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 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：本文对随机最优控制与轨迹优化中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求解随机最优控制问题的理论发展，并提供了以下算法的算法描述：采用重规划策略的开环控制器——模型预测路径积分（MPPI）、基于交叉熵（CE）方法的开环控制器，以及基于路径积分控制理论的参数化状态反馈控制器。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，以及流形上轨迹优化的MPPI方法。为进行教程演示，部分基于路径积分控制的控制器已在MATLAB和ROS2/Gazebo仿真环境中实现轨迹优化。仿真框架及源代码已开源发布于https://github.com/INHA-Autonomous-Systems-Laboratory-ASL/An-Overview-on-Recent-Advances-in-Path-Integral-Control。