Incorporating non-linear tire dynamics into a convex approach to shared steering control

Abstract

Active safety systems enabled by steer-by-wire technology can share control with a driver, augmenting the driver's steering commands to avoid collisions and prevent loss of control. The extent to which this can be done is limited by the controller's ability to anticipate dangerous scenarios in order to appropriately intervene and steer the vehicle to safety. However, the non-linear nature of tire dynamics poses a challenge in predicting and modifying vehicle behavior in real-time. In this paper, online successive linearizations of the future planned vehicle trajectory approximates these non-linear dynamics in a real-time, model predictive controller that shares control with a human driver. Simulation results of aggressive maneuvers demonstrate the usefulness of this approach as well as illustrate interesting interactions between the sometimes competing objectives of vehicle stability and collision avoidance.

Design of a Path-Tracking Steering Controller for Autonomous Vehicles

“…Inspired by Reference [7], which assumes that the tire-cornering stiffness keeps constant in the prediction horizon, we propose a new online successive linearization method by combining both the information of time k and step of the prediction horizon to accurately predict the propagation of lateral tire forces, as shown in Figure 4. In the linearized model, the equivalent cornering stiffness over the prediction horizon is: Figure 4.…”

“…The simulation is carried out with sampling time Ts = 0.02 s, and the simulated steering angle and the corresponding front lateral force are shown in Figure 7. We use Equations (21) and (22) and the tire-linearization method proposed in Reference [7] as a baseline prediction model to compare with our model, which provides steady-state information and is a combination of Equations (36)-(38). The prediction horizon length is chosen as 0.4 s with 20 steps.…”

“…For the second case, where the speed is 25 km/h and the maximum lateral acceleration is 7 m/s 2 , the steering angle is much larger than 5° at all three points, especially at point 2. The small-angle assumption is no longer valid under these We use Equations (21) and (22) and the tire-linearization method proposed in Reference [7] as a baseline prediction model to compare with our model, which provides steady-state information and is a combination of Equations (36)-(38). The prediction horizon length is chosen as 0.4 s with 20 steps.…”

“…However, when the steering angle and lateral slip angle are larger than 5 • , the model becomes inaccurate, especially in the region of tire-force saturation. Erlien et al [7] introduced an affine approximation linearization method to handle the nonlinearity of the tires in the model predictive control (MPC) scheme, however, this approach is inaccurate when the length of the prediction horizon is larger. Talvala et al [8] proposed a tire slip angle-related parameter to capture the nonlinearity even when the tire is saturated.…”

“…On the contrary, the unique global minimum of the linear MPC can be efficiently calculated by various methods in a limited number of iterations [20,21]. Several methods that combine MPC with a linear model were proposed in References [5,7,17]. Raffo et al [18] presented an MPC path-tracking controller with a linear kinematic model to achieve the desired performance during high-speed driving.…”