Formal verification of braking while swerving in automobiles

Many vehicle accidents result from collision with foreign objects. Automatic and provably safe collision avoidance systems are thus of prime importance to the automobile industry. Previous work on formally verifying car collision avoidance maneuvers typically only focuses on braking-only or swerving-only maneuvers. In this work, we study combined braking and swerving maneuvers and establish formally verified conditions under which safety from collision is ensured. One major constrain in performing such joint maneuvers is that a vehicle's tires have limited traction which can be used either for braking or swerving. So in essence, a combined maneuver can trade off braking ability for turning when it is advantageous to do so and vice-versa. In this work, we study the full continuous range of combined maneuvers, from maximal turning with little braking to maximal braking with little turning. We use a unicycle model with Ackermann's steering for the car's motion, and the circle of traction forces to model the trade-off between braking and swerving. Resulting vehicle kinematics are formulated as a hybrid program in differential dynamic logic dL. We use the automated theorem prover KeYmaera X to formally verify the correctness of the collision avoidance property. This verification provides a mathematical guarantee that a given maneuver can prevent the car from collision with obstacles under certain conditions. The employed method is generic with a purely symbolic model and, thus, can be applied to verify other types of collision avoidance systems exhibiting richer behaviour.