Turning is necessary for a traveling vehicle when changing lanes or avoiding obstacles. Furthermore, indicating the trajectory or exit point of turning is obviously necessary for safety in autonomous driving. A mathematical restriction in the running area or a potential function was much reported for these purposes. However, the parameter setting of these methods is very complex. Furthermore, confirming the direction of the moving vehicle is necessary. Clothoid curve is a well-known trajectory to slacken the sudden change in curvature from straight direction to turning. It is also well known that the curve matches the vehicle turning trajectory when steering is performed at a constant speed. Therefore, the use of a clothoid curve is extensively reported for target-trajectory-generation. This process requires more time to obtain the turning trajectory, because these methods determine the clothoid parameters while examining the passing point. However, the real-time operation of an autonomous vehicle requires quick determination. Therefore, the present study investigates a new method for determining a turning trajectory
consisting of a clothoid curve using the turning exit conditions.

First of all, a numerical analyses were carried out to obtain the relationship between the parameters of the unit clothoid curve and the end point coordinate position. Next, the relationship between the turning trajectory and the clothoid parameter were investigated using graphical features. Then, this paper showed a method to determine the clothoid parameter to travel to the specified exit point when automated turning. Also, this paper showed an algorithm to generate a lane-change trajectory by combining the clothoid curve. To apply for the automated traveling, a nonlinear control system was investigated to pass through the specified exit point. Also, a compensation method using a phase advancing transfer function were investigated to coincide well with the target trajectory because three variables were controlled by two inputs. This control system was examined using a radio controlled car. The experimental results showed well expected results and it showed that this method is effective and useful to pass through the specified exit point.

Dr. Eng. Takeshi Takiyama, Osaka City University, JAPAN; Dipl.-Ing. Jinichi Fujita, Osaka City University , Graduate school., JAPAN