PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles

TL;DR

This paper tackles runtime geofence enforcement for ground vehicles by introducing PCARNN-DCBF, a pipeline that preserves the control-affine structure of vehicle dynamics while learning residual corrections through a Physics-encoded Residual Neural Network. A preview-based Discrete Control Barrier Function converts safety into a linearized, real-time quadratic-program (QP) constraint that handles high relative degree and actuator saturation, enabling minimal intervention to maintain polygonal keep-ins. The dynamics are learned as a hybrid of physics and neural corrections, with drift and gain terms $(f,g)$ that remain affine in the control input $\mathbf{u}=[\dot{\delta},F_x]^T$, facilitating a tractable safety filter on the numerically integrated map $h\circ\Phi_{\tau}$ with a saturation-aware, bound–secant linearization. Experiments in CARLA show that PCARNN-DCBF outperforms analytical and unstructured neural baselines across electric and combustion vehicles, delivering higher containment reliability with modest data and robust performance across driving regimes. The study highlights how drivetrain topology informs the preferred learning architecture (split vs shared) and underscores the value of structure-preserving learning for safety-critical, real-time geofence enforcement.

Abstract

Runtime geofencing for ground vehicles is rapidly emerging as a critical technology for enforcing Operational Design Domains (ODDs). However, existing solutions struggle to reconcile high-fidelity learning with the structural requirements of verifiable control. We address this by introducing PCARNN-DCBF, a novel pipeline integrating a Physics-encoded Control-Affine Residual Neural Network with a preview-based Discrete Control Barrier Function. Unlike generic learned models, PCARNN explicitly preserves the control-affine structure of vehicle dynamics, ensuring the linearity required for reliable optimization. This enables the DCBF to enforce polygonal keep-in constraints via a real-time Quadratic Program (QP) that handles high relative degree and mitigates actuator saturation. Experiments in CARLA across electric and combustion platforms demonstrate that this structure-preserving approach significantly outperforms analytical and unstructured neural baselines.

Figures (4)

• Figure 1: geofencing architecture.
• Figure 2: System model: split model and shared model.
• Figure 3: Comparison of containment performance, intervention rate, and control smoothness across operating regimes for the Audi E-tron and Lincoln MKZ. Each panel illustrates how different architectures and control-affine formulations perform under low/high speed and steering conditions.
• Figure 4: Comparison of control linearity distributions for the Lincoln MKZ and Audi E-tron under varying $\gamma$ and model configurations. Each CDF shows how well the discrete control barrier function () maintains local linearity during operation.