across clean scenes, cluttered and random scenes, and non-Markovian tasks. Ablation studies further show that history-aware pretraining surpasses single-frame pretraining and direct frame stacking, while reducing inference latency and computational cost.