Control Allocation of All-Wheel Drive Vehicles: a Longitudinal Model

This paper offers a method to compute the control inputs for an all-wheel drive vehicle that moves along a specified path on rough terrain. The focus of this paper is on longitudinal motion only, using a half-car model with no suspensions. For a given path, we first compute the range of the admissible speeds and accelerations at every point along the path, subject to vehicle dynamics and constraints on the wheel/ground forces. A feasible velocity profile along the path is then computed to respect the admissible speeds and accelerations and satisfy given boundary conditions. While the velocity profile represents the accelerations of the center of mass, it remains to determine the control inputs (torques) for the two independent wheels. The challenge stems from the longitudinal model being an indeterminate system, having two control inputs but only one degree-of-freedom along the specified path. This inherent indeterminacy is resolved by adding a virtual suspension to the rigid vehicle model, which allows to explicitly compute the two individual wheel torques. The method is demonstrated for a vehicle moving at the time optimal speeds over a bump. A dynamic simulation of the vehicle with a stiff suspension shows that the two wheels maintain contact with the ground at all times, despite moving at the ultimate speeds. It is also shown that the all-wheel-drive model produces a larger set of admissible speeds and accelerations, and hence results in faster speeds and shorter motion times than the single drive (front or rear) model.