Quasi-Linear Optimal Path Controller Applied to Post Impact Vehicle Dynamics

This paper investigates brake-based path control of a passenger vehicle, aimed at reducing secondary collision risk, following an initial impact in a traffic accident. This risk may be reduced if lateral deviations from the preimpact path can be minimized, at least on straight roads. Numerical optimization has previously shown that coupled control of lateral forces and yaw moments can be applied to effectively minimize such path deviations. In this paper, a quasi-linear optimal controller (QLOC) is proposed to achieve this control target. QLOC uses nonlinear optimal control theory to provide a semiexplicit approximation for optimal post impact (PI) path control. The controller design method is novel, combining linear costate dynamics with nonlinear constraints due to tire friction limits. A fully closed-loop form of the controller is presented; it is applicable to multiple-event accidents occurring on straight roads, including adaptive estimation of the time instant at maximum deviation. The controller achieves performance that is very similar to that of open-loop numerical optimization. Assuming that the vehicle remains on the road surface after the impact and that the brake actuators remain operational, it is verified that the path controller is effective over a wide range of PI kinematic conditions. It is expected that the QLOC controller will prove useful in other cases where chassis systems directly control the vehicle path, e.g., in crash-imminent avoidance maneuvers.