Rotary Positional Embeddings (RoPE) This project builds on RoPE, originally a 1D technique for language models to encode relative position through complex rotations. We utilize 3D axial RoPE, which divides feature vectors into chunks (x, y, and z) to capture spatial relationships in three-dimensional space. However, standard RoPE assumes all modalities share a single, perfectly aligned coordinate frame—an assumption we relax through our learnable calibration layer.

3D Flow and Diffusion Actors Our architectural backbones are the state-of-the-art 3D Diffuser Actor (3DDA) and 3D FlowMatch Actor (3DFA). These models outperform 2D baselines by generating end-effector keyposes directly within 3D scene representations. We extend these specialized policies to handle uncalibrated real-world data.

Foundation VLA Models We leverage large-scale pre-trained backbones, specifically NVIDIA GR00T N1.5 and π 0.5​. By integrating our calibration mechanism into these multi-billion parameter models, we aim to combine their vast semantic knowledge with 3D operational precision.

Geometry-Aware Embeddings We draw inspiration from recent research in learnable positional encodings, such as ComRoPE and LieRE, which explore the use of Lie algebra to parameterize rotations in a way that respects geometric constraints.