Projected Attainable Speed Space: A Driving Efficiency Metric Connecting Instantaneous Evaluation to Travel Time
Authors: Xiaohua Zhao, Zhaowei Huang, Chen Chen, Haiyi Yang
Organizations: Beijing Key Laboratory of Traffic Engineering, Beijing University of Technology, Beijing, 100124, P.R.China
Abstract
Inefficient driving behaviors, such as overly conservative yielding, remain a key obstacle to deployment of autonomous vehicles (AVs). Instantaneous driving efficiency metrics are crucial for self-driving decision-making because they affect real-time performance evaluation and control optimization. However, commonly used indicators, including speed, relative speed, and inter-vehicle distance, are limited in capturing traffic context and in ensuring consistency between instantaneous outputs and travel-level outcomes. This study proposes the Projected Attainable Speed Space (PASS) model, a unified framework for driving efficiency assessment across instantaneous and travel-level analyses by integrating kinematic and spatial traffic information. PASS characterizes instantaneous driving efficiency with two coupled elements: potential for speed improvement (available acceleration space) and response to that potential (utilization of available acceleration space). Available acceleration space is referenced to projected attainable speed, derived from an idealized catch-up maneuver using relative speed and spacing to the leading vehicle; utilization is represented by the temporal change in available acceleration space. To ensure cross-scale consistency, time-aggregated PASS is defined as a travel-level efficiency metric. Trajectory data from a driving simulation experiment are used for parameter calibration to maximize agreement between time-aggregated PASS and observed travel times. Across 10 lane-change events, results show strong consistency, with an average coefficient of determination of 0.913, validating PASS for consistent efficiency evaluation across instantaneous and travel-level temporal scales. This study provides a unified, physically grounded framework that supports real-time decision-making and long-term performance analysis in autonomous driving.
End-to-end autonomous driving models often encounter performance bottlenecks, as training-time scaling leads to high computational costs and diminishing marginal returns. Existing planners typically adopt a one-shot generation paradigm, lacking secondary validation and active correction mechanisms to detect and revise suboptimal or unsafe trajectories during inference. To address this issue, we propose DriveVer, a lightweight, plug-and-play Test-Time Verifier that leverages the test-time scaling paradigm to enable autonomous driving systems to validate and refine trajectories without costly and heavy training. We construct a dedicated trajectory dataset based on the NAVSIM benchmark through condition-driven clustering and balanced sampling according to ego-vehicle states and navigation commands. Employing a dual-head architecture, DriveVer efficiently fuses candidate trajectories with multi-view visual representations and ego-vehicle kinematic features to simultaneously predict a safety confidence score and an absolute geometric refinement vector. Extensive experiments on the NAVSIM benchmark show that DriveVer significantly improves the performance of base planning models. Notably, as an extremely compact model with only 34M parameters, DriveVer introduces minimal computational overhead, achieving competitive results while maintaining real-time inference efficiency.
End to end (E2E) autonomous driving trajectory prediction is often trained with camera frames sampled at the highest available temporal frequency, assuming that denser sampling improves performance. We question this assumption by treating temporal sampling frequency as an explicit training set design variable. Starting from high frequency E2E driving datasets, we construct frequency sweep training sets by temporally subsampling camera frames along each trajectory. For each model dataset pair, we train and evaluate the same model under a fixed protocol, so the frequency response reflects how prediction performance changes with sampling frequency. We analyze this response from a capacity aware perspective. Sparse sampling may miss driving relevant cues, while dense sampling may add redundant visual content and off manifold noise. For finite capacity models, this can create a driving irrelevant capacity burden. We evaluate three smaller E2E models and a larger VLA style AutoVLA model on Waymo, nuScenes, and PAVE. Results show model and dataset dependent frequency responses. Smaller E2E models often show non monotonic or near plateau trends and achieve their best 3 second ADE at lower or intermediate frequencies. In contrast, AutoVLA achieves its best 3 second ADE and FDE at the highest evaluated frequency on all three datasets. Iteration matched controls suggest that the advantage of lower or intermediate frequencies for smaller models is not explained only by unequal training update counts. These findings show that temporal sampling frequency should be reported and tuned, rather than fixed to the highest available value.
Most autonomous driving safety benchmarks use time-to-collision (TTC) to assess risk and guide safe behaviour. However, TTC-based methods treat risk as a one-dimensional closing problem, despite the inherently two-dimensional nature of collision avoidance, and therefore cannot faithfully capture risk or its evolution over time. Here, we report evasive acceleration (EA), a hyperparameter-free and physically interpretable two-dimensional paradigm for risk quantification. By evaluating all possible directions of collision avoidance, EA defines risk as the minimum magnitude of a constant relative acceleration vector required to alter the relative motion and make the interaction collision-free. Using interaction data from five open datasets and more than 600 real crashes, we derive percentile-based warning thresholds and show that EA provides the earliest statistically significant warning across all thresholds. Moreover, EA provides the best discrimination of eventual collision outcomes and improves information retention by 54.2-241.4% over all compared baselines. Adding EA to existing methods yields 17.5-95.5 times more information gain than adding existing methods to EA, indicating that EA captures much of the outcome-relevant information in existing methods while contributing substantial additional nonredundant information. Overall, EA better captures the structure of collision risk and provides a foundation for next-generation autonomous driving systems.