rand is a random number generator between 0 and 1 to simulate randomness in reality for tests. The result of the above algorithm can be viewed as the subject vehicle's strategy or the aggressiveness that she or he wants to impose on the surrounding road users. However, this should be a value from 0 to 1, unconnected to the final control output. Hence, a Markov-based control strategy is proposed to build the connection. First, the Markov transition matrix based on one's driving habit is constructed based on experiments. The reason why insisting on experiments is that we can customize this matrix for different test applications. For example, we can collect different driving data from different drivers and abstract them into this matrix. When one special or random type of driving is required for the driving intelligence test. This matrix can be called for personalized behavior generating. We ask participants to repeat lane change under different driving speed 40 times and record their behaviors. For longitudinal control, the transitional probability to the next acceleration is given by the current velocity. For lateral control, the transitional matrix models the probability to the yaw angle increment based on the current velocity and current yaw angle. The results of a participant is reported in Note S6, Supporting Information.
Ideally, implanting the strategy interim \(\alpha_{sv}\) into the Markov transitional probability is the best. However, as \(\alpha_{sv}\) is an abstract variable, in order to connect the Small-Step strategy, the transitional probability above is not used directly. Inspired by \cite{Shin_2019}, the joint Markov chain is defined by