The issue of finding available parking spaces and mitigating congestion during parking is a persistent challenge for numerous car owners in urban areas. In this paper, we propose a novel method based on the A-star algorithm to calculate the optimal parking path to address this issue. We integrate a road impedance function into the conventional A-star algorithm to compute path duration and adopt a fusion function composed of path length and duration as the weight matrix for the A-star algorithm to achieve optimal path planning. Furthermore, we conduct simulations using parking lot modeling to validate the effectiveness of our approach, which can provide car drivers with a reliable optimal parking navigation route, reduce their parking costs, and enhance their parking experience.

In recent years, with the acceleration of urbanization and the improvement of road construction level in China, the number of cars has grown from 10 million in 2000 to 417 million in 2022, ranking first in the world. Although the rapid increase in the number of cars has improved people’s living convenience, it has also brought problems such as traffic congestion and environmental pollution. Due to the increasingly complex internal structure of parking lots and the insufficiently clear signage inside the parking lots, congestion often occurs in parking lots during peak periods. Providing reliable optimal parking navigation routes for car drivers has become crucial. This approach can not only save parking costs, reduce fuel consumption and environmental pollution, but also reduce internal congestion in parking lots, thereby greatly improving the utilization efficiency of parking spaces, and to a large extent, alleviating the problem of parking difficulties in cities.

Currently, methods for solving the single-source shortest path planning problem mainly include ant colony algorithm, Dijkstra algorithm, bee algorithm, A-star algorithm, particle swarm algorithm, genetic algorithm, etc. [

Traditional single-source shortest path algorithms only consider the shortest distance or time without taking into account the dynamic traffic conditions of the road network. To address this issue, this paper proposes an improved path planning model that integrates the theory of road impedance functions to calculate path travel time, and uses a fusion function of path length and travel time as the weight matrix for the A-star algorithm to achieve optimal path planning. This method solves the problem of requiring a long time to travel the optimal path when only considering the shortest distance, as well as the problem of having a very long optical path length when only considering the shortest time.

Currently, many works are studying the improvements and practical applications of the A-star algorithm. Erke et al. [

There are also many applications related to path planning in parking navigation systems. Dokur et al. [

The A-star algorithm is a common heuristic algorithm. heuristic search is a search in the state space that evaluates the position of each search to get the best position, and then searches from this position until the target. the A-star algorithm is often used to calculate the shortest path between two nodes, which is implemented by the valuation function

The above equation

The process of the A-star algorithm is shown in

(1) First, add the starting point to the open list, then traverse the open list, find the node with the minimum

(2) Check each adjacent node of the current node one by one. If the adjacent node is unreachable or in the close list, ignore it. Otherwise, if it is not in the open list, add it to the open list, and set the current square as its parent square. If it is in the open list, check if this path is closed. If it is closer, set its parent square as the current square and recalculate

(3) If the target point is added to the open list, it means that the shortest path has been found and the search is stopped. If the search for the target point fails and the open list is empty, it means that there is no path.

(4) From the target point, move each square along the parent square until the starting point is reached to form the shortest path.

The road impedance function is a fundamental technique that plays a critical role in transportation planning and control. It represents the operational distance, time, comfort, or a combination of these factors between paths on a transportation network. The road impedance function refers to the functional relationship between traffic load, travel time, and driving speed during travel. The principles of traffic distribution in transportation planning are applied based on the road impedance function.

The solution method for the road impedance function adopts a combination of empirical and theoretical approaches. The main idea of this solution method is to determine the theoretical model of the road impedance function based on the relationship between the three parameters of traffic flow theory: traffic volume Q, speed V, and density K. Traffic volume refers to the number of participants in the traffic passing through a certain path on the road in a unit of time. The value of traffic volume is the product of speed and density. The calculation process of the road impedance function model is as follows:

In the formula,

In the formula,

In the formula,

This paper proposes a fusion function that comprehensively considers the impact of path length and path duration consumption on the weight in the A-star algorithm, and the degree to which they affect the path weight can be represented by the fusion function.

In the above formula,

The value of

In the above formula,

In the above formula,

Obtaining data for vehicles driving in an underground parking lot is difficult. To visually compare and analyze the effectiveness of different path planning algorithm models, this paper creates an underground parking lot map as shown in

The obstacles in an underground parking lot are significantly different from those found outdoors. To increase the realism of the environment, the map simulates obstacles such as parking spaces, staircases, and elevators found in underground parking lots, as shown in

We can create a directed graph containing the entrance of the parking lot, the exit of the parking lot, parking spaces, road nodes, and obstacles based on the plan of the underground parking lot. At the same time, we can also construct other data about the N-order matrix

To compare and analyze the effectiveness of path planning algorithms, this paper takes the staircase entrance of a parking lot as the starting point and a certain parking space in the parking lot as the target point. The weight matrix representing the path distance, denoted as S(p,q), is used as the weight matrix for path planning. Similarly, the weight matrix representing the path duration, denoted as T(p,q), is also used for path planning. In addition, a joint function of path distance S(p,q) and path duration T(p,q) is used as the weight matrix for path planning. Based on the above three situations, the simulation results are shown in

Wight matrix | Time cost/s | Distance/m |
---|---|---|

Path length | 31 | 108 |

Path duration | 19 | 111 |

Fusion | 20 | 108 |

To compare and analyze the effectiveness of using path distance matrix and path duration matrix as weight matrices, the former representing path distance and the latter representing path duration, simulations were conducted for the optimal path from the starting point (shown in dark green in the figure) to the destination point (shown in red in the figure). When using the path distance matrix as the weight matrix, the simulation result in

Currently, the internal structure of parking lots in cities is complex, and the signage inside the lots is not clear enough, leading to traffic congestion during the parking process. In this paper, we propose an improved A-star algorithm to solve the path planning problem in parking lots, and combine an impedance function model to use a fusion matrix composed of path length and path duration as the weight matrix of the A-star algorithm to improve the traffic efficiency of vehicles in the parking lot. Simulation results show that considering the fusion function of both distance and travel time results in more reasonable paths than considering only one factor. The improved A-star algorithm can be used for parking lot path planning, reducing congestion during the parking process, improving user convenience, and reducing parking lot management costs, and will have practical value in the field of intelligent parking.

Thanks to Professor Zhang and Professor Deng for their guidance in the process of completing this article.

The authors received no specific funding for this study.

The authors declare that they have no conflicts of interest to report regarding the previous study.