用概率推断重写控制问题，让机器人更灵活地规划动作。
Model Predictive Control via Probabilistic Inference: A Tutorial and Survey
- 将控制问题转为概率推断，通过变分推理生成动作
- 提出基于玻尔兹曼分布的控制策略，支持多模态和约束处理
- 适合机器人、自动驾驶等需要实时决策的场景
本文系统介绍了基于概率推断的模型预测控制（PI-MPC）。PI-MPC将有限时域最优控制问题重新表述为对最优控制分布的推断，该分布以控制先验加权的玻尔兹曼形式表示，并通过变分推断生成动作。在教程部分，推导了该公式并解释了通过变分推断生成动作的过程，重点介绍了具有闭式采样更新的代表性算法——模型预测路径积分（MPPI）控制。在综述部分，围绕先验设计、多模态性、约束处理、可扩展性、硬件加速与理论分析等关键设计维度，梳理了现有研究。本文为机器人及其他控制应用的研究人员和实践者提供了统一的概念视角和实用入门路径。
原文摘要 · Abstract (English)
This paper presents a tutorial and survey on Probabilistic Inference-based Model Predictive Control (PI-MPC). PI-MPC reformulates finite-horizon optimal control as inference over an optimal control distribution expressed as a Boltzmann distribution weighted by a control prior, and generates actions through variational inference. In the tutorial part, we derive this formulation and explain action generation via variational inference, highlighting Model Predictive Path Integral (MPPI) control as a representative algorithm with a closed-form sampling update. In the survey part, we organize existing PI-MPC research around key design dimensions, including prior design, multi-modality, constraint handling, scalability, hardware acceleration, and theoretical analysis. This paper provides a unified conceptual perspective on PI-MPC and a practical entry point for researchers and practitioners in robotics and other control applications.
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