Automatically synthesizing consistent models is a key prerequisite for many testing scenarios in autonomous driving to ensure a designated coverage of critical corner cases. An inconsistent model is irrelevant as a test case (e.g., false positive); thus, each synthetic model needs to simultaneously satisfy various structural and attribute constraints, which includes complex geometric constraints for traffic scenarios. While different logic solvers or dedicated graph solvers have recently been developed, they fail to handle either structural or attribute constraints in a scalable way. In the current paper, we combine a structural graph solver that uses partial models with an SMT-solver and a quadratic solver to automatically derive models which simultaneously fulfill structural and numeric constraints, while key theoretical properties of model generation like completeness or diversity are still ensured. This necessitates a sophisticated bidirectional interaction between different solvers which carry out consistency checks, decision, unit propagation, concretization steps. Additionally, we introduce custom exploration strategies to speed up model generation. We evaluate the scalability and diversity of our approach, as well as the influence of customizations, in the context of four complex case studies.

自动合成一致的模型是自动驾驶中许多测试场景的关键先决条件，以确保对关键极端情况的指定覆盖。不一致的模型与测试用例无关（例如，误报）；因此，每个合成模型需要同时满足各种结构和属性约束，其中包括交通场景的复杂几何约束。虽然最近开发了不同的逻辑求解器或专用图求解器，但它们无法以可扩展的方式处理结构或属性约束。在当前的论文中，我们将使用部分模型的结构图求解器与 SMT 求解器和二次求解器相结合，以自动导出同时满足结构和数值约束的模型，而模型生成的关键理论属性，如完整性或多样性仍然得到保证。这需要在执行一致性检查、决策、单元传播、具体化步骤的不同求解器之间进行复杂的双向交互。此外，我们引入了自定义探索策略来加速模型生成。我们在四个复杂案例研究的背景下评估了我们方法的可扩展性和多样性，以及定制的影响。