Safe, Efficient and Socially-Compatible Decision of Automated Vehicles: A Case Study of Unsignalized Intersection Driving

Abstract

Safe and smooth interaction between other vehicles is one of the ultimate goals of driving automation. However, recent reports of demonstrative deployments of automated vehicles (AVs) indicate that AVs are still difficult to meet the expectation of other interacting drivers, which leads to several AV accidents involving human-driven vehicles (HVs) without the understanding about the dynamic interaction process. By investigating 4300 video clips of traffic accidents, it is found that the limited dynamic visual field of drivers is one leading factor in inter-vehicle interaction accidents. A game-theoretic decision algorithm considering social compatibility is proposed to handle the interaction with a human-driven truck at an unsignalized intersection. Starting from a probabilistic model for the visual field characteristics of truck drivers, social fitness and reciprocal altruism in the decision are incorporated in the game payoff design. Human-in-the-loop experiments are carried out, in which 24 subjects are invited to drive and interact with AVs deployed with the proposed algorithm and two comparison algorithms. Totally, 207 cases of intersection interactions are obtained and analyzed, which shows that the proposed decision-making algorithm can improve both safety and time efficiency, and make AV decisions more in line with the expectation of interacting human drivers. These findings can help inform the design of automated driving decision algorithms, to ensure that AVs can be safely and efficiently integrated into the human-dominated traffic.

Appendices

Appendix A: Utility Function

1.1 A.1 AV Utility

For a given interaction process, $\Delta t$ is defined as the time difference between the AV and HV’s arriving time at the conflict area. By normalizing the time difference $\Delta t$, the safety utility $u_\mathrm{s}$ of a two-vehicle interaction process can be described as follows, which is a value between $-1$ and 1. The safety utility of AV is $u_\mathrm{s,AV}=u_\mathrm{s}$, while the safety utility of HV depends on how well the AV can be observed by the HV driver.

$$\begin{aligned} u_\mathrm{s}=\left\{ \begin{array}{ll} \frac{\Delta t}{\Delta t_\mathrm{rsk}} - 1, &{} \Delta t \in [0,\Delta t_\mathrm{rsk}] \\ \frac{\Delta t - \Delta t_\mathrm{rsk}}{\Delta t_\mathrm{saf} - \Delta t_\mathrm{rsk}}, &{} \Delta t \in (\Delta t_\mathrm{rsk},\Delta t_\mathrm{saf}) \\ 1, &{} \Delta t \in [\Delta t_\mathrm{saf}, +\infty ) \end{array} \right. \end{aligned}$$

(A1)

where the parameters $\Delta t_\mathrm{rsk}$ and $\Delta t_\mathrm{saf}$ are the risky and safe thresholds of time difference $\Delta t$, respectively. As shown in Fig. A1, the overlapped path of interactive vehicles is defined as the conflict area. At time $t_0$, if AV arrives at the conflict area first, given HV’s location $P_\mathrm{HV0}$, velocity $v_\mathrm{HV}$, the distance to conflict area $L_\mathrm{HV}$, the thresholds $\Delta t_\mathrm{rsk}$, $\Delta t_\mathrm{saf}$ are determined as follow. If when HV arrives at conflict area (location $P_\mathrm{HV1}$), AV has just left conflict area meanwhile (location $P_\mathrm{AV1}$), this time difference is defined as $\Delta t_\mathrm{rsk}$. On the other hand, if AV has left the intersection (location $P_\mathrm{AV2}$), this time difference is defined as $\Delta t_\mathrm{saf}$, as shown in Eq. (A2). Similarly, if HV will arrive at the conflict area at time $t_0$, the corresponding safety utility can be calculated.

$$\begin{aligned} \left\{ \begin{array}{ll} \Delta t &{} = L_\mathrm{HV} / v_\mathrm{HV} \\ \Delta t_\mathrm{rsk} &{} = L_\mathrm{risk} / v_\mathrm{HV} \\ \Delta t_\mathrm{saf} &{} = L_\mathrm{safe} / v_\mathrm{HV} \\ \end{array} \right. \end{aligned}$$

(A2)

Fig. A1

Intersection driving description

Assuming the AV distance from the conflict area at time t is $L_\mathrm{AV}$, and the velocity is $v_\mathrm{AV}$, then $t_\mathrm{AV}=L_\mathrm{AV}/v_\mathrm{AV}$. If setting the maximum allowable velocity is $v_\mathrm{max}$, an efficiency time is defined as $t_\mathrm{eff,AV}=L_\mathrm{AV}/v_\mathrm{max}$. Then, the traffic efficiency utility of AV, $u_\mathrm{t,AV}$ is

$$\begin{aligned} u_\mathrm{t,AV}=\left\{ \begin{array}{ll} 1-\frac{t_\mathrm{AV}-t_\mathrm{eff,AV}}{t_\mathrm{eff,AV}}, &{} t_\mathrm{AV} \le t_\mathrm{eff, AV} \\ 1, &{} t_\mathrm{AV} > t_\mathrm{eff, AV} \end{array} \right. \end{aligned}$$

(A3)

The social fitness utility of AV $u_\mathrm{sf,AV}$ represents how much the AV decision fits to the HV decision, which is modeled in Eq. (A4) with the AV visibility probability $F(\theta )$ and the tacitness degree $f_\mathrm{tacit}(i,j)$. If $F(\theta )$ is small, the HV driver can hardly notice AV, so there is no cooperative driving behavior between them. The degree of tacit cooperation is explained in Table A1, in which (i, j) stand for AV and HV, respectively. When HV adopts the Yield strategy, if AV yields as well, the tacitness degree is $f_\mathrm{tacit}=0$, if AV does not yield, $f_\mathrm{tacit}=1$ is set.

$$\begin{aligned} u_\mathrm{sf,AV}=F(\theta )f_\mathrm{tacit} \end{aligned}$$

(A4)

Table A1 The tacitness degree $f_\mathrm{tacit}$ of AV under different conditions

1.2 A.2 HV Utility

The safety utility of HV, $u_\mathrm{s,HV}$ is designed as

$$\begin{aligned} u_\mathrm{s,HV}=\left\{ \begin{array}{cl} (u_\mathrm{s})^{F(\theta )}, &{} u_\mathrm{s} \ge 0 \\ (-u_\mathrm{s})^{F(\theta )}, &{} u_\mathrm{s} < 0 \end{array} \right. \end{aligned}$$

(A5)

where the AV visibility probability $F(\theta )$ is introduced to correct the safety utility $u_\mathrm{s}$. For example, when AV is in the blind zones or is almost invisible from the perspective of HV driver, it is assumed that there is no vehicle interacting with HV, and the maximum safety utility is achieved, $u_\mathrm{s,HV}=1$.

Similar to Eq. (A5), the traffic efficiency utility of HV is as follows:

$$u_{{{\text{t}},{\text{HV}}}} = \left\{ \begin{array}{l} 1 - \frac{{t_{{{\text{HV}}}} - t_{{{\text{eff}},{\text{HV}}}} }}{{t_{{{\text{eff}},{\text{HV}}}} }},\quad t_{{{\text{HV}}}} \le t_{{{\text{eff}},{\text{HV}}}} \hfill \\ 1,\quad \quad \quad \quad \quad \quad t_{{{\text{HV}}}} > t_{{{\text{eff}},{\text{HV}}}} \hfill \\ \end{array} \right.$$

(A6)

The reciprocal utility from the HV’s altruistic behavior is quantified with the traffic efficiency of AV and the AV visibility probability $F(\theta )$, i.e.,

$$\begin{aligned} u_\mathrm{altr,HV}(\theta )=F(\theta )u_\mathrm{t,AV} \end{aligned}$$

(A7)

Appendix B: Questionnaire

The questionnaire for the HV drivers’ evaluation on the AV-HV interaction is shown in Table B1. And the instruction for subject drivers are “Please score the items in Table B1 based on your feelings about your last interaction with the other vehicle.”

Table B1 Questionnaire for evaluation on the AV-HV interaction