## 1 Introduction
Thus, the trajectory prediction method that uses only digital maps is not suitable in ADAS for turning at intersections. Other studies on trajectory prediction proposed methods that stochastically predicted the future trajectory from the observed previous motion of the ego vehicle [19; 20; 26; 27]. However, stochastic prediction makes the risk assessment and decision making a more complex problem. Besides, there are no big advantages in using the stochastic methods for turning at intersections because the destination of the ego vehicle during turning is usually obvious and definitive. Thus, our proposal intends to provide a trajectory that is adaptive to the driver's input rather than the prediction method from digital maps. Further, our proposed method is more accurate at prediction than the stochastic methods. To enhance the accuracy of trajectory prediction, a smooth trajectory must be generated by considering both the driver's input and the vehicle's current state. However, on the one hand, the smoother the trajectory becomes, the higher the calculation costs incurred to generate the curve. On the other hand, trajectory predictions for ADAS require real-time calculation ability, and therefore, a higher calculation cost is not acceptable. Our main concern is balancing the smoothness and calculation cost of the curve while developing the trajectory prediction method. The main objective of this paper is to propose a trajectory prediction method in ADAS for safe turning at intersections without depending on V2V or V2I communication and to evaluate the effectiveness of the proposed trajectory prediction method. Our approach was to initially interpret features of the intersection based on several parameters. Then, we aimed to generate a smooth path as a solution to a problem that was defined as follows: to generate a smooth trajectory in a two-dimensional plane under conditions of the extracted parameters and the driver's steering wheel input. Whileevaluating the effectiveness of the proposed method, the following three points were emphasized: First, the objective was to evaluate the prediction accuracy--evaluating the accuracy of several trajectory prediction methods by comparing the predicted trajectories and an actual path in data acquisition experiments at real urban intersections; Second, the adaptability of the trajectory prediction method to ADAS for intersection turning--an important aspect of the evaluation of this adaptability is that the trajectory can be generated before driving into an intersection to allow sufficient time for assistance by ADAS; Third, a practical utility for various sizes and shapes of the intersections--to evaluate this point, the data acquisition experiments were conducted at various intersections that included acute or obtuse angle turns and from small to large intersections. In this paper, we present a method to predict the future intersection turning trajectory of the ego vehicle by focusing on right-turn scenarios at intersections. The main contributions of this paper are proposing a geometrical trajectory prediction method that generates a smooth and continuous curve for intersection turns and revealing the effectiveness of the proposal with a vehicle driving experiment at actual urban intersections. The structure of this paper is shown in Figure 1. Section 2 introduces several curve generation methods that can obtain a reasonably smooth curve at a modest calculation cost. Later, this section explains a derivation and an algorithm to generate a smooth curve using a Triclothooidal curve. Section 3 covers the definitions of parameters and coordinates to adopt the Triclothoidal curve to the vehicle turning trajectory at the intersections. Section 4 presents data acquisition experiments in urban intersections in Tokyo. Later, this section evaluates the effectiveness of our proposed method by comparing it with other conventional curve generation methods from the results of data acquisition experiments.