Neural Swarm Control Algorithm for Underwater Vehicles

TOMASZ PRACZYK, PIOTR SZYMAK

IT Department

Polish Naval Academy

Śmidowicza 69, 81-127, Gdynia

POLAND

Abstract: The paper presents the application of an evolutionary recurrent neural network to control the swarm

of underwater vehicles. In the swarm, one vehicle is the leader and the others are followers. The leader leads

the swarm along a predefined trajectory without regard for the followers while the followers follow the leader

and avoid collisions with all other vehicles. Avoiding collisions by the swarm with external obstacles is done by

changing the depth. The leader is responsible for detecting the obstacles and informing all the followers about

the need to change the depth. To follow the leader, the followers use the information about the distance to it.

Directional information is unavailable to them. To avoid collisions inside the swarm, the followers use short-

range sensors.

Key-Words: neural networks, swarm, autonomous underwater vehicles, evolutionary computation, control

Received: December 8, 2022. Revised: August 16, 2023. Accepted: September 22, 2023. Published: October 17, 2023.

1 Introduction

Underwater vehicles are robots that allow the imple-

mentation of many different tasks in the underwater

environment. We distinguish remotely operated ve-

hicles (ROV), i.e. unmanned vehicles that are con-

trolled by a human-operator and connected to him/her

using a special cable transmitting control signals and

often also energy, and autonomous vehicles (AUV)

that can operate without human assistance.

Autonomous vehicles can perform their tasks

not only independently but also in larger teams or

swarms. The team of vehicles is understood in the

paper as loosely cooperating vehicles, each of which

can also operate independently of the others and is

equipped with a global underwater dead reckoning

navigation system for this purpose. Providing vehi-

cles operating in teams with the ability to operate in-

dependently makes these vehicles expensive and of-

ten very complicated to operate.

Another solution is a swarm of vehicles under-

stood in the paper as a group of vehicles closely co-

operating and moving in a compact formation. If we

assume that one of these vehicles, say leader, is re-

sponsible for global navigation and guiding the entire

swarm along a predefined path, then the remaining

vehicles, say followers, can be relieved of the need

for expensive devices for long-range underwater nav-

igation and thus become cheaper, smaller and easier

to use.

However, for followers to be able to follow the

leader and at the same time avoid obstacles and neigh-

bors, an appropriate control system is necessary. The

proposed system is a recurrent neural network (RNN)

trained using a neuro-evolutionary algorithm called

Hill Climb Assembler Encoding (HCAE) [1].

The network is supplied with two types of in-

formation, i.e. information about the distance from

the leader which is provided by the leader itself via

an acoustic communication channel, and information

about nearby objects which is provided by vehicle

sensors. Leader-related directional information is un-

available to followers which means that they know

how far away the leader is, but they have no idea in

what direction they can expect it, which is a serious

difficulty for the neural control system. What is more,

information about the distance is provided rarely. It

is delivered to the followers one by one, which means

that the more vehicles are in the swarm the less often

each of them receives information about the distance

from the leader.

Information about nearby objects comes from sen-

sors and is obtained much more often than distance

information. The problem, in this case, is that the fol-

lowers do not know the nature of the observed object.

They do not know if it is another follower, a leader, or

an obstacle. To facilitate the task of the followers, it

was assumed that the leader is responsible for detect-

ing obstacles and avoiding them consists in changing

the depth - vehicles pass over the obstacle. However,

for the leader to be able to detect obstacles, none of the

followers must be in the field of view of the leader’s

sensors. What is more, the lack of danger of colli-

sion with obstacles (at least in theory) does not mean

that followers do not see them. The swarm can move

close to obstacles, with the effect that the sensors of

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the followers can still detect them. As a consequence,

followers have no fear of obstacles, but they still can

notice them and cannot distinguish them from swarm

vehicles.

To verify the proposed swarm control system, it

was tested in simulation conditions. Training of the

system took place on GPU servers, while the visu-

alization of swarm behavior was in MOOS IvP en-

vironment [2]. Both the leader and followers were

the same, i.e. they behaved according to the same

kinematic model. The swarm consisted of one leader

and four followers. The leader moved along a pre-

defined trajectory that had both straight sections and

turns. During the voyage, the leader did not pay at-

tention to other vehicles which means that in-swarm

collision avoidance was the task of the followers. The

tests were performed with and without external obsta-

cles.

The contribution of the paper is as follows:

1. Neural swarm control system for follower vehi-

cles is proposed,

2. The characteristic features of the system are: (i)

followers have to follow the leader based only on

distance information, directional information is

unavailable, (ii) distance information is rare, (iii)

followers cannot be in the field of view of the

leader sensors, (iv) follower sensors cannot dis-

tinguish external objects from in-swarm objects,

3. The system was verified in simulation condi-

tions.

The rest of the paper is as follows: section two out-

lines related work, section three details the proposed

system, section four reports experiments, and the final

section concludes the paper.

2 Related Work

The subject of robot swarm technology is increasingly

undertaken in world literature by both scientists and

practitioners. Papers in this field, however, mainly

apply to air, land, and sometimes surface robots. Due

to the complexity of the underwater environment and

the problems that the environment generates, papers

presenting examples of underwater swarms are rarer

than those referring to the aforementioned air and land

swarms.

Interesting examples of underwater swarms are

given in works [3], [4]. They present aggregation, dis-

persion, and diffusion swarm behaviors. Underwater

robots concentrate in one place for some purpose or

fill some space as much as possible.

The fountain maneuver and circle formation are

presented in [5], [6], [7]. In this case, the task of pray

vehicles is to evade predators.

Hunting swarm behavior is presented in [8], [9],

[10], [11]. In this case, the task of the vehicles is to

reach a target vehicle, and then to form an encircling

formation around the target.

Leader-following swarm strategy with a fixed for-

mation is demonstrated in [12], [13], [14]. A special

case of the leader-following approach is the applica-

tion of consensus algorithms [15], [16], [17]. The task

of the algorithm is to achieve a consensus on a com-

mon goal in a group of cooperating robots.

3 Swarm control system

The task of the swarm control system is to lead the

followers to a certain endpoint along a predetermined

trajectory. The followers, according to the assump-

tion, are low-cost vehicles that cannot independently

move over long distances. As a consequence, to reach

the destination point, they must follow another vehi-

cle (leader) that shows them the way. To follow the

leader, the followers are fed with information about

the distance from the leader. However, this informa-

tion is provided relatively rarely - the more vehicles

in the swarm, the less often this information reaches

the followers.

To reach their destination, in addition to following

the leader, the followers must avoid other vehicles in

the swarm. To observe the surroundings, the follow-

ers use two different sensors, i.e. cameras placed on

the sides and rear of the vehicles, and sonar looking

forward. The cameras have a maximum range of 5m,

while the sonar range is 30 meters. The angular ob-

servations range of the camera and sonar is shown in

Figure 1.

Figure 1: Follower observation sectors

It is assumed that external obstacles are avoided

by changing the depth and the decision to avoid ob-

stacles is made by the leader which sends a new depth

for all vehicles. For the leader to be able to detect ob-

stacles and inform followers about them, none of the

followers can enter the leader’s field of vision. Oth-

erwise, every follower noticed by the leader would be

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interpreted as an obstacle to be avoided.

The above solution to the problem of avoiding ob-

stacles by the whole swarm results from the inability

of the vehicles to distinguish obstacles from other ve-

hicles. Using sonar as the main long-range sensor, it

is very difficult to determine what object you are deal-

ing with. This makes it difficult for followers to adjust

the appropriate behavior strategy - when the object is

not dangerous because it moves in the same direction

and when the object is a threat because it does not

move or moves in the opposite direction. Moreover,

the echo seen in the sonar image may correspond to

several objects located at the same distance, but at dif-

ferent depths.

Due to the difficulties in interpreting the sonar im-

age, it was finally decided on a solution in which only

the leader detects obstacles and whatever it detects is

an obstacle that must be avoided. In turn, the follow-

ers are only responsible for avoiding other followers

and the leader. In this way, responsibility is divided

and each vehicle knows what it is dealing with in the

sonar image.

Since it is assumed that the leader deals only with

obstacles and moves along a predefined trajectory to

an endpoint, the task of keeping the swarm in its en-

tirety is the task of the followers only. To this end,

each follower is equipped with a recurrent neural net-

work that is fed with the following information:

1. Distance to the nearest object in sonar observa-

tion sector scaled to the range <0,1>,

2. Distances to the nearest objects in three camera

observation sectors scaled to the range <0,1>,

3. ∆DM

t=|DL

t−DD| − |DL

t−1−DD|, where

tis the distance to the leader received by the

follower at time tand DDis a desired distance

to the leader. ∆DMprovides the network with

information about whether the distance error in-

creases (∆DM>0) or decreases (∆DM<0)

in the period between two leader messages, and

how big is the change. It is a counterpart of the

rate of change of error with respect to time ap-

plied in PID controller.

4. DS

<0,1>,t =DS

TDL

max

, where DS







TDL

max Pt

k=1 ∆DM

k> T DL

max

−TDL

max Pt

k=1 ∆DM

k<−TDL

max

k=1 ∆DM

kotherwise

and TDL

max is the maximum acceptable error of

the distance to the leader. DS

<0,1>accumulates

the changes of distance errors over time. It

can be negative if the distance error is positive

at the very beginning of the swarm operation.

It is equivalent to the sum of errors in a PID

controller.

The task of the network is to determine the heading

and speed of the vehicle by the following formulas:

1. HD

t+1 =A360(Ht) + 180OH

t, where HDis a

desired heading, His actual heading, A360 is a

function which converts input angle to the range

<0,360), and OH, is output of the network cor-

responding to heading. In consequence, the task

of the network is not to determine the heading but

the change of the heading.

2. VD

t+1 =VmaxOV

t, where VDis a desired speed,

Vmax is maximum speed of the follower, and OV

is output of the network corresponding to speed.

The network does not specify the depth at which

the vehicle is to move. As already mentioned, the

depth at which each follower moves depends on the

leader. The leader sends the depth through the acous-

tic channel if it needs to be changed. The depth

change is handled by the low-level control system.

The neural network is trained using a neuro-

evolutionary algorithm called Hill Climb Assembler

Encoding [1]. It is an algorithm that represents a net-

work in the form of a matrix and constructs this matrix

in many successive evolutionary iterations. Unlike

other evolutionary algorithms, the genotype does not

represent the entire network (matrix) but some part of

it. As a consequence, the network is encoded not in

one genotype but in a sequence of genotypes coming

from other runs of the evolutionary process. The op-

eration of HCAE can be compared to a situation in

which the object subject to optimization is improved

little by little, piece by piece. Each piece is the re-

sult of a different evolutionary process. The detailed

specification of HCAE is given in [1].

4 Experiments

To verify the effectiveness of the swarm control sys-

tem described above, simulation tests were carried

out. During the tests, the task of the swarm consist-

ing of a leader and four followers was to move along

a predefined trajectory of 2000 meters. Two trajec-

tories were used to train the neural networks, and the

other two trajectories were used to verify the effec-

tiveness of the system. Each of the trajectories had

both straight sections and turns to the right and left.

In the first phase of testing, the vehicles had no ob-

stacles to deal with, while in the second phase, round

obstacles with a diameter of 20 meters were placed

along the route of the vehicles. Since it was assumed

that the leader can correctly detect obstacles and prop-

erly control the depth of the swarm, all obstacles were

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Figure 2: Example behavior of the swarm in the sce-

nario without obstacles (time in the images flows first

from left to right and then from top to bottom). The

visualization of vehicle behavior was carried out us-

ing the alogview MOOS application [2]

located under the trajectory of the swarm. As a conse-

quence, obstacles did not cause collisions, but if they

were within the range of the sensors, they were no-

ticeable by the control system.

All vehicles behaved by the kinematic model im-

plemented in the MOOS uSimMarine application [2].

The HCAE algorithm was used to train the networks

and the following fitness function was applied to eval-

uate the generated neural solutions: F(network)D=

NI+1

1+ED

max , where NIis the number of simulation

steps (see further), and ED

max is the maximum error of

the distance to the leader among all followers.

The number of steps in evaluating each of the

evolved networks (NI) depended on their effective-

ness. The evaluation was interrupted in four situa-

tions. Firstly, when ED

max > T DL

max, i.e. if any fol-

lower was further from the leader than the assumed

threshold TDL

max. Secondly, when any follower entered

the leader’s field of vision. Thirdly, when all follow-

ers made the same decisions regarding the direction

of movement and speed for a short period. Fourthly,

when vehicles collided, i.e. the distance between any

pair of vehicles was less than 2 meters.

The more important parameters of the simulations

are as follows: the number of followers=4, DD=

30m, TDL

max = 40m, Vmax = 2m/s, the time interval

between successive sensor data=1s, the time interval

between successive messages containing information

about the distance to the leader=4s (as already men-

tioned, information about the distance was received

by the followers one by one, it was sent by the leader

to each follower every 1s, first to follower no. 1,

then to follower no. 2, and so on), simulation time

step=0.1s, the number of input neurons in the net-

work=6 (four inputs for observation sectors, one input

for ∆DM

t, and one input for DS

<0,1>,t), the number of

output neurons in the network=2 (one for heading and

one for speed), the number of hidden neurons=12.

In the first phase of testing, when the vehicles did

not have to deal with obstacles, initially there were no

restrictions on the turning speed of the leader. This

speed depended only on the leader’s maneuverability.

It turned out, however, that in the absence of restric-

tions on the behavior of the leader, the followers were

unable to follow the leader without entering the field

of vision of its sonar.

To avoid the above problems, the turning maneu-

ver of the leader was slowed down in such a way

that at a distance of 10 meters, the leader could only

change course by 30 degrees. After using this solu-

tion, it turned out that the followers can effectively

follow the leader and not enter the field of vision of

its sensors. The vast majority of neural networks that

were constructed during the learning process were

able to control the followers along both test trajec-

tories, from the start point to the endpoint. Example

behavior of the swarm is depicted in Figure 2.

Regardless of the neural network, the behavior of

followers was very similar. Very often they moved

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Figure 3: Example behavior of the swarm in the sce-

nario with obstacles (if the vehicles are covered by

an obstacle, it means that they are over the obstacle

- in the alogview MOOS application used to visual-

ize the simulation results, all additional objects are

always presented in the foreground in relation to the

vehicles.)

close to each other, observing the behavior of neigh-

bors with the help of sensors. This behavior could

help followers to follow the leader even when infor-

mation about the distance from the leader is very rare.

By observing the neighbors, each follower obtains in-

direct information about the behavior of the leader.

A change in the direction of movement by a neigh-

bor may be due to the change in the direction of the

leader’s movement and the message about the dis-

tance received a moment ago by the neighbor. Al-

though only one follower at a time receives a dis-

tance message that allows it to adjust its behavior to

follow the leader, other vehicles in its vicinity, see-

ing the change in the neighbor’s behavior, can do the

same even though they have no information about the

leader’s location.

The behavior that allows the followers to avoid the

field of vision of the leader is to reduce speed or even

stop when the leader is making a turn toward the fol-

lowers. This behavior can be seen, for example, in

sub-figures (3,2), (3,3), (2,5) in matrix-Figure 2.

In the second phase of the tests, obstacles were in-

troduced into the environment. They had a circular

shape, and a diameter of 20 meters and were placed

at the end of the leader’s trajectory, i.e. on a straight

long section leading to the endpoint. During the sim-

ulation, it was assumed that the swarm moves above

obstacles that are detected by the leader - each time

the leader detects an obstacle, it orders a change of

depth to avoid obstacles by moving over them. This

approach means that the followers did not have to

avoid obstacles. All they had to do was to follow the

leader in a situation where, in addition to other vehi-

cles, obstacles indistinguishable from vehicles were

also visible in the sonar image. The exemplary be-

havior of a swarm in the presence of obstacles is pre-

sented in Figure 3.

The addition of obstacles on the trajectory of vehi-

cles introduced difficulties in the evolution of effec-

tive neural networks, i.e. those that were able to lead

a swarm from the starting point to the endpoint of the

trajectory. In contrast to the test scenario without ob-

stacles, the number of effective neural networks for

the scenario with obstacles decreased significantly. In

this case, only about 10% of the runs of the evolution-

ary process resulted in the generation of fully effective

neural networks.

As for the reaction of followers to obstacles, it oc-

curred only when vehicles passed over obstacles. Ob-

stacles on the side of the followers did not cause any

disturbances in proper movement behind the leader.

They were usually at a safe distance from the vehi-

cles and consequently were not considered a threat

that required a response. On the other hand, obstacles

located directly under the followers generated sonar

echoes in close proximity to the vehicles. In this case,

the reaction was mostly a slight change of course, as if

the obstacles were gently pushing the followers away.

There were also cases when followers considered ob-

stacles as an imminent collision hazard and performed

an evasive maneuver consisting of making a full circle

to the left or right - see sub-figures (1,4), (2,4), (3,4)

in matrix-Figure 3. After performing this maneuver,

the followers returned to the swarm.

5 Conclusions

The paper presents the use of recurrent neural net-

works constructed in an evolutionary way to control

underwater vehicles acting as followers in a swarm

consisting of one leader and a group of followers.

The only task of the followers is to follow the leader

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while avoiding collisions with neighboring vehicles.

No specific formation of followers is required.

During the experiments, the results of which are

presented in the paper, the vehicles were unable to

distinguish obstacles from other vehicles in the swarm

using the only long-range sensor which was sonar. In

consequence, it was decided that avoiding collisions

with obstacles external to the swarm is the responsi-

bility of the leader which detects obstacles and, in the

event of a threat, decides to change the depth for the

entire swarm. However, for the leader to be able to

detect obstacles and not confuse them with followers,

none of the followers must be in the field of vision

of the leader sonar. Such a limitation was a serious

challenge for the neural control system, especially on

bends.

If we assume that the leader is able to quickly de-

tect obstacles and change the immersion depth of the

swarm, then we can conclude that the followers are

not at risk of colliding with external objects. How-

ever, if followers move near obstacles, they are still

visible to them, which makes it difficult to follow the

leader because it is not known whether the detected

object is another vehicle or an obstacle. The impos-

sibility of correctly interpreting information from the

sonar is another problem that the neural control sys-

tem had to face.

An additional difficulty for the system was also the

limited information available for decision-making.

To follow the leader, the followers were supplied with

information about the distance to it. However, this

information was provided rarely, one by one to each

follower. Directional information was not available to

the followers. In addition, the followers used limited-

range sensors such as sonar and cameras to avoid col-

lisions.

Despite all the challenges that the neural control

system had to face, the simulations, the results of

which are presented in the paper, showed that the use

of recurrent neural networks as a high-level control

system of the followers, i.e. the system determining

the direction of movement and speed of vehicles, al-

lows for collective movement of vehicles along the

route designated by the leader. As it turned out, ve-

hicles equipped with a neural network can follow the

leader both in an ideal, obstacle-free marine environ-

ment where every nearby object is a threat - it is just

another vehicle in a swarm that can lead to a collision

and in an environment containing obstacles in which

followers have to deal with both other vehicles that

may pose a threat and with underwater objects that do

not pose a threat because they are at a different depth

away from the swarm.

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Contribution of individual authors to

the creation of a scientific article

(ghostwriting policy)

Tomasz Praczyk is the author of the swarm control

system, he conducted the system learning and simu-

lations. Piotr Szymak is the author of the text.

Sources of funding for research

presented in a scientific article or

scientific article itself

The paper is supported by European Defence Agency

Project No. B-746-ESM1-GP, entitled “Swarm of

Biomimetic Underwater Vehicles II (SABUVIS II)”.

Conflict of Interest

The authors have no conflicts of interest to declare

that are relevant to the content of this article.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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