## 2 Overall Architecture of Proposed Algorithm  
The core functions of autonomous driving can be categorized into four categories, namely perception, localization, motion planning, and control, with the interactions between the autonomous vehicle and the environments depicted in Figure 1. The perception module has a role to detect the surrounding objects around the autonomous vehicle. In this study, a geometric model-free approach [25] has been used to process the LiDAR point clouds from the six IBEO Lux sensors. This algorithm provides the local position, heading angle, and velocity of the moving objects with a grid-base static obstacle map. The localization module estimates the current global position and heading angle of the autonomous vehicle with respect to the high-definition map. A map-matching algorithm with a multi-rate Kalman filter has been used based on the measurement of GPS/INS sensors, LiDAR, and an around-view camera. The control module determines the steering-wheel angle, throttle, and brake inputs to track the desired path and acceleration. The last module, motion planning, is mainly discussed in this article. The architecture of the proposed motion-planning algorithm for an uncontrolled intersection is shown in Figure 2. The motion-planning algorithm consists of two parts with three sub-modules. The first part, target state prediction with uncertainty estimation, is composed of the three sub-modules intention inference, state prediction, and the recursive covariance estimator. These modules have been utilized to predict the future trajectory of the approaching targets and estimate the prediction uncertainty based on the result of driving intention inference and a recursive covariance estimator. The second part, the robust motion planner for intersection passing, consists of the three sub-modules driving mode decision, defining MPC constraint decision, and solving SMPC. The driving mode of the autonomous vehicle has been determined among 'Cross', 'Yield', and 'Stop' modes according to the uncontrolled intersection theory. Depending on the driving mode, predicted states of the target, and estimated prediction uncertainty, the hard and chance constraints for the SMPC problem have been defined to satisfy the safety index thresholds, which are derived from the human driving data. Finally, the desired acceleration is calculated by the SMPC. Figure 1: Overall architecture of the autonomous driving system. Before proceeding further with the discussion in this paper, the safety indexes for the intersection scenario have been defined as shown in Figure 3. From both a safety and performance perspective, the clearance and time to collision (TTC) have been widely used as an important index for the research of advanced driving-assistant systems (ADAS) and autonomous vehicles. However, the driving situation of an intersection is quite different from nominal driving conditions. Therefore, the clearance and TTC have been modified to consider the conflict point between intersection-approaching vehicles as follows:  
\[ \begin{array}{l}C_{conf}=d_{DTC,ego}+d_{DTC,target}\\ TTC_{conf}=\frac{d_{DTC,ego}}{v_{ego}}+\frac{d_{DTC,target}}{v_{target}}\end{array}  \tag{1}\]  
where '_conf_' and '_DTC_' are the abbreviation of 'conflict point' and 'distance to conflict point'. \(d_{DTC,ego}\) and \(d_{DTC,target}\) represent the remaining distance to the conflict point of ego and the target vehicle. \(v_{ego}\) and \(v_{target}\) are the velocity of the ego and target vehicle, respectively. In addition, the proposed safety index considers the trade-off of cross priority between two vehicles encountered at an intersection. The trade-off relationship of each term in \(TTC_{conf}\) applies equally to \(C_{conf}\). Therefore, \(C_{conf}\) and \(TTC_{conf}\) is the suitable safety index that can be utilized for all driving situations. In addition, the remaining distance to the stop line of the intersection is denoted as \(d_{DTI}\), where '_DTI_' means the distance to the intersection.