Rotation-Aware Point-Cloud Embeddings for Vision-Based In-Hand Reorientation

Point-cloud goals provide a direct way to specify dexterous in-hand reorientation: instead of defining an object-specific pose frame or estimating 6D pose at test time, the policy is given the desired 3D geometry of the object. Yet raw point-cloud goal conditioning is poorly conditioned for policy learning. Current and goal clouds are unordered, independently sampled, and often visibility-dependent, so their discrepancy entangles object rotation with permutation, resampling, and unstable correspondence structure. For this reason, prior point-cloud manipulation methods typically add structure outside the representation itself, such as explicit pose or relative-pose inputs, dense flow features, or distillation from privileged teachers. We close this gap by learning a rotation-aware point-cloud embedding whose Euclidean latent distance is calibrated to the SO(3) geodesic error between object orientations. The resulting representation turns current-goal comparison into a smooth control signal, allowing a model-free RL policy to act from current and goal point-cloud embeddings, proprioception, and centroid metadata, without object pose, relative pose, dense flow, or teacher-action supervision. In in-hand reorientation experiments, this interface matches privileged-state and distillation-based baselines while avoiding brittle test-time computation of structured pose or flow inputs. These results suggest that point-cloud goals become practical for this task when the representation, rather than an external module, encodes the task-relevant geometry of rotation. We also show evidence that generic visual point-cloud pretraining is insufficient for such a current-goal comparison because it discards the task-relevant state and preserves only shape features.