A Point-to-Ray Framework for Generating Smooth Parallel Parking Maneuvers

The problem of generating smooth parallel parking maneuver for autonomous car-like vehicles is considered, wherein the vehicle moves forward from the starting point to an intermediate point and then traces a path backward to the parking position. Any error in accurately reaching the intermediate point leads to maneuver replanning and hence puts extra computational burden on the planner. Addressing the issue, this letter formulates the problem in a point-to-ray framework connecting the parking position to all points in a neighborhood of the intermediate point. Exploiting its asymptotic convergence, four parameter logistic (4PL) curve based S-shaped path is proposed as a solution with a single maneuver connecting the intermediate point neighborhood to the parking position. Inherent to the 4PL curve, the maneuver presents a continuous steering profile with zero steering angle at the ends. Parking slot collision avoidance and steering limit of the vehicle are satisfied by deducing closed-form analytic conditions on the two design parameters. Together with the robustness to intermediate point variation, comparison with existing approaches highlights computational and design advantages. The proposed approach is validated using a double-tracked Ackermann steering vehicle model.