$A_{0}$: An Affordance-Aware Hierarchical Model for General Robotic Manipulation

Robotic manipulation faces critical challenges in understanding spatial affordances-the “where” and “how” of object interactions-essential for complex manipulation tasks like wiping a board or stacking objects. Existing methods, including modular-based and end-to-end approaches, often lack robust spatial reasoning capabilities. Unlike recent point-based and flow-based affordance methods that focus on dense spatial representations or trajectory modeling, we propose $A_{0}$, a hierarchical affordance-aware diffusion model that decomposes manipulation task into highlevel spatial affordance understanding and low-level action execution. $\quad A_{0}$ leverages the Embodiment-Agnostic Affordance Representation, which captures object-centric spatial affordances by predicting contact point and postcontact trajectories. $A_{0}$ is pre-trained on 1 million contact points data and fine-tuned on annotated trajectories, enabling generalization across platforms. Key components include Position Offset Attention for motion-aware feature extraction and a Spatial Information Aggregation Layer for precise coordinate mapping. The output is executed by the action execution module. Experiments on multiple robotic systems (Franka, Kinova, Realman and Dobot) demonstrate $A_{0}$ 's superior performance in complex tasks, showcasing its efficiency, flexibility, and real-world applicability.