Robust responsibility-sensitive safety: Noise disturbed adaptive cruise control

Vehicle safety is crucial for the development of autonomous vehicles. The concept of RSS (responsibility sensitive safety) is proposed as a formal method to guarantee safety, and several longitudinal RSS formulations are proposed. However, even for highly accurate autonomous vehicles, its dynamics is stochastic, and may lead to the RSS violation due to disturbances. This research investigates the stochasticity of the adaptive cruise control empirically, and proposes a robust RSS regarding longitudinal driving. We firstly show that there exists certain time-variant stochasticity in the ACC controlled vehicle using real world dataset, and numerically calculated the probability that the RSS may be violated when the noise is considered, which reveals that RSS violation is inevitable under certain scenarios. Then, an explicit solution of the noise disturbed ACC is derived. Next, a robust RSS framework is established, by employing the Markov chain derived from the Euler-Maruyama scheme of the stochastic ACC system. The research extends the conventional RSS framework.