Real-Time Embedded NMPC for Autonomous Vehicle Path Tracking with Curvature-Aware Speed Adaptation and Sensitivity Analysis

Local path tracking is a critical challenge for autonomous vehicles, requiring precise trajectory following under nonlinear dynamics, strict constraints, and real-time execution. While Nonlinear Model Predictive Control (NMPC) has emerged as a leading approach, many existing methods decouple velocity planning from tracking, lack formal stability guarantees, or do not demonstrate feasibility on embedded platforms. We present a unified NMPC framework that integrates curvature-aware velocity adaptation directly into the cost function. The controller makes use of cubic spline paths, recursive feasibility constraints, and Lyapunov-based terminal costs to ensure stability. The nonlinear optimization problem is implemented in CasADi and solved using IPOPT, with warm-starting and efficient discretization techniques enabling real-time performance. Our approach has been validated in the CARLA simulator across a variety of urban scenarios, including straight roads, intersections, and roundabouts. The controller achieves a mean cross-track error of 0.10 m on straight roads, 0.44 m on roundabouts, and 1.36 m on tight intersections, while maintaining smooth control inputs and bounded actuator effort. A curvature-aware cost term yields a 14.4% reduction in lateral tracking error compared to the curvature-unaware baseline. Benchmarking results indicate that the Raspberry Pi 5 outperforms the NVIDIA Xavier AGX by 1.5–1.6×, achieving mean execution times of 38–45 ms across all scenarios. This demonstrates that advanced NMPC can run in real time on low-cost consumer hardware ($80 vs. $700). Systematic ablation studies reveal the critical role of state weighting (Q) and input regularization (R): removing Q degrades tracking by 10% and destabilizes control effort (+54% acceleration, +477% steering), while omitting R induces oscillatory behavior with +907% acceleration effort. Euler integration provides no computational benefit (+8% solver time) while degrading accuracy by 25%, confirming RK4 as strictly superior. Sensitivity analysis via Latin Hypercube Sampling identifies the prediction horizon (N) and discretization timestep (Δt) as dominant parameters. Per-scenario Pareto analysis yields a balanced operating point (N=15, Δt=0.055 s) used for all primary evaluations, while a global sweep identifies a robust alternative (N=12, Δt=0.086 s) suitable for general deployment tuning. This framework bridges the gap between spline-based local planning and stability-guaranteed NMPC, offering a simulation-validated, real-time solution for embedded autonomous driving research. Future work will focus on hardware-in-the-loop and full-vehicle deployment, integration with high-level decision-making, and learning-enhanced MPC.