Recent advances in path integral control for trajectory optimization: An overview in theoretical and algorithmic perspectives
ANNUAL REVIEWS IN CONTROL(2024)
Abstract
This paper presents a tutorial overview of path integral (PI) 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 the github page.
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Key words
Stochastic optimal control,Trajectory optimization,Hamilton-Jacobi-Bellman equation,Feynman-Kac formula,Path integral,Variational inference,KL divergence,Importance sampling,Model predictive path integral control,Policy search,Policy improvement with path integrals,Planning on manifolds
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