Post-Collision Trajectory Restoration for a Single-track Ackermann Vehicle using Heuristic Steering and Tractive Force Functions

Post-collision trajectory restoration is a safety-critical capability for autonomous vehicles, as impact-induced lateral motion and yaw transients can rapidly drive the vehicle away from the intended path. This paper proposes a structured heuristic recovery control law that jointly commands steering and tractive force for a generalized single-track Ackermann vehicle model. The formulation explicitly accounts for time-varying longitudinal velocity in the lateral-yaw dynamics and retains nonlinear steering-coupled interaction terms that are commonly simplified in the literature. Unlike approaches that assume constant longitudinal speed, the proposed design targets the transient post-impact regime where speed variations and nonlinear coupling significantly influence recovery. The method is evaluated in simulation on the proposed generalized single-track model and a standard 3DOF single-track reference model in MATLAB, demonstrating consistent post-collision restoration behaviour across representative initial post-impact conditions.