# Trajectory Distribution Control for Model Predictive Path Integral Control using Covariance Steering

arXiv: https://arxiv.org/abs/2109.12147 · HTML: https://mlsanity.com/paper/2109.12147/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2021.

## Built on by (most cited first, 8 of 8)

- [Deep Model Predictive Optimization](https://mlsanity.com/paper/2310.04590/) (2023)
- [Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions](https://mlsanity.com/paper/2502.15006/) (2025)
- [DualShield: Safe Model Predictive Diffusion via Reachability Analysis for Interactive Autonomous Driving](https://mlsanity.com/paper/2601.15729/) (2026)
- [GP-guided MPPI for Efficient Navigation in Complex Unknown Cluttered Environments](https://mlsanity.com/paper/2307.04019/) (2023)
- [Lightweight Temporal Transformer Decomposition for Federated Autonomous Driving](https://mlsanity.com/paper/2506.23523/) (2025)
- [PegasusFlow: Parallel Rolling-Denoising Score Sampling for Robot Diffusion Planner Flow Matching](https://mlsanity.com/paper/2509.08435/) (2025)
- [Fixed Horizon Linear Quadratic Covariance Steering in Continuous Time with Hilbert-Schmidt Terminal Cost](https://mlsanity.com/paper/2510.21944/) (2025)
- [HOLO-MPPI: Multi-Scenario Motion Planning via Hierarchical Policy Optimization](https://mlsanity.com/paper/2606.16480/) (2026)

## Abstract (arXiv)

This paper presents a novel control approach for autonomous systems operating under uncertainty. We combine Model Predictive Path Integral (MPPI) control with Covariance Steering (CS) theory to obtain a robust controller for general nonlinear systems. The proposed Covariance-Controlled Model Predictive Path Integral (CC-MPPI) controller addresses the performance degradation observed in some MPPI implementations owing to unexpected disturbances and uncertainties. Namely, in cases where the environment changes too fast or the simulated dynamics during the MPPI rollouts do not capture the noise and uncertainty in the actual dynamics, the baseline MPPI implementation may lead to divergence. The proposed CC-MPPI controller avoids divergence by controlling the dispersion of the rollout trajectories at the end of the prediction horizon. Furthermore, the CC-MPPI has adjustable trajectory sampling distributions that can be changed according to the environment to achieve efficient sampling. Numerical examples using a ground vehicle navigating in challenging environments demonstrate the proposed approach.