Algebraic General Trajectory Formula for Semitrailer Truck Vehicles

Generating the drive path for autonomous vehicles represents a significant challenge and requires the vehicle trajectory to be accurately predicted. This study proposes an algebraic analytical method for deriving the general trajectory formula (GTF) of a semitrailer truck. The GTF provides the means to accurately predict the trajectory of any point on the semitrailer truck and is a function of seven parameters: four parameters relating to the semitrailer truck dimensions and three parameters relating to the truck turning conditions. The validity of the proposed GTF is demonstrated by means of an illustrative example. The results confirm that the GTF provides a simple, effective, and accurate method for performing the trajectory prediction of semitrailer truck motion. Note to Practitioners—The inspiration of this article comes from the problem of the semitrailer truck vehicles’ difference in the trajectories of the front and rear inner wheels as a vehicle turns, which is defined as the “difference of radius between inner wheels (DRIW).” It should be noted that, in order to determine the DRIW, the trajectory of the rear inner wheel (TRIW) must first be predicted, which is quite complicated. Existing predictions are mostly based on real vehicle testing or curve fitting. However, this study proposes an algebraic general trajectory formula (GTF) for semitrailer trucks based on seven parameters relating to the truck dimensions and truck turning conditions, respectively. The proposed GTF is computationally straightforward and is capable of predicting the trajectory of any point of the truck in real time under almost all realistic turning conditions. Preliminary motion simulation for the TRIW suggests that the GTF is correct, and this approach is feasible. However, the proposed method is only suitable for the truck with a single semitrailer. In future research, we will address the GTF of the truck with multiple semitrailers, and the results will be available for more types of trucks.