Certified Handoff Between Global Search and Local Planning for Automated Parallel Parking

A closed-form feasibility certificate for the single-trial reverse parking maneuver, reducing the existence of a curvature-continuous solution from a given entry pose to the sign of a scalar quadratic discriminant — an O(1) test with no iteration or root-finding, and equivalently a line–circle intersection. Evaluated backward from the parked pose, the certificate defines the set of viable entry poses, and that set becomes the goal region of a forward hybrid-A* search, so the global-to-local handoff is feasible by construction rather than by chance. The local planner re-solves from the pose actually reached, absorbing grid-snap error. Validated in a Monte Carlo study against tracked, collision-checked outcomes, with a nonlinear path-frame law executing the maneuver in reverse under steering saturation.