[Paper Review] Automatic Generation of Challenging Road Networks for ALKS Testing based on Bezier Curves and Search

Florian Klück, Lorenz Klampfl+1 more|arXiv (Cornell University)|Mar 1, 2021

Autonomous Vehicle Technology and Safety4 citations

TL;DR

This paper presents a search-based approach using Bézier curves and genetic algorithms to automatically generate challenging road networks for testing Automated Lane Keeping Systems (ALKS). By evolving control points to maximize lateral deviation, the method efficiently identifies failure-inducing road geometries, with Configuration C showing improved diversity and reduced invalid test cases despite higher computational cost.

ABSTRACT

In this paper, we outline an approach for automatic generation of challenging road networks for virtual testing of an automated lane keep system. Based on a set of control points, we construct a parametric curve that represents a road network, which defines the dynamic driving task an automated lane keep system equipped vehicle has to perform. Changing control points has global influence on the resulting road geometry. Our approach uses search to find a set of control points that results in a challenging road geometry, eventually forcing the vehicle to leave the intended path. We evaluated our approach in three different search-configurations regarding test efficiency and practical applicability for automatic virtual testing of an automated lane keep system.

Motivation & Objective

• To address the challenge of efficiently testing Automated Lane Keeping Systems (ALKS) in virtual environments with realistic, failure-inducing road geometries.
• To reduce the manual effort in generating diverse and complex test scenarios for ALKS validation.
• To improve test efficiency by automatically identifying road configurations that cause ALKS to deviate from the intended path.
• To explore different search configurations that balance diversity, validity, and computational cost in test case generation.

Proposed method

• Road networks are modeled as parametric Bézier curves defined by a set of control points, enabling global influence over road geometry with minimal parameter changes.
• A genetic algorithm evolves populations of control point sets, where fitness is determined by the extent of lateral deviation (crossing center or side lines) in simulation.
• Each individual in the population is evaluated in a simulation pipeline (BeamNG.research), with failure defined as >95% of the vehicle's bounding box crossing the center or side line.
• To enhance diversity, the discrete Fréchet distance between Bézier curves is used to measure similarity between test cases, guiding the selection of new, dissimilar individuals.
• Three search configurations are evaluated: random seed population (A), restart on failure (B), and guided seed generation with validity checks (C).
• Invalid test cases—those with overly sharp curves—are filtered out during preprocessing to ensure realistic and executable simulations.

Experimental results

Research questions

• RQ1 Can a search-based method using Bézier curves effectively generate diverse, failure-inducing road geometries for ALKS testing?
• RQ2 How do different genetic algorithm configurations impact test efficiency and the diversity of failing test cases?
• RQ3 To what extent can validity checks and similarity metrics improve the quality and efficiency of generated test cases?
• RQ4 Does guiding seed population generation toward valid and dissimilar road shapes reduce redundancy and increase failure discovery?

Key findings

• Configuration A generated an average of 27 failing test cases per run, but with low average Fréchet distance (2.2–8.2), indicating high similarity and limited diversity.
• Configuration B achieved higher diversity, with an average of 2.25 failing test cases per run and maximum Fréchet distances up to 120, but suffered from high invalid test case rates (27–57 per run) and inefficient restarts.
• Configuration C reduced invalid test cases significantly (17–29 per run) and increased distinct failing cases (4–6 per run), achieving higher average Fréchet distances (58.7–73.79), indicating better diversity.
• Despite higher computational cost due to validity checks, Configuration C demonstrated the best balance between test quality and diversity, with 6 failing cases in 255 test cases in one run.
• All configurations successfully generated at least one failing test case per run, confirming the method’s ability to identify ALKS failure scenarios.
• The use of Fréchet distance as a diversity metric helped detect distinct failure-inducing road shapes, especially in runs with higher maximum distances.