This paper presents a tutorial overview of path integral (PI) control approaches for stochastic optimal control and trajectory optimization. We concisely summarize the theoretical development of path integral control to compute a solution for stochastic optimal control and provide algorithmic descriptions of the cross-entropy (CE) method, an open-loop controller using the receding horizon scheme known as the model predictive path integral (MPPI), and a parameterized state feedback controller based on the path integral control theory. We discuss policy search methods based on path integral control, efficient and stable sampling strategies, extensions to multi-agent decision-making, and MPPI for the trajectory optimization on manifolds. For tutorial demonstrations, some PI-based controllers are implemented in Python, MATLAB and ROS2/Gazebo simulations for trajectory optimization. The simulation frameworks and source codes are publicly available at https://github.com/INHA-Autonomous-Systems-Laboratory-ASL/An-Overview-on-Recent-Advances-in-Path-Integral-Control.

翻译：本文对用于随机最优控制和轨迹优化的路径积分控制方法进行了教程式综述。我们简要总结了路径积分控制的理论发展历程，以计算随机最优控制的解，并提供了交叉熵方法（一种采用滚动时域方案的的开环控制器，即模型预测路径积分）、以及基于路径积分控制理论的参数化状态反馈控制器的算法描述。我们讨论了基于路径积分控制的策略搜索方法、高效稳定的采样策略、向多智能体决策的扩展，以及针对流形上轨迹优化的MPPI。为进行教程演示，我们在Python、MATLAB和ROS2/Gazebo仿真环境中实现了若干基于路径积分的控制器，用于轨迹优化。仿真框架和源代码可在https: //github.com/INHA-Autonomous-Systems-Laboratory-ASL/An-Overview-on-Recent-Advances-in-Path-Integral-Control 公开获取。