Conditions for Undershoot Responses in Circular Path-Following Vehicle Control with the Rotational and Expansionary Coordinate Transformation

Abstract

This paper discusses the conditions for the undershoot responses in a circular path-following vehicle control. As a method to follow the circular path, it is known to combine the rotational and expansionary coordinate transformation to the vehicle kinematic model. However, the undershoot responses in which the output moves in the opposite direction to the reference value occurred under certain initial conditions of the vehicle. It is necessary to clarify the cause of the undershoot responses because the undershoot responses delay the time for following the vehicle to the reference value. The occurrence of the undershoot responses is related to the zeros of the transfer function. To derive the initial conditions of the vehicle that occurs the undershoot responses, in this paper, we analyze the zeros of the transfer function including the zero input response. Furthermore, we confirm the conditions for the occurrence of the undershoot responses through the numerical simulations.