Toward Single-Step MPPI via Differentiable Predictive Control

Model predictive path integral (MPPI) is a sampling-based method for solving complex model predictive control (MPC) problems, but its real-time implementation faces two key challenges: the computational cost and sample requirements grow with the prediction horizon, and manually tuning the sampling covariance requires balancing exploration and noise. To address these issues, we propose Step-MPPI, a framework that learns a sampling distribution for efficient single-step lookahead MPPI implementation. Specifically, we use a neural network to parameterize the MPPI proposal distribution at each time step, and train it in a self-supervised manner over a long horizon using the MPC cost, constraint penalties, and a maximum-entropy regularization term. By embedding long-horizon objectives into training the neural distribution policy, Step-MPPI achieves the foresight of a multi-step optimizer with the millisecond-level latency of single-step lookahead. We demonstrate the efficiency of Step-MPPI across multiple challenging tasks in which MPPI suffers from high dimensionality and/or long control horizons.