Barrier Function Conformal Safety Clearance Certification with CVaR for Driving Trajectory Selection

Pei Yu Chang; Qadeer Ahmed

eess.SYAug 27, 2026

Barrier Function Conformal Safety Clearance Certification with CVaR for Driving Trajectory Selection

Authors: Pei Yu Chang, Qadeer Ahmed

Organizations: Department of Mechanical and Aerospace Engineering,The Ohio State University, Columbus, OH 43212 USA

Abstract

Autonomous driving motion planners generate and select candidate trajectories while accounting for interactions with surrounding agents. However, these evaluations do not certify the actual safety clearance of the selected trajectory. The framework evaluates the trajectory selected by ant planners and calibrates the gap between its plan time margin and realized safety clearance. A differentiable separating axis barrier margin deterministically lower bounds exact signed oriented-bounding-box (OBB) safety clearance, connecting the statistical certificate to safety margin. At plan time, the margin is evaluated using either a nominal prediction and sampled lower tail Conditional Value-at-Risk (CVaR), while post-selection conformal calibration over exchangeable drive sessions absorbs prediction and sampling errors. Conformal calibration provides statistical validity independently of predictor correctness. The method is evaluated on a frozen 300 session nuPlan study using native Predictive Driver Model (PDM) Closed loop proposals. At 10% target miscoverage, sampled lower CVaR reduces the conformal correction from 1.43m to 0.03m and increases the rate of nonnegative safety clearance certificates from 68.7% to 87.3%. Across all evaluated statistics, exact-clearance coverage remains above the 90% target at 93.3--96.7%.

Figures & tables

Statistic	$\eta$	$\widehat{q}$	Exact cov.	Cert. rate	Unit FC
Nominal	.10	1.43	.933	.687	.007
CVaR .30	.10	0.03	.960	.873	.020
CVaR .10	.10	0.03	.967	.873	.020
Nominal	.05	3.66	.967	.407	.007
CVaR .30	.05	0.24	.973	.860	.020
CVaR .10	.05	0.24	.973	.840	.013

TABLE I: Session level conformal evaluation on the nuPlan PDM benchmark. Exact cov. denotes the event in Theorem 1 ; Unit FC is the unit level false certification rate. Certification uses

\rho=0

Fig. 1: Exact safety clearance coverage versus target coverage $1-\eta$ over 150 held-out test sessions. Error bars denote 95% Wilson intervals, and the dashed line indicates the target coverage.

	Nominal			CVaR .10
City	$\widehat{q}$	Cov.	Cert.	$\widehat{q}$	Cov.	Cert.
Boston	.66	.88	.88	.24	.98	.90
Pittsburgh	.15	.92	.92	.03	.96	.90
Singapore	2.70	.94	.60	.02	.98	.88

TABLE II: Within-city conformal evaluation at

\eta=0.10

and

\rho=0

using 50 calibration and 50 test sessions per city. Cov. denotes exact safety clearance coverage and Cert. the certificate rate.

Fig. 2: Illustrative paired CLS-NR pedestrian scene. The top panels compare native PDM and the proposed method at an intervention frame; the closest dynamic agent is shown in red, with solid and dashed paths indicating subsequent motion. At the illustrated frame, the exact OBB safety clearance is $0.73$ m for native PDM and $1.12$ m for the proposed method. The lower panel shows the safety clearance traces over the complete rollout. The vertical line marks the illustrated frame, while the horizontal dashed lines mark contact at $0$ m and the $1$ m clearance threshold.

Fig. 3: Illustrative paired CLS-NR traffic-light traversal. The top panels compare native PDM and the proposed method at the native PDM minimum safety clearance; the proposed trajectory has already diverged following an earlier intervention. At the illustrated frame, the exact OBB safety clearance is $0.53$ m for native PDM and $1.02$ m for the proposed method.

Metric	Native PDM	Proposed	Difference
Minimum clearance [m]	1.223	1.238	+0.016
5th-percentile clearance [m]	1.603	1.625	+0.022
Overlap exposure	.0277	.0255	-.0023
Exposure below 0.5 m	.0591	.0562	-.0029
Exposure below 1.0 m	.2497	.2377	-.0120

TABLE III: Safety clearance diagnostic for 50 scenarios from 30 drive sessions. Exposure denotes the fraction of frames below the indicated exact OBB safety clearance.

Autonomous Driving Safety Evaluation

Autonomous driving safety evaluation studies how to measure, test, and improve the safety of self-driving systems in routine and hazardous conditions.

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PC-Diffuser: Path-Consistent Capsule CBF Safety Filtering for Diffusion-Based Trajectory Planner

Eugene Ku, Yiwei Lyu

Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA

Constrained Motion Planning Trajectory Generation Diffusion-Based Planning Control Barrier Functions Safety Filtering Safe Motion Planning+1

Open paper AskPDF arXiv

Autonomous driving in complex traffic requires planners that generalize beyond hand-crafted rules, motivating data-driven approaches that learn behavior from expert demonstrations. Diffusion-based trajectory planners have recently shown strong closed-loop performance by iteratively denoising a full-horizon plan, but they remain difficult to certify and can fail catastrophically in rare or out-of-distribution scenarios. To address this challenge, we present PC-Diffuser, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning. The key idea is to make safety an intrinsic part of trajectory generation rather than a post-hoc fix: we enforce forward invariance along the rollout while preserving the diffusion model's intended path geometry. Specifically, PC-Diffuser (i) evaluates collision risk using a capsule-distance barrier function that better reflects vehicle geometry and reduces unnecessary conservativeness, (ii) converts denoised waypoints into dynamically feasible motion under a kinematic bicycle model, and (iii) applies a path-consistent safety filter that eliminates residual constraint violations without geometric distortion, so the corrected plan remains close to the learned distribution. By injecting these safety-consistent corrections at every denoising step and feeding the refined trajectory back into the diffusion process, PC-Diffuser enables iterative, context-aware safeguarding instead of post-hoc repair...

Abstract

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