Stochastic Control Formulation of The Car Overtake Problem
Johansson, Karl Henrik
Baras, John, S.
In this paper, we consider the classic car overtake problem. There are three cars, two moving along the same direction in the same lane while the third car moves in the direction opposite to that of the ﬁrst two cars in the adjacent lane. The objective of the trailing car is to overtake the car in front of it avoiding collision with the other cars in the scenario. The information available to the trailing car is the relative position, relative velocities with respect to other cars and its position and past actions. The relative position and relative velocity information is corrupted by noise. Given this information, the car needs to make a decision as to whether it wants to overtake or not. We present a control algorithm for the car which minimizes the probability of collision with both the cars. We also present the results obtained by simulating the above scenario with the control algorithm. Through simulations we study the eﬀect of the variance of the measurement noise and the time at which the decision is made on the probability of collision.