RIGID: Relational Spatial Alignment for Vision-Language-Action Models

1 Queen Mary University of London, United Kingdom
2 University College London, United Kingdom
3 VGG, University of Oxford, United Kingdom

* Equal supervision and corresponding authors.

Motivation

Direct feature alignment can collapse the VLA feature space. RIGID aligns single-view and cross-view attention maps with a frozen 3D teacher to transfer spatial knowledge while preserving the VLA's representation capacity.

Figure 1: point-wise alignment versus relational alignment, with stable and effective rank comparisons showing rank loss after direct alignment and rank preservation with RIGID.
Figure 1. Aligning pairwise relationships leaves the VLA free to retain its own feature basis. In the reported analysis, RIGID preserves stable and effective rank, while direct alignment reduces both.

Abstract

Spatial understanding is essential for robots to perceive their surrounding environments and execute actions. Existing approaches typically encode 3D awareness into vision-language-action (VLA) models by directly aligning their representations with pre-trained 3D foundation models. However, we observe that such direct geometric feature alignment essentially exploits 3D foundation priors as a form of low-rank regularization in the feature space, resulting in severe rank collapse of the pre-trained VLA representations. In contrast, we shift the focus from enforcing point-wise equality to aligning pair-wise relationships. We propose a representation-alignment method that enables the injection of 3D spatial awareness without compromising the model's original expressivity. Extensive experiments on public benchmarks, our new spatial reasoning benchmark, and real-world manipulation scenarios demonstrate that our approach effectively incorporates 3D spatial representations into VLA reasoning, achieving robust performance and strong open-world generalization across diverse manipulation tasks.

Method Overview

We extract self- and cross-attention (attn.) maps from both the VLA and the 3D foundation models to serve as relational affinity matrices.

Figure 2: multi-view RGB inputs enter a VLA student and a frozen 3D teacher. Single-view and cross-view attention maps are aligned alongside action training.
Figure 2. RIGID aligns the VLA’s single-view and cross-view attention with a frozen 3D teacher. The VLA is adapted with LoRA and trained jointly with the action objective.

Experiment Results

RIGID matches the best reported average on LIBERO at 98.5% and reaches 75.0% on LIBERO-Plus.

Original Tables 1 and 2 from the paper: LIBERO and LIBERO-Plus success rates. RIGID achieves 98.5% and 75.0% average success, respectively.
Original results from the paper. Click the tables to view at full resolution.

Real-world Experiments

Six kitchen manipulation tasks on a Franka Emika Panda, using wrist and side-view RGB cameras. With a π₀ backbone, RIGID achieves the highest reported average success rate among the three evaluated methods.

Figure 7: Franka robot in a toy kitchen with side and wrist cameras, plus six tasks: placing a pot in the sink, opening a microwave, taking off a fork, stacking bowls, picking a block in a pan, and pouring water into the sink.
Figure 7. Robot setup and six tasks: (a) placing the pot in the sink, (b) opening the microwave, (c) taking off the fork, (d) stacking the bowls, (e) picking the block in the pan, and (f) pouring water into the sink. The agent-view camera is used only for visualization.
Figure 8: success rates for π₀, Spatial Forcing, and RIGID on six tasks. For RIGID the rates are 10, 40, 90, 60, 90, and 90 percent. Displayed averages are 41, 55, and 62 percent, respectively.
Figure 8. Success rates across six tasks, with 10 trials per task per method. Picking the block in the pan reaches 90% with RIGID, compared with 70% for Spatial Forcing and 20% for π₀.
Supplementary video. Real-world manipulation demonstrations · 1 min 51 sec.Download video ↓