Spline Policy: A Structured Representation for Robot Policies

2026-06-05

AI Summary

Traditional robot imitation learning relies on fixed-resolution action chunks, which struggle to capture the geometric and temporal structure of tasks. This work proposes Spline Policy, the first approach to incorporate quadratic splines into policy outputs, enabling compact parameterization of continuous trajectories. The method supports multi-resolution querying, local editing, uncertainty propagation, and seamless integration with downstream controllers without retraining the backbone network. Evaluated across low-dimensional motion, simulated, and real-world dexterous manipulation tasks—combined with diffusion models, flow matching, and vision-language-action architectures—the approach demonstrates superior compatibility, resampleability, controllability, and capability in uncertainty estimation.

Abstract

Modern imitation-learning policies for robot manipulation often represent actions as fixed-resolution action chunks, which are simple and effective but expose limited geometric and temporal structure before execution. This paper studies Spline Policy (SP), a structured representation that replaces action chunks with spline parameters while keeping the policy backbone unchanged. The predicted spline can be decoded as a compact continuous trajectory, queried at different temporal resolutions, constrained or edited in parameter space, and passed to downstream controllers. For quadratic spline outputs, the same representation can also be converted into a state-dependent vector field through an analytical distance-field construction. Under the regularity and projection assumptions of this construction, the induced dynamics do not increase the distance to the generated spline, yielding a principled local corrective mechanism around the predicted motion. The spline output further supports uncertainty propagation from observations to spline parameters, trajectories, and flow fields, and can be combined with classical control mechanisms such as null-space collision avoidance without retraining the policy backbone. We instantiate SP with diffusion, flow-matching, transformer-based, and vision-language-action backbones. Experiments in low-dimensional motion learning, simulated manipulation under matched backbones, dexterous manipulation, and real-robot case studies show that SP remains compatible with modern policy learners while exposing useful motion-structure properties, including compact decoding, temporal resampling, local correction around predicted motions, uncertainty evaluation, and controller compatibility.

Problem

• robot policies
• action representation
• geometric structure
• temporal structure
• imitation learning

Innovation

• Spline Policy
• structured policy representation
• continuous trajectory generation
• local corrective dynamics
• uncertainty propagation