Worst-Case Analysis of Automotive Collision Avoidance Systems

Automotive collision avoidance (CA) systems help drivers to avoid collisions through autonomous interventions by braking or steering. If the decision to intervene is made too early, the intervention can become a nuisance to the driver, and if the decision is made too late, the safety benefits of the intervention will be reduced. The decision to intervene is commonly based on a threat function. The dimensionality of the input state space for the threat function is, in general, very large, making exhaustive evaluation in real vehicles intractable. This paper presents a method for efficient estimation of a conservative bound on CA system performance, i.e., the worst-case performance. Closed-form expressions are derived for the worst-case performance, in terms of early or unnecessary interventions, with regard to longitudinal or lateral prediction and measurement errors. In addition, we derive closed-form expressions for robust avoidance scenarios, in which no unnecessary intervention will occur. For a system example, numerical results show how decision timing and robustness depend on scenario and system parameters. The method can be used for defining system requirements, system verification, system tuning, or system sensitivity analysis with regard to scenario variations and sensor measurement errors.