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

arXiv: https://arxiv.org/abs/2309.12566 · HTML: https://mlsanity.com/paper/2309.12566/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2023.

## Built on by (most cited first, 5 of 5)

- [Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review](https://mlsanity.com/paper/2407.13734/) (2024)
- [BiC-MPPI: Goal-Pursuing, Sampling-Based Bidirectional Rollout Clustering Path Integral for Trajectory Optimization](https://mlsanity.com/paper/2410.06493/) (2024)
- [Optimality and Suboptimality of MPPI Control in Stochastic and Deterministic Settings](https://mlsanity.com/paper/2502.20953/) (2025)
- [Reservoir Predictive Path Integral Control for Unknown Nonlinear Dynamics](https://mlsanity.com/paper/2509.03839/) (2025)
- [Path Integral Value Matching for Linear Quadratic Stochastic Optimal Control](https://mlsanity.com/paper/2608.10777/) (2026)

## Abstract (arXiv)

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.