Vehicle Guidance System
4.2 Vehicle Detection and Tracking
4.3.2 Parking Space Assignment and Path Planning
The Parking space assignment process is based on graph theory. So in order to find the most optimal space, the shortest paths from the vehicle’s location to the parking spaces must be computed. Thus we need to first convert the original map into a Directional Graph. For example, the map in Fig. 4.36 can be converted into the graph in Fig. 4.37. This graph is represented by. where represents the set of the={ , } vertices on the graph, and represents the set of edges on the graph. consists of the pedestrian exits, vehicle entrances and exits, as well as the junctions inside the parking lot.
It is denoted as =E U Ex U En U J, where U should be replaced by the union symbol Di(t) construction
0 No display
1 ←
2 ↑
3 →
4 ←↑
5 ↑→
6 ← →
7 ← ↑→
in math types, where Ex is the set of vehicle exits and En is the set of vehicle entrances.
Fig. 4.37 Parking lot graph.
Based on thevehicle’scurrentlocation and thedistribution offreespaces,parking space assignment assigns an optimal space where the cost of driving from the current location to the assigned space is minimized. The cost is designed in accordance with most drivers’common parking behaviors,including:
a.thecostfrom the driver’scurrentlocation to theparking space,cost(c1): smaller c1 value means the vehicle can get to the parking space in a shorter amount of time;
b. the cost from the parking space to the vehicle exits, cost(c2): this distance corresponds to the time needed to drive the vehicle out of the parking lot;
c. the cost from the parking space to pedestrian exits, cost(c3): this distance corresponds to the time needed to walk out of the parking lot.
The above three distance factors measure the time needed to park and leave as well asthevehicleowner’swalking time.In orderto achievethe optimality ofthe parking space assignment, in this study we define a cost function as follows:
1
where C is the cost of going to the parking space, ciis individual cost, and wiis the degree of importance of each individual cost, where
1
1
n i i
w
. The cost of c2 and c3 are determined by the distance from the parking space to the exit. They are both fixed and can be obtained by referring to a table without any calculation. c1, on the other hand is based not only on the distance from the vehicle to the parking space, but also on the degree of congestion, the junctions, and the widths of the roads along the path. The more vehicles that are on the path, the slower the vehicle can move, so the cost from the vehicle to the parking space will increase. Similarly, if there are more junctions or more narrow roads on the path the cost will also increase. The followings are four path factors that will increase the cost:． The coefficient k1, to represent the increase in cost due to vehicles moving in the same direction;
． The coefficient k2, to represent the increase in cost due to vehicles moving in the opposite direction;
． The impact of the width of the road is defined as ( ) ( i) w R
w R , where w R is the width of( i) the road Ri, and w R( ) is the average width of roads inside the parking lot;
．The coefficient k3, to represent the increase in cost due to the fact that a vehicle must slow down at a junction.
The more vehicles that are travelling in the same direction, the greater the impact on vehicle towards the rear, so the cost of passing through the road Riis L R( i)k1n1, where L(Ri) is the length of Ri and n1 is the number of vehicles in front of the current vehicle.
The number of vehicles in the opposite direction will also affect the time when they meet,
therefore causing the vehicle to slow down. The time when they meet is fixed, so the cost increased by the reverse traffic is represented by n2 , where nk2 2 is the number of vehicles that are coming from the opposite direction. When the vehicles pass through junctions, they are likely to slow down and will only continue to move along after observing whether there are other vehicles on either side of the junction. This increase in cost is represented by n3 , where nk3 3 is the number of junctions a vehicle must pass through.In conclusion,thecostoftravelling from thevehicle’scurrentlocation to the assigned parking space (c1) is as follows:
1( ) the number of vehicles that may come from the opposite direction.
R1
Take the red line in Fig. 4.38 as an example. The vehicle needs to travel along a part of R1 denoted by O1 then along R2, R3, R4, R5, and finally a part of R7 denoted by O7. When it is travelling on R3, there is a green vehicle in front of it. So its cost on that road is increased to R3 × k1. Then again on road R4 it meets a vehicle coming from the opposite
direction (represented by the black line), which increases the cost by k2. Therefore, the cost c1of the red vehicle passing through this path to the assigned parking space is:
1 1 2 3 1 4 2 5 7 3
1 2 3 4 5 7
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) 5
w R w R w R w R w R w R
c O R R k R k R O k
w R w R w R w R w R w R
4.3.3 Experimental Results
In this study, the simulated parking lot is shown in Fig. 4.39. In this figure, the blue regions represent the pedestrian exits, the green regions represent the vehicle exits, the orange regions represent the vehicle entrances, the red blocks represent occupied parking spaces, and the light blue blocks represent the remaining available parking spaces.
Fig. 4.39 Parking lot plan.
a. Parking Space Assignment for a Single Vehicle
Assuming that there are initially four empty parking spaces. We must first assign parking spacesto thevehiclebased on theshortestdistancesfrom thevehicle’scurrent location, the vehicle exit, or the pedestrian exits, as shown in Figure 4.40 (a), (b), (c) respectively. Then we must consider the two costs at the same time. Figure 4.40 (d), (e), (f) show theassignmentsbased on minimaltotalcostofthe vehicle’slocation and vehicle exit,thevehicle’slocation and pedestrian exit,and thevehicle exitand pedestrian exit, respectively. Finally, in Figure 4.40 (g) we take into account the combined cost of the vehicle’slocation,vehicleexitand pedestrian exit.From theexperimentresults,wecan
see that the system is able to assign the parking space with the lowest cost to the vehicle waiting to park.
(a) (b) (c)
(d) (e) (f)
(g)
Fig. 4.40 Parking space assigning for single vehicle.
(a) (b) (c)
(d) (e) (f)
(g)
Fig. 4.41 Parking space assigning for two vehicles.
b. Parking Space Assignment for Multiple Vehicles
Next, we assign parking spaces to two vehicles at the same time. Given the same four empty spaces as above, the conditions for the assignment are also the same as the above scenario. The results are shown in Figure 4.41. (a) ~ (g). It can be seen by the experiments that even when there are multiple vehicles, the system is still able to assign the parking spaces with the lowest cost to each vehicle.