Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Control

Abstract

This paper develops a control approach with correctness guarantees for the simultaneous operation of lane keeping and adaptive cruise control. The safety specifications for these driver assistance modules are expressed in terms of set invariance. Control barrier functions (CBFs) are used to design a family of control solutions that guarantee the forward invariance of a set, which implies satisfaction of the safety specifications. The CBFs are synthesized through a combination of sum-of-squares program and physics-based modeling and optimization. A real-time quadratic program is posed to combine the CBFs with the performance-based controllers, which can be either expressed as control Lyapunov function conditions or as black-box legacy controllers. In both cases, the resulting feedback control guarantees the safety of the composed driver assistance modules in a formally correct manner. Importantly, the quadratic program admits a closed-form solution that can be easily implemented. The effectiveness of the control approach is demonstrated by simulations in the industry-standard vehicle simulator Carsim. Note to Practitioners—Safety is of paramount importance for the control of automated vehicles. This paper is motivated by the problem of designing controllers that are provably correct for the simultaneous operation of two driver assistance modules, lane keeping and adaptive cruise control. This is a challenging problem partially, because the lateral and longitudinal dynamics of the vehicles are coupled, with few results known to exist that provide formal guarantees. In this paper, we employ an assume-guarantee formalism between these two subsystems, such that they can be considered individually; based on that, we use optimization to design safe sets that serves as “supervisors” for vehicle behavior, such that the trajectories of the closed-loop system are confined within the safe sets using predetermined bounds on wheel force and steering angle. The feedback controller is constructed by solving convex quadratic programs online, which can also be given in closed form, making the implementation much easier. One particular advantage of this control approach is that the safety set and the performance controller can be designed separately, which enables the integration of a legacy controller into a correct-by-construction solution.