1 2 a t2) v0 = q v2x + v2y + a t v0x = v0cos (θ0) v0y = v0sin (θ0). (2)

Define an agent's current state information as s = (x,y,θ,vx,vy), which includes the x,y positions in the coordinate space, and the yaw angle θ, and the velocities in the X and Y directions. The inverse kinematics can be used to calculate the actions for behavior cloning purpose. With the Bicycle action space, we propose a model to approximate the vehicle dynamics with the goal of minimizing the discrepancy between the predicted vehicle states and the recorded vehicle states. More specifically, define the vehicle's coordinates as x,y in the global coordinate system, and the predicted coordinates as ˆx,ˆy, the goal is to minimize (x ˆx)2 + (y ˆy)2. Define the current vehicle's state information as s, which includes the coordinates of the vehicle in the global coordinate system (x,y), the vehicle's yaw angle θ, the vehicle's speed in the x and y direction vx,vy.