Undershoot response analysis of circular path-following control of an autonomous vehicle

Abstract

This study concerned the circular path-following control of a vehicle. For a circular path, two methods can be applied to the vehicle system, namely, rotational coordinate transformation and expansionary coordinate transformation. Via numerical simulations of the application of these two methods, we discovered that the former provides undershoot in its initial response; however, this does not appear if the latter method is also applied to the former. The undershoot phenomenon is undesirable for tracking control. In order to investigate the reason for the occurrence of the undershoot phenomenon, a condition for the undershoot was derived from an analysis of the first step response in the control system model. The obtained condition depended on the relationship between the initial value and the target value of the vehicle. As a result, we found that the former method satisfied the undershoot condition. Second, we analyzed the condition for the method which included expansionary coordinate transformation, and we found that this approach includes additional feedforward control input in comparison with the former method. Subsequently, we demonstrated that the feedforward input allowed the latter system to avoid undershoot.

Keywords

• vehicle
• undershoot
• path-following control
• time-state control
• nonholonomic systems
• rotational coordinate transformation
• expansionary coordinate transformation