Modified Hybrid A* Collision-Free Path-Planning for Automated Reverse Parking

Parking a vehicle in tight spaces is a challenging task to perform due to the scarcity of feasible paths that are also collision-free. This paper presents a strategy to tackle this kind of maneuver with a modified Hybrid-A* path-planning algorithm that combines the feasibility guarantee inherent in the standard Hybrid A* algorithm with the addition of static obstacle collision avoidance. A kinematic single-track model is derived to describe the low-speed motion of the vehicle, which is subsequently used as the motion model in the Hybrid A* path-planning algorithm to generate feasible motion primitive branches. The model states are also used to reconstruct the vehicle centerline, which, in conjunction with an inflated binary occupancy map, facilitates static obstacle collision avoidance functions. Simulation study and animation are set up to test the efficacy of the approach, and the proposed algorithm proves to consistently provide kinematically feasible trajectories that are also collision-free.

💡 Research Summary

The paper addresses the challenging problem of autonomous reverse parking in tightly constrained environments, where feasible, collision‑free trajectories are scarce. It proposes a modified Hybrid‑A* path‑planning algorithm that augments the classic Hybrid‑A*’s inherent guarantee of kinematic feasibility with explicit static‑obstacle collision avoidance. The authors first derive a low‑speed single‑track (bicycle) vehicle model that captures front‑wheel steering dynamics under a no‑side‑slip assumption. The model expresses the rear‑axle velocity and steering angle as inputs and yields the vehicle’s longitudinal, lateral, and yaw motions. These equations are used both to generate motion primitives and to reconstruct the vehicle’s centerline for collision checking.

In the planning loop, each iteration expands the most promising node (the one with the lowest total cost) from a priority queue. From this node, five motion primitives are simulated over a fixed time horizon: reverse with maximum left steering, reverse with moderate left steering, reverse straight, reverse with moderate right steering, and reverse with maximum right steering. All primitives share the same rear‑axle reverse speed (negative value) and differ only in steering angle. After simulation, each primitive’s terminal state is evaluated for collisions using an inflated binary occupancy map that approximates the full vehicle footprint. Primitives that intersect occupied cells are discarded; collision‑free terminals are inserted back into the queue.

The cost function combines a quadratic heuristic term—measuring Euclidean distance in (x, y, θ) space to the goal, weighted by a positive‑definite matrix—and an accumulated action cost proportional to the number of expansion steps taken. The heuristic drives the search toward the goal, while the action cost differentiates between paths that reach the same state via different numbers of maneuvers, encouraging shorter, more efficient solutions. The scaling of the action cost is kept small relative to the heuristic to avoid distorting goal proximity assessment.

Simulation experiments are conducted in MATLAB/Simulink for vehicle dynamics and Unreal Engine for visual validation. Various parking scenarios featuring adjacent parked cars, curbs, and narrow gaps are tested. Results consistently show that the modified Hybrid‑A* generates trajectories that satisfy both kinematic constraints (including reverse motion) and collision‑free requirements, even in highly constrained spaces where the unmodified Hybrid‑A* would produce infeasible paths. The approach is demonstrated to be robust, computationally tractable, and readily extensible to forward parking or other low‑speed maneuvers.

In conclusion, the study delivers a practical, real‑time path‑planning framework for autonomous reverse parking by integrating a single‑track kinematic model, a set of carefully designed reverse motion primitives, and a rigorous collision‑checking mechanism within the Hybrid‑A* search. The method bridges the gap between theoretical feasibility and real‑world safety, paving the way for reliable autonomous valet parking and related low‑speed autonomous driving applications. Future work is suggested to incorporate dynamic obstacle avoidance, multi‑vehicle coordination, and hardware‑in‑the‑loop testing to further validate and expand the algorithm’s applicability.