Hermite Curves as Trajectory Priors for Vision-Language-Action Models

2026-08-02

AI Summary

This work addresses the issue of non-smooth trajectories and discontinuous boundaries in vision–language–action (VLA) models, which arises from the lack of structured representations for action segments. To this end, it introduces piecewise cubic Hermite curves as trajectory priors into the VLA framework for the first time, explicitly enforcing smoothness and continuity through endpoint positions and velocities. Three implementation variants are proposed: Hermite Tokens (autoregressive prediction), Hermite Scaffold (action decomposition), and Hermite Regularization (auxiliary regularization), all embedding the structured prior as a learning inductive bias rather than a runtime constraint. Experiments demonstrate that Hermite Regularization significantly improves task success rates—boosting performance from 63.4% to 90.0% on LIBERO, LIBERO-plus, and real-robot benchmarks—without incurring additional inference overhead.

Abstract

Despite recent progress in Vision-Language-Action (VLA) models for robotic manipulation, the action chunk remains a weakly structured interface. Existing work typically flatten each chunk into per-timestep controls, relying on implicit data learning that manifests as jagged motion and boundary discontinuities during physical execution. To address these limitations, we introduce Hermite trajectory priors, parameterizing the chunk trajectory as a piecewise cubic Hermite curve defined by endpoint positions and velocities to explicitly enforce smoothness and continuity. We instantiate this fixed operator across discrete autoregressive and continuous generative paradigms via three variants: (1) Hermite Tokens, which predict quantized boundary variables autoregressively; (2) Hermite Scaffold, which decomposes clean actions into a base scaffold and residuals; and (3) Hermite Regularization, which applies the prior strictly as an auxiliary training objective. Across simulation benchmarks and real-robot platforms, Hermite Regularization achieves superior performance among these three variants, improving π0.5 baseline success rates from 95.9% to 98.7% on LIBERO, 85.7% to 90.9% on LIBERO-plus, and 63.4% to 90.0% across four real-robot tasks without additional inference overhead. Trajectory analyses reveal that explicitly structuring trajectory priors serves most effectively as a learning inductive bias rather than a runtime constraint.

Problem

• Vision-Language-Action models
• action chunk
• trajectory smoothness
• boundary discontinuities
• robotic manipulation

Innovation

• Hermite curves
• trajectory priors
• Vision-Language-Action models
• smoothness constraint
• inductive bias