标题： 安全规划与控制的约束扩散器 显示英文标题

标题： Constrained Diffusers for Safe Planning and Control

摘要： 扩散模型由于能够表示关于动作和轨迹的多模态分布，在规划和控制任务中表现出显著潜力。然而，在约束下确保安全性仍然是扩散模型的关键挑战。本文提出了一种名为受限扩散器的新框架，该框架能够在无需重新训练或架构修改的情况下将约束纳入预训练的扩散模型。受到约束优化的启发，我们为反向扩散过程应用了一种受限朗之万采样机制，通过三种迭代算法联合优化轨迹并实现约束满足：投影法、原始-对偶法和增广拉格朗日方法。此外，我们将离散控制屏障函数作为受限扩散器的约束，以保证在线实现中的安全性。在Maze2D、运动和PyBullet球跑任务的实验表明，我们提出的方法在静态和时变约束环境中实现了约束满足，并且计算时间更少，与现有方法具有竞争力。 显示英文摘要

摘要： Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge for diffusion models. This paper proposes Constrained Diffusers, a novel framework that incorporates constraints into pre-trained diffusion models without retraining or architectural modifications. Inspired by constrained optimization, we apply a constrained Langevin sampling mechanism for the reverse diffusion process that jointly optimizes the trajectory and realizes constraint satisfaction through three iterative algorithms: projected method, primal-dual method and augmented Lagrangian approaches. In addition, we incorporate discrete control barrier functions as constraints for constrained diffusers to guarantee safety in online implementation. Experiments in Maze2D, locomotion, and pybullet ball running tasks demonstrate that our proposed methods achieve constraint satisfaction with less computation time, and are competitive to existing methods in environments with static and time-varying constraints.