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 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 control barrier functions 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 control barrier functions 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.
Highlights
Recent years have witnessed a growing number of safety or convenience modules for automobiles [1], [2]
In [22], the system dynamics are represented as discrete-time linear parameter-varying systems, and contracts are established for the variables that couple the two subsystems; controlledinvariant sets are constructed for the Adaptive Cruise Control (ACC) and Lane Keeping (LK) subsystems individually to meet the terms of the contracts using an iterative algorithm, such that the overall controller is guaranteed to ensure the safety of the composed system
The safety specifications are “hard constraints” that must be satisfied for all time, while the performance objectives are “soft constraints” that can be overridden when they are in conflict with safety
Summary
Recent years have witnessed a growing number of safety or convenience modules for automobiles [1], [2]. In [22], the system dynamics are represented as discrete-time linear parameter-varying systems, and contracts are established for the variables that couple the two subsystems; controlledinvariant sets are constructed for the ACC and LK subsystems individually to meet the terms of the contracts using an iterative algorithm, such that the overall controller is guaranteed to ensure the safety of the composed system. Despite these very interesting initial contributions, many safety guarantee problems on the composition of LK and ACC are still largely open and deserve further investigation. X1, ..., xn is denoted as Σ[x1, ..., xn], and as Σm[x1, ..., xn] if its degree is m
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