Intelligent Car Park Assist
Using Fish Swarm Algorithm
SPYRIDON A. KAZARLIS,
Dept. of Informatics, Computers and Telecommunications Engineering
International Hellenic University,
Terma Magnesias St., 62124 Serres,
GREECE
Abstract:—In this paper a novel Intelligent Car Park Assist System is presented that uses an Evolutionary
Computation method called “Fish Swarm Algorithm” or FSA, inspired from the behavior of schools of fish. The
work focuses on the “parallel park” problem where a car needs to park between two already parked cars with a
gap between them. The modeled car adopts the Ackermann model for moving, and has to complete the park task
in 3 moves. Every move consists of steering the wheel at an angle and moving the car at a specific distance. For
finding the optimal car moves to park successfully, a paradigm of the FSA algorithm is used. Simulation results
confirm both the modelling soundness and the optimization capabilities of the FSA method.
Key-Words: - Fish Swarm Algorithm, Intelligent Car Park Assist, Evolutionary Computation, Ackermann
Steering Model.
Received: March 29, 2024. Revised: September 11, 2024. Accepted: October 13, 2024. Published: December 4, 2024.
1. Introduction
This paper presents the application of an
Evolutionary Computation method called “Fish
Swarm Algorithm” or FSA on the problem of
parallel car park in an automated and optimized way,
leading to an Intelligent Car Park Assist system.
In this section, a brief introduction on both the
“Parallel Car Park problem” and the “Fish Swarm
Algorithm” will be given.
1.1 Parallel Car Park Problem
The parallel car park task [1] is one of the most
difficult to master driving maneuvers, especially for
young drivers.
Fig.1 Depiction of the parallel car park problem
And in most countries it is a mandatory task to
accomplish in the practical exams for getting a
driving license. For this reason several car
manufacturers offer “Intelligent Parallel Park Assist”
systems, especially in their high priced models, in
order to assist the driver in such situations. Cars
equipped with such systems offer a wide range of
help for the driver, from simply indicating the
distance of the car to the front and back cars, to
showing him an upper 360 degrees view of the car
and its surroundings, or finally perform the parallel
park completely autonomously, with the driver
holding the role of a passenger.
Historically, such systems date back to 1990, where
the French Institute for Research in Computer
Science (INRIA) developed an autonomous car park
system for a Ligier car [2]. In more recent years
(2003) Toyota Motor Corporation introduced the
Intelligent Parking Assist System (IPAS) that was
first placed on a Toyota Prius hybrid model [3].
Later, such systems were placed on Lexus cars
(2006), the Ford Lincoln model by Ford in 2009 as
“Active Park Assist” system [4], and the BMW
series 5 model in 2010, as the ‘Parking Assistance”
system. Following that, in 2012 Ford generalized
the use of its “Active Park Assist” on more models,
like the Ford Focus, Fusion, Escape, Explorer and
Flex. The same year Toyota produced an upgraded
system that equipped models like the Toyota Prius
5, Lexus LS460 and LS460L. Audi introduced a
similar system placed on the A6 model, and
Mercedes Benz developed the “Parktronic” system
Engineering World
DOI:10.37394/232025.2024.6.20
Spyridon A. Kazarlis
E-ISSN: 2692-5079
188
Volume 6, 2024
that equipped models like CLS-Class, C-Class, E-
Class, S-Class, M-Class, etc. In 2014 Jeep Company
supplied its Cherokee model with its “Parksense”
system and in 2015 BMW put a similar system on
the BMW i3 model that was controlled by a
smartwatch.
In the literature, there are many scientific papers
contributing to the solution of this problem, like Xu,
Chen and Xie [5], who propose a system based on
vision that is able to recognize a possible parking
place and find a path for driving the car in it. In the
work of Wang and Zhu [6] a fuzzy controller is
constructed for an intelligent car park system. In the
work of Ji, Wang, Zhao, Lin, Zang & Li [7] a neural
network is trained to act as a PID controller for
vehicle parallel parking. In the work of Saleh, Ismail
& Riman, [8] a new geometric-based algorithm is
proposed for parallel car parking of a car-like robot
that achieves better performance, especially in
narrow spaces. In the work of Nakrani & Joshi [9],
the authors propose a Fuzzy system to cope with
parallel parking in dynamically changing
environments and they continue their research in
[31] where they propose a fuzzy-based adaptive
dimension parking algorithm (FADPA) that also
copes for obstacle avoidance. And in the work of
Rashid, Rahman, Islam, Alwahedy & Abdulahi [10]
the authors propose yet another fuzzy logic
controller for automated parallel parking.
1.2 Fish Swarm Algorithm
Fish Swarm Algorithm (FSA or AFSA) is an
Evolutionary Computation optimization method,
first introduced by Li et al. in 2002 [11], and
belongs to the family of Swarm Intelligence
methods [12]. It is inspired by the behavior of
schools of fish in their quest for prey. It employs
artificial fish in the role of agents that search the
search space of an optimization problem. It mimics
four different behaviors found in schooling fish,
namely: Prey, Swarm, Follow and Random
behavior.
Prey behavior simulates the individual quest of
every fish to find prey or food (good solutions)
within its visibility distance (Visual). Swarm
behavior mimics the fish clustering tendency, where
every fish tends to avoid danger by assembling in a
group (convergence). Follow behavior simulates the
behavior of an individual fish to follow neighbor
fish that have already found food sources (exploit
good solutions). Finally, Random behavior gives
every fish (or agent) the chance to search the
surrounding space for food (good solutions)
independently of the other fish, and in a random
manner. In figure 2 a simplified pseudocode of the
FSA method is provided, where Visual is a metric of
the radius inside which the fish can see its
surrounding fish, and Step is the maximum distance
the fish can travel when its position changes.
Fig.2 Pseudocode of the FSA optimization method
Since 2002, there have been many papers in the
literature concerning improved and hybrid models
of FSA to solve different real-world optimization
problems.
Such problems include data clustering [13], image
segmentation [14], fault diagnosis [15], power
allocation scheme [16], parameter optimization of
the deep auto-encoder [17], spoiled meat detection
[18], manufacturing [19], risk probability prediction
[20], guidance error estimation [21], navigation
[22], wireless sensor network [23], energy
management [24] and motion estimation in video
encoding [30].
Read N, Visual, Step, Try, Iter; i=0
For fish=1 to N
position(fish) = random
fitness(fish) = Fitness (position(fish))
Endfor
While (i < Iter)
For fish=1 To N
calculate no of neighbors nf of fish (inside Visual)
If (nf >= 1) then // Follow Behavior
find neigboring fish nfb with best fitness
If (fitness(nfb) > fitness(fish) then
Move fish a Step towards nfb
else //Swarm behavior)
calculate the geometrical center nfc of neighbor fish
If (fitness (nfc) > fitness(fish)) then
Move fish a Step towards nfc
Else //Prey behavior)
t=0
While (t<Try AND Better Solution Not Found)
select a random position rfv inside Visual
If (fitness(rfv)>fitness(fish)) then
move fish a Step towards rfv
Endif
t = t + 1
Endwhile
If (Better Solution Not Found) then
//Random behavior
move fish a random Step inside Visual
Endif
Endif
Endif
Else //Prey behavior)
t=0
While (t<Try AND Better Solution Not Found)
select a random position rfv inside Visual
If (fitness(rfv)>fitness(fish)) then
move fish a Step towards rfv
Endif
t = t + 1
Endwhile
If (Better Solution Not Found) then
//Random behavior
move fish a random Step inside Visual
Endif
Endif
Endfor
i = i + 1;
Endwhile
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1.3 Paper Structure
In Section 2 a thorough description is given for the
exact parallel car park problem that is dealt with in
this work. In Section 3 the Fish Swarm Algorithm
used in this work is discussed. Section 6 describes
the parameters and the setup for the simulation
experiments, while Section 5 presents the results of
the executed simulation experiments. Finally
conclusions are discussed in Section 6.
2.
The Car Park Problem
In this work a simple version of the Parallel Car
Park problem [1], [6], [7], [8], [9], [10] is adopted,
that can be seen in figure 3.
Fig.3 Depiction of the Parallel Car Park problem.
The type of car employed in this work has the
following characteristics:
Length: 5 meters
Wheelbase: 3 meters
Width: 2 meters
Steering Model: Ackermann
Steering Angle: 30 degrees
The car movement is modeled after the Ackermann
model [25], [26] that can be described by the
differential equations shown in eq.1.
Eq.1
where x, y denote the global vehicle position in
meters, l (el) is the wheelbase in meters, θ is the
global vehicle heading in radians, ψ is the vehicle
steering angle in radians, and v is the vehicle speed
in m/sec.
The gap between the parked cars is set to 8 meters
and the initial car position is set as for the car to be
parallel to the second parked car (Fig.3) and having
a one (1) meter clearance from it.
The car movement is encoded in the following way:
the car is allowed to make three (3) distinct
movements in order to park successfully. Each
movement is described by a) the steering angle, and
b) the travel distance of the car, as shown in eq.2
Movementi, (i=1..3) = [ Steeringi , Distancei ] Eq.2
The travel distance of the car is metered using the
center of the rear axle as the reference travelling
point. During a single movement, the steering angle
remains constant and does not change. In this way,
the whole movement can be described by a total of
six (6) parameters, as shown in eq.3
Solution=[𝑆𝑡𝑒𝑒𝑟𝑖𝑛𝑔1 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒1
𝑆𝑡𝑒𝑒𝑟𝑖𝑛𝑔2 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒2
𝑆𝑡𝑒𝑒𝑟𝑖𝑛𝑔3 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒3] Eq.3
During the three movements, the simulation
monitors and counts possible collisions with the
parked cars or the pavement (Fig.3). Moreover, in
the case of a collision, the simulation calculates how
severe the collision was, by calculating the volume
of the corresponding polygons of the car and
obstacle that intersect. This collision metric, that is
analog to the collision severity, is used to penalize
the corresponding solutions, in a proportional way.
This leads the FSA algorithm a) to avoid such
“colliding” invalid solutions and b) it produces a
gradient towards “no-collision” acceptable solutions
that facilitates FSA to follow this gradient towards
feasible optimality and converge to a final
acceptable solution.
The objective function of each solution is judged
according to the following criteria:
The distance between the vehicle and the
pavement
The degree of parallelization of the car to the
pavement
The equality of distances of the car with the front
and back obstacles (parked cars) or the degree of
centering inside the empty space.
From the above, it is evident that this problem can
be classified as a constrained multi-objective
problem. Thus, in order to build a consolidated
fitness function, one can build it as a weighted sum
of the individual objective functions [27].
The objective value of each produced solution (sol)
is calculated according to eq. 4.
Obj(sol)=apdist(sol)+bparal(sol)+ccent(sol) Eq.4
where pdist(sol) is the minimum distance between
the car and the pavement, paral(sol) is the absolute
difference of the y values of the centers of the front
and rear axles, and cent(sol) is the absolute
difference between the minimum distances of the
car with the front and rear obstacles (parked cars).
Coefficients a, b and c are weight coefficients that
can be chosen arbitrarily, in order to emphasize in
each optimization objective.
And in order to handle the collision constraints, one
can build a penalty function for the violation of the
constraints and add it to the objective function [28].
Parked Cars
Original Car Position
Final Car Position
Pavement
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So, the fitness function of each produced solution is
built by adding the penalty value to the objective
value:
Fitness(sol) = Obj(sol) + pPenalty(sol) Eq.5
where Penalty(sol) is a metric of possible collision
of the car with the obstacles, that is proportional to
the severity or the volume of the collision, and p is a
penalty coefficient.
3.
Fish Swarm Algorithm
The paradigm of FSA that is used in this work is
more or less a classical FSA implementation and is
based on the pseudocode of figure 2. A worth-
mentioning detail that is omitted from the
pseudocode, for simplicity reasons, is that in order
to accept a new fish position (e.g. when in Follow
behavior (fitness(nfb) > fitness(fish) is true) there is
another extra criterion that has to be met. This
criterion is the crowding criterion [29] that suggests
that a new fish position will be accepted only if the
new position is not very crowded with fish. In the
literature this is expressed by the equation:
nf / n < δ Eq.6
where nf is the number of neighboring fish in the
new position (within Visual), n is the total fish
number and δ is a real number in the range [0..1].
This crowding criterion is added to the algorithm in
order to avoid premature convergence of the
algorithm and help it maintain a solution diversity,
in order to facilitate and pluralize its search effort.
However, it is rather evident that in the early stages
of FSA where the fish population will be scattered
throughout the search space, eq. 6 will be easily
satisfied. But as the population converges eq. 6 will
be more and more difficult to satisfy as nearly all
fish may probably end up within each-others visual
range. To cope with this, one has to progressively
adapt either the δ coefficient, or the Visual range of
fish, during the FSA execution, in a gradient manner
as the population of fish converges.
In order to circumvent this, this work introduces a
different crowding criterion, which works in a
relative and not absolute manner, and is shown in
eq. 7
neighbors(newpos) / neighbors(oldpos) < d Eq.7
where neighbors() is a function that returns the
number of surrounding fish inside the Visual range,
newpos is the new position under check to be
occupied by the fish, and oldpos is the current fish
position in the search space. Parameter d is a
number a little greater than 1 (eg. d=1.2). This
allows the fish to move to areas that are sparser than
the current, but also allows them to move to areas
that are also a little more crowded. So, in this way,
the population is allowed to slowly converge
towards the optimum. If d is less than one, then the
population is prohibited from converging, as it
prohibits the newpos from being more crowded than
the oldpos. On the other hand, if d is much larger
than 1 then FSA will converge at a high rate
(premature convergence). So, a middle value of,
let’s say, 1.1 to 1.5 should be chosen.
In this work, all code has been developed and
executed in the MATLAB R2020a environment.
4.
Simulation Parameters
In order to conduct the simulations and obtain
results, the following FSA parameters have been
used:
The value of Visual has been set to 5 for the
“Steering Angle” parameters and to 0.5 for “Travel
Distance” parameters. The value of Step has been
set to 60% of Visual. The number Try that denotes
the number of tries to find prey, during the Prey
behavior, has been set to 3. Crowding parameter d
has been set equal to 1.5. Concerning the fitness
function (Eq. 4 & 5) the parameter values are set as:
a=2, b=2, c=1, p=10.
Concerning the Ackermann steering model, the
number of allowed moves is 3, having 2 parameters
for every move (Steering and Distance), leading
thus to a total number of 6 variables (Eq. 3). The
range of each Steering variable is [-30..30] degrees,
and the range of each Travel-Distance variable is
[-5..5] meters.
The simulation setup was twofold and includes
Setup1 and Setup2. In Setup1 the fish number N is
equal to 50 and the number of algorithm iterations
“Iter” is set to 100. In Setup2 the number of fish was
doubled and the parameter values were N=100 and
Iter=100.
5.
Simulation Results
The FSA algorithm is a stochastic algorithm. This
dictates that a number of simulation runs have to be
conducted in order to extract useful performance
results.
For this reason a number of ten (10) runs have been
executed for each setup (Setup1 and Setup2). The
results can be shown in Table 1 and Table 2
respectively.
In the result tables, negative steering angles mean
right turns, while positive steering angles mean left
turns. Similarly, positive distances mean forward
motion while negative ones mean moving in
reverse. Each table line shows the best solution
achieved at each run.
As can be seen from the results Setup1 achieves a
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50% success rate, while Setup2, that uses double the
number of fish, achieves an 80% success rate. In
fact every fitness value below 2.5 corresponds to a
successful parking. Two such successful but
different cases, found by FSA, are depicted in
figures 4 and 5.
Table 1. Results of the FSA for Setup1
R
u
n
Steer.
Angle
1
Steer.
Angle
2
Steer.
Angle
3
Dist
ance
1
Dista
nce 2
Dist
ance
3
Fitness
Res
ult
1
-29,98
-10,55
29,99
-4,22
-0,66
-3,60
3,303215
Fail
2
-14,01
11,21
-19,03
-4,84
-3,45
1,52
4,379467
Fail
3
-23,96
29,87
13,81
-4,61
-3,88
1,37
3,065357
Fail
4
-16,27
-29,81
29,95
1,28
-4,98
-3,73
2,12648
Succ
5
29,98
-15,48
26,48
1,80
-4,77
-4,73
0,011434
Succ
6
2,10
-28,11
29,99
1,79
-4,88
-4,63
0,004783
Succ
7
-29,99
-24,90
30,00
-4,35
-0,35
-3,82
3,245316
Fail
8
-27,50
22,62
-29,58
-4,64
-4,14
1,22
0,687886
Succ
9
-29,99
-20,38
30,00
-4,88
0,25
-3,91
3,245707
Fail
10
-23,76
29,98
-27,18
-4,92
-3,07
0,77
2,207561
Succ
Best Fitness
0,004783
Average Fitness
2,227721
Success %
50%
Table 2. Results of the FSA for Setup2
R
u
n
Steer.
Angle
1
Steer.
Angle
2
Steer.
Angle
3
Dist
ance
1
Dista
nce 2
Dist
ance
3
Fitness
Res
ult
1
9,22
-23,77
28,07
2,05
-4,98
-4,73
0,05836
Succ
2
9,89
-28
29,98
1,49
-4,58
-4,67
0,00233
Succ
3
-28,95
24,71
-21,23
-4,53
-4,43
1,35
0,510983
Succ
4
4,43
-27,46
30
1,74
-4,86
-4,61
0,008628
Succ
5
18,5
-21,38
28,38
1,78
-4,86
-4,63
0,009209
Succ
6
-13,62
-29,96
29,97
1,61
-4,96
-4,09
1,544968
Succ
7
-30
25,31
30
-4,6
-0,77
-3,17
3,262214
Fail
8
-29,99
-20,67
30
-4,05
-0,76
-3,74
3,278723
Fail
9
15,48
-23,29
27,54
1,83
-4,69
-4,84
0,010583
Succ
10
-29,51
29,99
-0,38
-4,73
-4,38
1,42
0,704797
Succ
Best Fitness
0,00233
Average Fitness
0,939079
Success %
80%
Figure 4 depicts a more or less classical 3-move
solution for parallel parking that was rather expected
from the optimization algorithm.
It is worth mentioning that the solution of figure 5
suggests that the specific parallel car park problem
is in fact able to be solved with only two moves
instead of three, a fact that is truly remarkable, and
is attributed to the rather large space reserved for the
parking place (8 meters) in the specific problem.
Fig.4 Successful classic parking solution found by FSA
(3 moves)
Fig.5 A rather two-move solution found by FSA
6.
Conclusions
In this work an implementation of the Fish Swarm
Algorithm (FSA) was used to address the problem
of Parallel Car Parking. The results show that both
the 3-moves Ackermann model adopted and the
search ability of FSA are practically justified. FSA
shows a very good 80% success rate that may get
even better by increasing the algorithm’s resources,
in terms of the number of fish and the number of
iterations. The solutions produced are compre-
hensible and to a large extent, expected. However,
some of them are also very interesting, as they
suggest that near optimal solutions may be achieved
with less than the nominal 3 moves that comprise
the encoded solutions. One major advantage of
Evolutionary Algorithms, such as FSA, is that they
are theoretically able to attack any kind of problem
and therefore any kind of car parking problem, and
not only the one described in this paper. So it is
anticipated that FSA would exhibit similar
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performance in other kinds of parking or other car
movement problems, like for example, entering a
ferry boat in reverse. Future work may include the
application of different Evolutionary Computation
methods on this problem, such as Genetic
Algorithms or Particle Swarm Optimization. Also
different parking problems can be addressed, with
different topologies or in more narrow spaces, in
order to test the generalization abilities of the
proposed optimization method.
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