Liu, Y., Davenport, C., Gafford, J., Mazzola, M. et al., "Development of A Dynamic Modeling Framework to Predict Instantaneous Status of Towing Vehicle Systems," SAE Technical Paper 2017-01-1588, 2017, doi:10.4271/2017-01-1588.
A dynamic modeling framework was established to predict status (position, displacement, velocity, acceleration, and shape) of a towed vehicle system with different driver inputs. This framework consists of three components: (1) a state space model to decide position and velocity for the vehicle system based on Newton’s second law; (2) an angular acceleration transferring model, which leads to a hypothesis that the each towed unit follows the same path as the towing vehicle; and (3) a polygon model to draw instantaneous polygons to envelop the entire system at any time point. Input parameters of this model include initial conditions of the system, real-time locations of a reference point (e.g. front center of the towing vehicle) that can be determined from a beacon and radar system, and instantaneous accelerations of this system, which come from driver maneuvers (accelerating, braking, steering, etc.) can be read from a data acquisition system installed on the towing vehicle. The output of the model is instantaneous polygons that render approximate outline of the towing vehicle system at any time point. The instantaneous polygons will be converted to control areas for system control. This model was validated for predicting instantaneous shapes of the system with one towing vehicle and four towed units. This model can be easily modified and extended to be used for other tractor-trailer systems or even road trains.