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.

Verifying Physics-Informed Neural Network Fidelity using Classical Fisher Information from Differentiable Dynamical System

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.

Systematic Literature Review on Vehicular Collaborative Perception -- A Computer Vision Perspective

The effectiveness of autonomous vehicles relies on reliable perception capabilities. Despite significant advancements in artificial intelligence and sensor fusion technologies, current single-vehicle perception systems continue to encounter limitations, notably visual occlusions and limited long-range detection capabilities. Collaborative Perception (CP), enabled by Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communication, has emerged as a promising solution to mitigate these issues and enhance the reliability of autonomous systems. Beyond advancements in communication, the computer vision community is increasingly focusing on improving vehicular perception through collaborative approaches. However, a systematic literature review that thoroughly examines existing work and reduces subjective bias is still lacking. Such a systematic approach helps identify research gaps, recognize common trends across studies, and inform future research directions. In response, this study follows the PRISMA 2020 guidelines and includes 106 peer-reviewed articles. These publications are analyzed based on modalities, collaboration schemes, and key perception tasks. Through a comparative analysis, this review illustrates how different methods address practical issues such as pose errors, temporal latency, communication constraints, domain shifts, heterogeneity, and adversarial attacks. Furthermore, it critically examines evaluation methodologies, highlighting a misalignment between current metrics and CP's fundamental objectives. By delving into all relevant topics in-depth, this review offers valuable insights into challenges, opportunities, and risks, serving as a reference for advancing research in vehicular collaborative perception.