Towards Bi-Dimensional driver models for automated driving system safety requirements: Validation of a kinematic model for evasive lane-change maneuvers

Preventing traffic accidents is of paramount importance for society's well-being. The topic is particularly relevant for driving automation given the high expectations about automated vehicles and the difficulty in estimating reliable safety figures for those complex systems. Under this premise, the present manuscript investigates how to derive a safety benchmark model for evasive lane-change maneuvers that can also be applied in microsimulation frameworks. The approach leverages a jerk-limited bang-bang kinematic model for lane-change and validates its minimum time prediction against other kinematic approaches and vehicle dynamical models based on a robust minimum-time optimal control formulation. It is shown how kinematic modeling does not embrace steering angle constraints (at low-speed) and misses the inertia effect (at high-speed) thus introducing discrepancies. However, due to the introduction of a braking model, it can be safely claimed that the low-speed discrepancy between the kinematic and the dynamic models lies in a region where stopping is still the most efficient reaction. Moreover, a method is shown to compute the effective lateral acceleration for a kinematic model to match the dynamical system's maneuvering. The kinematic lane-change model can thus constitute a valid performance benchmark provided that conservative assumptions are used when calibrating its maximum lateral acceleration.