  Autonomous vehicles face tremendous challenges while interacting with human
drivers in different kinds of scenarios. Developing control methods with safety
guarantees while performing interactions with uncertainty is an ongoing
research goal. In this paper, we present a real-time safe control framework
using bi-level optimization with Control Barrier Function (CBF) that enables an
autonomous ego vehicle to interact with human-driven cars in ramp merging
scenarios with a consistent safety guarantee. In order to explicitly address
motion uncertainty, we propose a novel extension of control barrier functions
to a probabilistic setting with provable chance-constrained safety and analyze
the feasibility of our control design. The formulated bi-level optimization
framework entails first choosing the ego vehicle's optimal driving style in
terms of safety and primary objective, and then minimally modifying a nominal
controller in the context of quadratic programming subject to the probabilistic
safety constraints. This allows for adaptation to different driving strategies
with a formally provable feasibility guarantee for the ego vehicle's safe
controller. Experimental results are provided to demonstrate the effectiveness
of our proposed approach.
