Model Predictive Path Integral Control

A sampling-based MPC that randomly samples large numbers of control sequences each cycle, simulates them, and averages them weighted by cost.

MPPI is a sampling-based form of model predictive control, proposed between 2015 and 2017 by Georgia Tech's Grady Williams, Evangelos Theodorou, and colleagues, with theoretical roots in path-integral optimal control and information theory. Like ordinary MPC, it executes only the first step of the optimized result each cycle, then starts over from the new state. What's different is how it solves: centered on the previous cycle's control sequence, it adds random noise and samples hundreds or thousands of candidate control sequences, forward-simulates each with the dynamics model to get a cost S, then computes a weighted average of all of them using exp(−S/λ), where λ is a temperature parameter — smaller values favor the lowest-cost samples more heavily. It needs no gradients or linearization, the cost function need not be smooth (a collision penalty is fine), the dynamics can even be a neural network, and each sample is independent, making it well suited to GPU parallelization. The drawback is needing large numbers of samples, with efficiency dropping as action dimension grows. Compared to the cross-entropy method, which uses only the lowest-cost batch of samples to update, MPPI instead uses every sample, weighted exponentially.

ExampleOn a 1:5-scale AutoRally off-road car, MPPI simulated thousands of 2–3-second trajectories in parallel on a GPU at a 40–60 Hz control rate, executing aggressive driving on a dirt track. ROS 2's Nav2 navigation framework also includes a built-in MPPI controller, sampling 1,000 trajectories per cycle by default and running above 50 Hz on an ordinary CPU.

Also called

MPPI, Information-Theoretic MPC, IT-MPC

Related

Model Predictive Control · Sampling-based MPC · Cross-Entropy Method · DIAL-MPC · ROS 2 Navigation Stack (Nav2) · Optimal Control

Sources

Williams et al.: Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving (arXiv:1707.02342, T-RO)
Williams, Aldrich, Theodorou: Model Predictive Path Integral Control using Covariance Variable Importance Sampling (arXiv:1509.01149)
Nav2 MPPI Controller README

As of

2026-09