Model Predictive Control via Probabilistic Inference: A Tutorial and Survey

TL;DR

This paper provides a comprehensive tutorial and survey on Probabilistic Inference-based Model Predictive Control (PI-MPC), explaining its formulation, key algorithms like MPPI, and organizing existing research around core design aspects.

Contribution

It offers a unified conceptual framework for PI-MPC, deriving the formulation, explaining action generation, and organizing existing research for easier understanding and application.

Findings

Derives the PI-MPC formulation and explains variational inference for action generation.

Highlights Model Predictive Path Integral (MPPI) control as a key algorithm.

Organizes PI-MPC research around design dimensions like constraints and scalability.

Abstract

This paper presents a tutorial and survey on Probabilistic Inference-based Model Predictive Control (PI-MPC). PI-MPC reformulates finite-horizon optimal control as inference over an optimal control distribution expressed as a Boltzmann distribution weighted by a control prior, and generates actions through variational inference. In the tutorial part, we derive this formulation and explain action generation via variational inference, highlighting Model Predictive Path Integral (MPPI) control as a representative algorithm with a closed-form sampling update. In the survey part, we organize existing PI-MPC research around key design dimensions, including prior design, multi-modality, constraint handling, scalability, hardware acceleration, and theoretical analysis. This paper provides a unified conceptual perspective on PI-MPC and a practical entry point for researchers and practitioners in robotics and other control applications.