Recent Advances in Path Integral Control for Trajectory Optimization: An Overview in Theoretical and Algorithmic Perspectives

TL;DR

This paper provides a comprehensive tutorial overview of recent theoretical and algorithmic developments in path integral control for stochastic optimal control and trajectory optimization, including practical implementations and extensions.

Contribution

It summarizes recent advances in path integral control theory, algorithms, and applications, offering a unified tutorial and open-source implementations.

Findings

Introduction of the cross-entropy (CE) method for PI control

Development of model predictive path integral (MPPI) for trajectory optimization

Extensions to multi-agent decision-making and manifold optimization

Abstract

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.