Motion Planning for Autonomous Vehicles using Optimization over Graphs of Convex Sets

Motion planning for autonomous vehicles requires generating collision-free and dynamically feasible trajectories in complex environments under real-time constraints. While nonlinear optimal control formulations provide high-fidelity solutions, they are computationally demanding and sensitive to initialization, whereas geometric planning methods scale well but often decouple path selection from trajectory optimization. This paper studies the extent to which optimization over Graphs of Convex Sets (GCS) can approximate solutions of nonlinear optimal control problems in the context of autonomous driving. The free space is represented as a finite union of convex regions organized as a directed graph, allowing nonconvex geometry to be handled through discrete connectivity decisions while maintaining convex trajectory constraints within each region. Vehicle motion is parameterized using Bezier curves for the spatial path and a polynomial time-scaling function for temporal evolution. Under small-slip and linear tire assumptions, a simplified dynamic bicycle model enables approximate enforcement of dynamic feasibility through convex constraints on trajectory derivatives. The approach is evaluated in CommonRoad scenarios involving static obstacle avoidance and lane-changing maneuvers, and is compared against a nonlinear discrete-time optimal control formulation. The results indicate that the GCS-based method generates collision-free and dynamically consistent trajectories that closely match those obtained from the nonlinear program, while exhibiting improved computational efficiency and reduced sensitivity to initialization. These findings suggest that GCS provides a structured approximation of nonlinear motion planning problems, capturing dominant geometric and dynamic effects while preserving convexity in the continuous relaxation.

White-Box Neural Ensemble for Vehicular Plasticity: Quantifying the Efficiency Cost of Symbolic Auditability in Adaptive NMPC

We present a white-box adaptive NMPC architecture that resolves vehicular plasticity (adaptation to varying operating regimes without retraining) by arbitrating among frozen, regime-specific neural specialists using a Modular Sovereignty paradigm. The ensemble dynamics are maintained as a fully traversable symbolic graph in CasADi, enabling maximal runtime auditability. Synchronous simulation validates rapid adaptation (~7.3 ms) and near-ideal tracking fidelity under compound regime shifts (friction, mass, drag) where non-adaptive baselines fail. Empirical benchmarking quantifies the transparency cost: symbolic graph maintenance increases solver latency by 72-102X versus compiled parametric physics models, establishing the efficiency price of strict white-box implementation.