Stochastic Modeling and Optimal Control for Automated Overtaking

• This paper proposes a solution to the overtaking problem where an automated vehicle tries to overtake a human-driven vehicle, which may not be moving at a constant velocity. Using reachability theory, we first provide a robust time-optimal control algorithm to guarantee that there is no collision throughout the overtaking process. Following the robust formulation, we provide a stochastic reachability formulation that allows a trade-off between the conservative overtaking time and the allowance of a small collision probability. To capture the stochasticity of a human driver's behavior, we propose a new martingale-based model where we classify the human driver as aggressive or nonaggressive. We show that if the human driver is nonaggressive, our stochastic time-optimal control algorithm can provide a shorter overtaking time than our robust algorithm, whereas if the human driver is aggressive, the stochastic algorithm will act on a collision probability of zero, which will match the robust algorithm. Finally, we detail a simulated example that illustrates the effectiveness of the proposed algorithms. 

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Keyword

Behavioral research

Economic and social effects

Stochastic control systems

Transport properties

Automated vehicles

Collision probability

Constant velocities

Optimal controls

Reachability theory

Robust formulations

Stochastic algorithms

Time optimal control

Stochastic systems

Publication and Content Type

ref (subject category)

kon (subject category)