This paper provides a tutorial and a survey of probabilistic inference-based model predictive control (PI-MPC) for robotics. PI-MPC defines an optimal control distribution shaped by trajectory cost, a control prior, and a temperature parameter. In the tutorial part, we derive this view and describe action generation via variational inference, highlighting Model Predictive Path Integral (MPPI) control as a representative algorithm. In the survey part, we organize the PI-MPC literature around the principal design choices identified in the tutorial: prior distribution design, multi-modal distribution handling, constraint satisfaction, scalability to high-degree-of-freedom robots, hardware acceleration, and theoretical foundations. Overall, this paper aims to serve as a coherent entry point for researchers and practitioners interested in understanding, implementing, and extending PI-MPC.

翻译：本文为机器人学中基于概率推理的模型预测控制（PI-MPC）提供了一份教程与综述。PI-MPC定义了一种由轨迹成本、控制先验及温度参数共同塑造的最优控制分布。在教程部分，我们推导了这一视角，并通过变分推理描述了动作生成过程，重点介绍了作为代表性算法的模型预测路径积分（MPPI）控制。在综述部分，我们围绕教程中识别出的核心设计选择对PI-MPC文献进行了梳理：先验分布设计、多模态分布处理、约束满足、对高自由度机器人的可扩展性、硬件加速以及理论基础。总体而言，本文旨在为有意理解、实现和扩展PI-MPC的研究者与实践者提供一个连贯的入门指南。