Model Predictive Path Integral PID Control for Learning-Based Path Following

arXiv cs.RO / 4/1/2026

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Key Points

The paper proposes a learning-based MPPI--PID control method that optimizes PID gains using MPPI at each control step to avoid high-dimensional optimization over full control input sequences.
By optimizing in low-dimensional gain space, the approach improves sample efficiency and produces smoother, more continuous control inputs than direct MPPI input-sequence sampling.
The authors provide theoretical analysis, including an information-theoretic view connecting MPPI and MPPI--PID, plus results on how optimization dimensionality affects sample efficiency and how PID structure influences input continuity.
Experiments on mini-forklift learning-based path following using a residual-learning dynamics model (physical model + neural network) and real-data system identification show better tracking than fixed-gain PID and comparable tracking to conventional MPPI with reduced input increments.
The method preserves strong performance with substantially fewer samples, indicating it can be more practical for real-time settings where sampling budgets are limited.

Abstract

Classical proportional--integral--derivative (PID) control is widely employed in industrial applications; however, achieving higher performance often motivates the adoption of model predictive control (MPC). Although gradient-based methods are the standard for real-time optimization, sampling-based approaches have recently gained attention. In particular, model predictive path integral (MPPI) control enables gradient-free optimization and accommodates non-differentiable models and objective functions. However, directly sampling control input sequences may yield discontinuous inputs and increase the optimization dimensionality in proportion to the prediction horizon. This study proposes MPPI--PID control, which applies MPPI to optimize PID gains at each control step, thereby replacing direct high-dimensional input-sequence optimization with low-dimensional gain-space optimization. This formulation enhances sample efficiency and yields smoother inputs via the PID structure. We also provide theoretical insights, including an information-theoretic interpretation that unifies MPPI and MPPI--PID, an analysis of the effect of optimization dimensionality on sample efficiency, and a characterization of input continuity induced by the PID structure. The proposed method is evaluated on the learning-based path following of a mini forklift using a residual-learning dynamics model that integrates a physical model with a neural network. System identification is performed with real driving data. Numerical path-following experiments demonstrate that MPPI--PID improves tracking performance compared with fixed-gain PID and achieves performance comparable to conventional MPPI while significantly reducing input increments. Furthermore, the proposed method maintains favorable performance even with substantially fewer samples, demonstrating its improved sample efficiency.