Model Predictive Path Integral Control using Covariance Variable Importance Sampling

In this paper we develop a Model Predictive Path Integral (MPPI) control algorithm based on a generalized importance sampling scheme and perform parallel optimization via sampling using a Graphics Processing Unit (GPU). The proposed generalized importance sampling scheme allows for changes in the drift and diffusion terms of stochastic diffusion processes and plays a significant role in the performance of the model predictive control algorithm. We compare the proposed algorithm in simulation with a model predictive control version of differential dynamic programming.

💡 Research Summary

The paper presents a novel Model Predictive Path Integral (MPPI) control algorithm that integrates the path‑integral optimal control framework with model predictive control (MPC) while addressing a key limitation of traditional path‑integral methods: the reliance on sampling from uncontrolled dynamics. In the classic formulation, the optimal control law is expressed as an expectation over trajectories generated by the system’s stochastic differential equation (SDE) without any control input. Because the probability of drawing low‑cost trajectories from this “zero‑control” distribution is typically vanishingly small—especially for systems with low intrinsic noise or strong nonlinearities—the Monte‑Carlo approximation becomes inefficient and often fails to converge in real‑time applications.

To overcome this, the authors develop a generalized importance‑sampling scheme that simultaneously modifies both the drift (mean) and diffusion (covariance) of the sampling distribution. Building on Girsanov’s theorem, they introduce a controllable scaling matrix (A_t) that reshapes the diffusion term, yielding a new sampling process \