Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving differential equations and modeling physical systems by embedding physical laws into the learning process. However, rigorously quantifying how well a PINN captures the complete dynamical behavior of the system, beyond simple trajectory prediction, remains a challenge. This paper proposes a novel experimental framework to address this by employing Fisher information for differentiable dynamical systems, denoted $g_F^C$. This Fisher information, distinct from its statistical counterpart, measures inherent uncertainties in deterministic systems, such as sensitivity to initial conditions, and is related to the phase space curvature and the net stretching action of the state space evolution. We hypothesize that if a PINN accurately learns the underlying dynamics of a physical system, then the Fisher information landscape derived from the PINN's learned equations of motion will closely match that of the original analytical model. This match would signify that the PINN has achieved comprehensive fidelity capturing not only the state evolution but also crucial geometric and stability properties. We outline an experimental methodology using the dynamical model of a car to compute and compare $g_F^C$ for both the analytical model and a trained PINN. The comparison, based on the Jacobians of the respective system dynamics, provides a quantitative measure of the PINN's fidelity in representing the system's intricate dynamical characteristics.

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.

The synthesis of Control Barrier Functions (CBFs) often involves demanding computations or a meticulous construction. However, structural properties of the system dynamics and constraints have the potential to mitigate these challenges. In this paper, we explore how equivariances in the dynamics, loosely speaking a form of symmetry, can be leveraged in the CBF synthesis. Although CBFs are generally not inherently symmetric, we show how equivariances in the dynamics and symmetries in the constraints induce symmetries in CBFs derived through reachability analysis. This insight allows us to infer their CBF values across the entire domain from their values on a subset, leading to significant computational savings. Interestingly, equivariances can be even leveraged to the CBF synthesis for non-symmetric constraints. Specifically, we show how a partially known CBF can be leveraged together with equivariances to construct a CBF for various new constraints. Throughout the paper, we provide examples illustrating the theoretical findings. Furthermore, a numerical study investigates the computational gains from invoking equivariances into the CBF synthesis.

This paper presents a prediction algorithm that estimates the vehicle trajectory every five milliseconds for an autonomous vehicle. A kinematic and a dynamic bicycle model are compared, with the dynamic model exhibiting superior accuracy at higher speeds. Vehicle parameters such as mass, center of gravity, moment of inertia, and cornering stiffness are determined experimentally. For cornering stiffness, a novel measurement procedure using optical position tracking is introduced. The model is incorporated into an extended Kalman filter and implemented in a ROS node in C++. The algorithm achieves a positional deviation of only 1.25 cm per meter over the entire test drive and is up to 82.6% more precise than the kinematic model.

Autonomous vehicle navigation in structured environments requires planners capable of generating time-optimal, collision-free trajectories that satisfy dynamic and kinematic constraints. We introduce V*, a graph-based motion planner that represents speed and direction as explicit state variables within a discretised space-time-velocity lattice. Unlike traditional methods that decouple spatial search from dynamic feasibility or rely on post-hoc smoothing, V* integrates both motion dimensions directly into graph construction through dynamic graph generation during search expansion. T o manage the complexity of high-dimensional search, we employ a hexagonal discretisation strategy and provide formal mathematical proofs establishing optimal waypoint spacing and minimal node redundancy under constrained heading transitions for velocity-aware motion planning. We develop a mathematical formulation for transient steering dynamics in the kinematic bicycle model, modelling steering angle convergence with exponential behaviour, and deriving the relationship for convergence rate parameters. We further demonstrate V*'s performance in simulation studies with cluttered and dynamic environments involving moving obstacles, showing its ability to avoid conflicts, yield proactively, and generate safe, efficient trajectories with temporal reasoning capabilities for waiting behaviours and dynamic coordination. Autonomous navigation requires planning algorithms that can compute time-efficient and dynamically feasible trajectories. Among the diverse approaches to motion planning, optimal pathfinding algorithms are recognized for their ability to guarantee high-quality solutions by minimizing path costs under strict constraints. This makes them particularly valuable in environments where precision and efficiency are critical. Classical pathfinding methods such as the Dijkstra ( 1) and A* ( 2) algorithms have been widely adopted for solving shortest path problems on graphs due to their efficiency.

This paper introduces an AI-enabled, interaction-aware active safety analysis framework that accounts for groupwise vehicle interactions. Specifically, the framework employs a bicycle model-augmented with road gradient considerations-to accurately capture vehicle dynamics. In parallel, a hypergraph-based AI model is developed to predict probabilistic trajectories of ambient traffic. By integrating these two components, the framework derives vehicle intra-spacing over a 3D road surface as the solution of a stochastic ordinary differential equation, yielding high-fidelity surrogate safety measures such as time-to-collision (TTC). To demonstrate its effectiveness, the framework is analyzed using stochastic numerical methods comprising 4th-order Runge-Kutta integration and AI inference, generating probability-weighted high-fidelity TTC (HF-TTC) distributions that reflect complex multi-agent maneuvers and behavioral uncertainties. Evaluated with HF-TTC against traditional constant-velocity TTC and non-interaction-aware approaches on highway datasets, the proposed framework offers a systematic methodology for active safety analysis with enhanced potential for improving safety perception in complex traffic environments.

Model validity is key to the accurate and safe behavior of autonomous vehicles. Using invalid vehicle models in the different plan and control vehicle frameworks puts the stability of the vehicle, and thus its safety at stake. In this work, we analyze the validity of several popular vehicle models used in the literature with respect to a real vehicle and we prove that serious accuracy issues are encountered beyond a specific lateral acceleration point. We set a clear lateral acceleration domain in which the used models are an accurate representation of the behavior of the vehicle. We then target the necessity of using learned methods to model the vehicle's behavior. The effects of model validity on state observers are investigated. The performance of model-based observers is compared to learning-based ones. Overall, the presented work emphasizes the validity of vehicle models and presents clear operational domains in which models could be used safely.

Automated driving has become more and more popular due to its potential to eliminate road accidents by taking over driving tasks from humans. One of the remaining challenges is to follow a planned path autonomously, especially when uncertainties in self-localizing or understanding the surroundings can influence the decisions made by autonomous vehicles, such as calculating how much they need to steer to minimize tracking errors. In this paper, a modified geometric pure pursuit path-tracking algorithm is proposed, taking into consideration such uncertainties using the unscented transform. The algorithm is tested through simulations for typical road geometries, such as straight and circular lines.

Over the years, complex control approaches have been developed to control the motion of a bicycle. Reinforcement Learning (RL), a branch of machine learning, promises easy deployment of so-called agents. Deployed agents are increasingly considered as an alternative to controllers for mechanical systems. The present work introduces an RL approach to do path following with a virtual bicycle model while simultaneously stabilising it laterally. The bicycle, modelled as the Whipple benchmark model and using multibody system dynamics, has no stabilisation aids. The agent succeeds in both path following and stabilisation of the bicycle model exclusively by outputting steering angles, which are converted into steering torques via a PD controller. Curriculum learning is applied as a state-of-the-art training strategy. Different settings for the implemented RL framework are investigated and compared to each other. The performance of the deployed agents is evaluated using different types of paths and measurements. The ability of the deployed agents to do path following and stabilisation of the bicycle model travelling between 2m/s and 7m/s along complex paths including full circles, slalom manoeuvres, and lane changes is demonstrated. Explanatory methods for machine learning are used to analyse the functionality of a deployed agent and link the introduced RL approach with research in the field of bicycle dynamics.

This paper presents a novel approach to improving autonomous vehicle control in environments lacking clear road markings by integrating a diffusion-based motion predictor within an Active Inference Framework (AIF). Using a simulated parking lot environment as a parallel to unmarked roads, we develop and test our model to predict and guide vehicle movements effectively. The diffusion-based motion predictor forecasts vehicle actions by leveraging probabilistic dynamics, while AIF aids in decision-making under uncertainty. Unlike traditional methods such as Model Predictive Control (MPC) and Reinforcement Learning (RL), our approach reduces computational demands and requires less extensive training, enhancing navigation safety and efficiency. Our results demonstrate the model's capability to navigate complex scenarios, marking significant progress in autonomous driving technology.