In this work, we propose a compositional data-driven approach for the formal
estimation of collision risks for autonomous vehicles (AVs) while acting in a
stochastic multi-agent framework. The proposed approach is based on the
construction of sub-barrier certificates for each stochastic agent via a set of
data collected from its trajectories while providing an a-priori guaranteed
confidence on the data-driven estimation. In our proposed setting, we first
cast the original collision risk problem for each agent as a robust
optimization program (ROP). Solving the acquired ROP is not tractable due to an
unknown model that appears in one of its constraints. To tackle this
difficulty, we collect finite numbers of data from trajectories of each agent
and provide a scenario optimization program (SOP) corresponding to the original
ROP. We then establish a probabilistic bridge between the optimal value of SOP
and that of ROP, and accordingly, we formally construct the sub-barrier
certificate for each unknown agent based on the number of data and a required
level of confidence. We then propose a compositional technique based on
small-gain reasoning to quantify the collision risk for multi-agent AVs with
some desirable confidence based on sub-barrier certificates of individual
agents constructed from data. For the case that the proposed compositionality
conditions are not satisfied, we provide a relaxed version of compositional
results without requiring any compositionality conditions but at the cost of
providing a potentially conservative collision risk. Eventually, we also
present our approaches for non-stochastic multi-agent AVs. We demonstrate the
effectiveness of our proposed results by applying them to a vehicle platooning
consisting of 100 vehicles with 1 leader and 99 followers. We formally estimate
the collision risk by collecting data from trajectories of each agent.Comment: This work has been accepted at IEEE Transactions on Control of
Network System