ExAMPC: the Data-Driven Explainable and Approximate NMPC with Physical Insights

TL;DR

ExAMPC tackles the challenge of safely deploying NMPC in complex, safety-critical settings by fusing physics-informed, data-driven approximations with explainable AI. It encodes NMPC trajectories via a low-dimensional Legendre-Spline representation and enforces continuous-time constraints through a convex-hull based safety envelope, augmented by a physics-driven training loss. By coupling SHAP and Symbolic Regression with regression models, ExAMPC provides interpretable insights into both the optimization process and the resulting KPI predictions, and it offers a warm-start capability to speed online NMPC. Experimental validation in autonomous valet parking and autonomous racing demonstrates substantial reductions in constraint violations and dramatic reductions in trajectory dimensionality, underscoring the approach’s practical potential for real-world, safety-critical control tasks.

Abstract

Amidst the surge in the use of Artificial Intelligence (AI) for control purposes, classical and model-based control methods maintain their popularity due to their transparency and deterministic nature. However, advanced controllers like Nonlinear Model Predictive Control (NMPC), despite proven capabilities, face adoption challenges due to their computational complexity and unpredictable closed-loop performance in complex validation systems. This paper introduces ExAMPC, a methodology bridging classical control and explainable AI by augmenting the NMPC with data-driven insights to improve the trustworthiness and reveal the optimization solution and closed-loop performance's sensitivities to physical variables and system parameters. By employing a low-order spline embedding, we reduce the open-loop trajectory dimensionality by over 95%, and integrate it with SHAP and Symbolic Regression from eXplainable AI (XAI) for an approximate NMPC, enabling intuitive physical insights into the NMPC's optimization routine. The prediction accuracy of the approximate NMPC is enhanced through physics-inspired continuous-time constraints penalties, reducing the predicted continuous trajectory violations by 93%. ExAMPC also enables accurate forecasting of the NMPC's computational requirements with explainable insights on worst-case scenarios. Experimental validation on automated valet parking and autonomous racing with lap-time optimization, demonstrates the methodology's practical effectiveness for potential real-world applications.

Figures (7)

• Figure 1: ExAMPC framework: employing operational closed-loop data to approximate the NMPC and a performance monitor then explain them using XAI
• Figure 2: Physics-inspired continuous-time constraints penalty with RESAFE/COL's convex hull in comparison with a baseline method
• Figure 3: Approximate NMPC: Continuous states trajectory embedding through Legendre-Spline coefficients, prediction using Random Forest Regressor, and spline decoding with the extrema of the regional convex hulls
• Figure 4: Insights into the control action trends through a SHAP explainability of the approximate NMPC's Legendre-Spline coefficients
• Figure 5: Performance prediction on the cost function KPI: reverse engineering different controller tuning in an AVP use case