Model Checking Collision Avoidance of Nonlinear Autonomous Vehicles

Autonomous vehicles are expected to be able to avoid static and dynamic obstacles automatically, along their way. However, most of the collision-avoidance functionality is not formally verified, which hinders ensuring such systems' safety. In this paper, we introduce formal definitions of the vehicle's movement and trajectory, based on hybrid transition systems. Since formally verifying hybrid systems algorithmically is undecidable, we reduce the verification of nonlinear vehicle behavior to verifying discrete-time vehicle behavior overapproximations. Using this result, we propose a generic approach to formally verify autonomous vehicles with nonlinear behavior against reach-avoid requirements. The approach provides a Uppaal timed-automata model of vehicle behavior, and uses Uppaal STRATEGO for verifying the model with user-programmed libraries of collision-avoidance algorithms. Our experiments show the approach's effectiveness in discovering bugs in a state-of-the-art version of a selected collision-avoidance algorithm, as well as in proving the absence of bugs in the algorithm's improved version.