用条件扩散模型生成有时间结构的控制序列，解决干摩擦下的运动启动难题。
A Study of Conditional Diffusion Models for Open-Loop Control under Dry Friction and Stiction
- 用1D U-Net生成受初始和目标状态约束的控制序列
- 在低样本下比随机搜索和CEM降低终端误差与卡顿步数
- 适合需要高时序一致性的开环控制任务
扩散模型近年来作为规划与控制的表达性生成先验崭露头角。本文研究了用于带干摩擦和粘滞力点质量系统的开环控制的动作扩散（Action Diffusion）方法。该基准中，运动仅在输入超过静摩擦阈值后才开始，因此有效控制占据动作序列空间中一个狭小且具有时间结构的子集。采用紧凑的条件1D U-Net生成受限于初始和目标状态的控制序列。与均匀随机射击、同结构数据集先验的随机射击及交叉熵法（CEM）相比，结果表明动作扩散在低样本条件下显著降低终端误差与卡顿步数。这说明条件扩散能有效生成时间连贯的控制序列，通过条件化并重组训练先验中的结构化控制基元，实现状态到状态的开环控制。
原文摘要 · Abstract (English)
Diffusion models have recently emerged as expressive generative priors for planning and control. This paper studies Action Diffusion, an action-sequence diffusion formulation used as an open-loop proposal distribution for a point-mass system with dry friction and stiction. In this benchmark, motion starts only when the applied input exceeds a static-friction threshold, so effective controls occupy a small and temporally structured subset of the action-sequence space. A compact conditional 1D U-Net generates bounded control sequences conditioned on initial and target states. We compare it with uniform random shooting, random shooting from the same structured dataset prior, and the Cross-Entropy Method (CEM). Results show that Action Diffusion reduces terminal error and stuck steps, especially in low-sample regimes. These results indicate that conditional diffusion provides an effective mechanism for generating temporally coherent control sequences that overcome stiction by conditioning and recombining structured control primitives from the training prior for state-to-state open-loop control.
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