🤖 AI Summary
This work addresses the low sample efficiency and discontinuous control inputs of traditional Model Predictive Path Integral (MPPI) control in high-dimensional settings, as well as the limited adaptability of fixed-gain PID controllers in complex path-tracking tasks. The authors propose an MPPI–PID framework that performs sampling-based optimization not in the high-dimensional control sequence space, but in the low-dimensional space of PID gains—a novel approach that significantly improves sample efficiency and yields smoother control signals. Integrating residual learning for dynamics modeling with real-time gain adaptation, the method achieves tracking performance comparable to conventional MPPI using drastically fewer samples in a miniature forklift path-following experiment, while substantially reducing control effort compared to fixed-gain PID. A theoretical analysis further unifies MPPI and MPPI–PID from an information-theoretic perspective, clarifying how dimensionality affects both sample efficiency and input continuity.
📝 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.