Model Predictive Path Integral Control as Preconditioned Gradient Descent
The paper analyzes Model Predictive Path Integral (MPPI) control using variational optimization to prove convergence guarantees. It reformulates trajectory optimization as minimizing a free-energy objective function F(θ) over decision distributions. By deriving an exact preconditioned gradient descent update, the authors show that for Gaussian models, this method perfectly recovers the classical MPPI iteration.