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Models for off-road vehicles, such as farm equipment and military vehicles, require an off-road tire model in order to properly understand their dynamic behavior on off-road driving surfaces. Extensive literature can be found for on-road tire modeling, but not much can be found for off-road tire modeling. This paper presents an off-road tire model that was developed for use in vehicle handling studies. An on-road, dry asphalt tire model was first developed by performing rolling road force and moment testing. Off-road testing was then performed on dirt and gravel driving surfaces to develop scaling factors that explain how the lateral force behavior of the tire will scale from an on-road to an off-road situation. The tire models were used in vehicle simulation software to simulate vehicle behavior on various driving surfaces. The simulated vehicle response was compared to actual maximum speed before sliding vs. turning radius data for the studied vehicle to assess the tire model.

Dynamic game theory brings together different features that are keys to many situations in control design: optimization behavior, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely, the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degree of freedom (DOF) vehicle handling performance model is put into discrete form to develop the game equations of motion.

Vehicle stability is maintained by proper interactions between the driver and vehicle stability control system. While driver describes the desired target path by commanding steering angle and acceleration/deceleration rates, vehicle stability controller tends to stabilize higher dynamics of the vehicle by correcting longitudinal, lateral, and roll accelerations. In this paper, a finite-horizon optimal solution to vehicle stability control is introduced in the presence of driver's dynamical decision making structure. The proposed concept is inspired by Nash strategy for exactly known systems with more than two players, in which driver, commanding steering wheel angle, and vehicle stability controller, applying compensated yaw moment through differential braking strategy, are defined as the dynamic players of the 2-player differential linear quadratic game.

This paper outlines the development of a simulation-based process for assessing the handling performance of a given set of tires on a specific vehicle. Based on force and moment data, a Pacejka tire model was developed for each of the five sets of tires used in this study. To begin with, simple handling metrics including under-steer gradient were calculated using cornering stiffness derived from the Pacejka model. This Pacejka tire model was subsequently combined with a 3DOF non-linear vehicle model to create a simulation model in MATLAB/Simulink®. Other handling metrics were calculated based on simulation results to step and sinusoidal (General Motors Company) steering inputs. Calculated performance metrics include yaw velocity overshoot, yaw velocity response time, lateral acceleration response time and steering sensitivity. In addition to this, the phase lag in lateral acceleration and yaw rate of the vehicle to a sinusoidal steering input were also calculated.

In this paper a yaw stability control algorithm along with an emergency roll control strategy have been developed. The yaw stability controller and emergency roll controller were both developed using linear two degree-of-freedom vehicle models. The yaw stability controller is based on Lyapunov stability criteria and uses vehicle lateral acceleration and yaw rate measurements to calculate the corrective yaw moment required to stabilize the vehicle yaw motion. The corrective yaw moment is then applied by means of a differential braking strategy in which one wheel is selected to be braked with appropriate brake torque applied. The emergency roll control strategy is based on a rollover coefficient related to vehicle static stability factor. The emergency roll control strategy utilizes vehicle lateral acceleration measurements to calculate the roll coefficient. If the roll coefficient exceeds some predetermined threshold value the emergency roll control strategy will deploy.

Dynamic “Game Theory” brings together different features that are keys to many situations in control design: optimization behavior, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In previous studies, it was shown that vehicle stability can be represented by a cooperative dynamic/difference game such that its two agents (players), namely, the driver and the vehicle stability controller (VSC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the VSC command is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degree of freedom (DOF) vehicle handling performance model is put into discrete form to develop the game equations of motion. This study focus on the uncertainty in the inputs, and more specifically, the driver's steering input.