用多项式显式建模物理信号交互，提升机器人控制性能
PRISM: Polynomial Representations for Interaction-Structured Motor Control
- 用因子化多项式模块高效捕捉观测变量间的高阶交互
- 在人形行走和接触丰富操作任务中超越标准MLP与更大模型
- 无需力觉或接触标签即可实现柔顺行为，适合硬件部署
机器人策略通常采用多层感知机（MLP）将观测映射为动作。然而，机器人观测是物理变量，许多动作相关线索并非来自单一变量，而是其交互作用——功率、惯性效应、接触、滑移和柔顺性均依赖可观测信号的乘积。本文提出PRISM，一种将可观测物理变量间多项式交互显式表达、可学习且紧凑的策略表示方法。不同于枚举所有多项式项，PRISM使用因子化多项式模块高效暴露高阶交互特征。在强化学习中，保持标准MLP主干，但在其后逐步激活逐元素多项式函数；在模仿学习中，以可端到端训练的多项式层替代扩散策略中的线性本体感受条件。在人形机器人行走和接触丰富的操作任务中，PRISM的表现优于标准MLP策略及容量相当的更大MLP，表明交互结构无法仅靠容量弥补。此外，它无需力觉、力矩、触觉输入、接触标签或阻抗控制即可实现无传感器柔顺行为。结果表明，多项式表示应成为具身运动控制的标准架构选择。
原文摘要 · Abstract (English)
Robot policies are typically MLPs mapping observations to actions. Yet robot observations are physical variables, and many action-relevant cues arise not from individual variables but from their interactions; power, inertial effects, contact, slip, and compliance depend on products among observable signals. We introduce PRISM, a policy representation that makes polynomial interactions among observable physical variables explicit, learnable, and compact. Rather than listing all polynomial terms, PRISM uses a factorized polynomial module to expose higher-order interaction features efficiently. In reinforcement learning, it keeps the standard MLP backbone but applies a gradually activated element-wise polynomial function after it. In imitation learning, it replaces linear proprioceptive conditioning in Diffusion Policy with a polynomial layer trained end-to-end. Across humanoid locomotion and contact-rich manipulation, PRISM improves performance over standard MLP policies and larger MLPs with matched capacity, showing that interaction structure cannot be replaced by capacity alone. It also yields sensorless compliant behavior without force, wrench, tactile input, contact labels, or admittance control. These results suggest that polynomial representations should become a standard architectural choice for embodied motor control. The project page is available at https://lsh3163.github.io/prism/
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