The Hand-gesture-based Control Interface with Wearable Glove System

Vladislav Berezhnoy, Dmitry Popov, Ilya Afanasyev and Nikolaos Mavridis

Institute of Robotics, Innopolis University, Universitetskaya Str. 1, Innopolis, 420500, Russia

Keywords:

Gesture-based Control Interface, Glove System, Fuzzy C-means (FCM) Clustering, Arduino, V-REP Simula-

tor.

Abstract:

The paper presents an approach to building a gesture-based control interface with a wearable glove system

and a real-time gesture recognition algorithm. The glove-based system is a wireless wearable device with

hardware components, including Arduino Nano controller, IMU and ﬂex sensors, and software for gesture

recognition. Our gesture recognition methodology requires two stages: 1) Building a library of dynamic

gesture models with the reference human gesture graphs; 2) Gesture capturing and evaluating with fuzzy c-

means (FCM) clustering and constructing grammars of gestures by fuzzy membership functions. The system

tests were provided with 6 different dynamic gestures to control position and orientation of a quadcopter in V-

Rep simulator that has demonstrated encouraging results with a reasonable quality of real-time gesture-based

quadcopter control.

1 INTRODUCTION

The gesture-based control interface has a great po-

tential for more natural, intuitively understandable,

customizable and convenient human-machine inter-

action, which can extend capabilities of widespread

graphical and command line interfaces, which we

use nowadays with mouse and keyboard. There-

fore, development of advanced hardware and soft-

ware approaches to hand-gesture recognition is im-

portant for many 3D applications such as control of

computers and robots, interaction with the computer-

generated environment (virtual or augmented real-

ity), sign language understanding, gesture visualiza-

tion, games control, enhancement of communication

ability for disabled people, etc. Many recent studies

discuss various methods to solve gesture recognition

problem of certain gesture classes by computer vision

based systems (Suryanarayan et al., 2010; Suarez and

Murphy, 2012; Rautaray and Agrawal, 2015; Wachs

et al., 2011; Zabulis et al., 2009), wearable sensor-

based systems (Luzhnica et al., 2016; Park et al.,

2015) or even integrated systems, which simultane-

ous use both vision-based devices and wearable sen-

sors (Arkenbout et al., 2015; Mavridis et al., 2012).

The classiﬁcation of gesture classes depends on ges-

ture difﬁculties, applications and level of recognition

accuracy (e.g. surgical systems require higher accu-

racy than entertainment or communication applica-

tions) (Suarez and Murphy, 2012; Wachs et al., 2011).

Computer vision-based techniques are one of the most

frequently used approaches, which apply RGB cam-

era and image processing algorithms (Manresa et al.,

2005; Alﬁmtsev, 2008), Kinect sensors and depth

maps (Suryanarayan et al., 2010; Suarez and Mur-

phy, 2012; Ren et al., 2013; Dominio et al., 2014;

Afanasyev and De Cecco, 2013) and Time-of-Flight

(ToF) cameras (Gudhmundsson et al., 2010) for ges-

ture tracking and hand motion detection. Although

these solutions can be computationally expensive,

they may suffer from lack of robustness in cluttered

background or poor motion scenarios (e.g. by using

just a single gesture). Moreover, they often demon-

strate sensitivity to the environment, illumination con-

ditions, scene, background details and camera param-

eters (resolution, frame rate, distortion, auto-shutter

speed, etc.) that can affect recognition quality (Luzh-

nica et al., 2016; Wachs et al., 2011). Therefore, many

investigations focus also on wearable gesture recog-

nition systems with the ability to track dynamic ges-

tures for the complicated work environment in real-

time with reasonable computational cost and higher

accuracies (Kumar et al., 2012; Luzhnica et al., 2016;

Kenn et al., 2007; Battaglia et al., 2016). The overall

goal of hand gesture recognition is to ﬁnd similarity

between an unknown performed gesture (called rec-

ognizable model) and a known class of gestures (pat-

terns of gestures). Once the suitable hand gesture fea-

tures have been extracted and a gesture set has been

selected, gesture classiﬁcation can be accomplished

448

Berezhnoy, V., Popov, D., Afanasyev, I. and Mavridis, N.

The Hand-gesture-based Control Interface with Wearable Glove System.

DOI: 10.5220/0006909304480455

In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2018) - Volume 2, pages 448-455

ISBN: 978-989-758-321-6

by standard machine learning techniques or special-

purpose classiﬁers (Suarez and Murphy, 2012), which

are frequently based on Neural Networks (Gawande

and Chopde, 2013), Bayesian networks (Suk et al.,

2010), Hidden Markov Models (Bansal et al., 2011),

etc. The main drawback of these methods is high

computational complexity for forming gesture pat-

terns and recognizing dynamic gestures that may limit

their feasibility for real-time applications. Another

approach with an attractive algorithm of dynamic ges-

ture recognition based on fuzzy ﬁnite state automata

(for human’s wrist detection from video stream) was

proposed in (Devyatkov and Alﬁmtsev, 2007; Alﬁmt-

sev, 2008), and inspired the authors of this paper to

contribute and update this methodology for gesture

recognition with inertial IMU and ﬂex sensors built

in a wearable glove.

In this paper, we focus on the development of a

wearable gesture recognition system, which consists

of sensor-integrated glove hardware and hand gesture

recognition software for human control of computer-

based objects and machines (see, Fig. 1). Our ges-

ture recognition approach comes down to (1) tracking

the trajectories of hand movements along the coor-

dinate axes x(t), y(t) and z(t); (2) building a recog-

nizable model for the gesture G[x(t),y(t),z(t)], using

the tracked trajectories; (3) a comparison of the rec-

ognizable gesture model with the reference gesture

patterns E

[x(t), y(t),z(t)] by computing the similar-

ity function C[G, E

] to deﬁne a relation to the i-th

gesture class. These wearable glove system and hand-

gesture-based software were used for the creation of

control interface to manipulate a quadcopter model in

V-Rep simulator, demonstrating successful real-time

gesture-based control of the quadcopter position and

orientation with 6 different dynamic gestures.

The paper is organized as follows: Section 2

presents our wearable glove system for gesture recog-

nition, Section 3 formalizes the dynamic pattern con-

struction methodology, and Section 4 describes how

we use the FCM clustering algorithm to recognize a

gesture pattern. Finally, we test our approach to build-

ing a gesture-based control interface with the glove

system and a real-time gesture recognition algorithm

in Section 5 and conclude in Section 6.

2 DEVELOPMENT OF A

WEARABLE GLOVE SYSTEM

FOR GESTURE RECOGNITION

Numerous wearable glove-bases systems already ex-

ist (Dipietro et al., 2008). In our work, we have taken

into account existing techniques but utilized a novel

recognition approach.

In our system, to recognize an unknown gesture

the following information is required:

1) Pitch, roll and yaw hand rotations relative to the

surface;

2) Acceleration projections on each coordinate axis;

3) The numerical value of the bending for each ﬁnger.

The objectives 1 and 2 can be solved using the

integrated sensor MinIMU-9 v2, which consists of

an accelerometer, magnetometer, and gyroscope, and

measures projections to calculate pitch, roll and yaw.

The objective 3 is reached using the ﬂex sensors.

We organized gesture-based control interface with the

wearable glove-based system, using sensors’ connec-

tion to hardware with the Arduino Nano controller,

Bluetooth (BT) wireless data transmission and Java

application (see, a functional diagram in Fig. 1). The

software executes gesture evaluation with fuzzy c-

means (FCM) clustering algorithm (Bezdek et al.,

1984) and computation of a similarity function be-

tween recognizable gesture models and dynamical

reference gesture patterns from gestures’ library. This

glove-based system was tested by controlling an Un-

manned Aerial Vehicle (UAV) in V-Rep simulator.

The hardware components of the wearable glove sys-

tem are shown in Fig. 2.

3 CONSTRUCTION OF DYNAMIC

GESTURE PATTERNS

The method, which constructs dynamic gesture pat-

terns performed by a hand motion, consists of two

stages: 1) Capturing and tracking regions of interest

[x(t), y(t)], containing x(t) and y(t) trajectory pro-

jections of hand motion on the coordinate axes over

time; 2) Building a pattern E

[x(t), y(t)] and recog-

nizable gesture model G[x(t),y(t)], using the tracked

trajectories. When performing a gesture for recog-

nition, it is enough to execute it once. But for the

construction of the reference gesture models (classes)

the same gesture needs to be performed repeatedly.

The motion trajectories of each repeated gesture, of

course, are not the same. For example, each hand

motion trajectory (x(t),y(t)), drawing the letter "N",

will form a set of trajectories (x

(t),y

(t)) included in

certain boundaries at the n-fold repetition of gesture

j = 1, 2, ...,n, which are a gesture pattern E with own

characteristic features, as shown in Fig. 3.

The Stage 2 of our approach is related to the

methodology of dynamic gesture recognition based

on fuzzy ﬁnite state automata proposed by (Devy-

atkov and Alﬁmtsev, 2007). As far as this methodol-

The Hand-gesture-based Control Interface with Wearable Glove System

449

Figure 1: The functional diagram of wearable glove-system for gesture-based control of UAV.

Figure 2: The hardware components of the glove system.

ogy was published in Russian, let us describe the main

principles for the recognition of the gesture, drawing

the letter "N". The generalization of gesture patterns

E for different hand trajectories in the form of letter

"N" can be represented as a graph shown in Fig. 3.

According to this graph, vertex I includes a set of

points (coordinates) that belongs to the beginning of

the gesture, vertices II and III correspond to the points

Figure 3: The wearable glove system with the dynamic ges-

ture graph in the form of letter "N".

of the trajectory bending, vertex IV contains the end

points of the trajectory. It serves as a basis for pattern

gesture construction.

The ﬁrst task of gesture pattern construction

according to trajectories (x

(t),y

(t)) is an al-

gorithmic deﬁnition of movement trajectory points

),y

)) at time t

, which correspond to the

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

450

m-th vertex of the graph. To solve this task, we used

fuzzy c-means (FCM) clustering algorithm (Bezdek

et al., 1984; Nayak et al., 2015).

Let us remind the main deﬁnitions for c-means

clustering. The set of points for the motion trajectory

relative to one vertex is called a cluster. The num-

ber of measurement points is denoted as N. Each c-th

cluster includes a subset of the values of the charac-

teristic features of the vectors p

= [p

, p

,..., p

where k = 1, ..., N - is the total number of points, m

- number of features. For the considered gesture, m

= 4. The features of each k-th point are based on the

trajectory x(t) and y(t) at the corresponding time t











= x(t

dx(t)

t=t

= y(t

dy(t)

t=t

(1)

The clustering algorithm c-means is based on a

method for minimizing an objective function, which

should be created such way to: (1) Minimize a dis-

tance between a cluster’s point and the cluster center;

(2) Maximize a distance between clusters’ centers.

Although the approach of applying FCM cluster-

ing algorithm to gesture classiﬁcation is used long

ago (Li, 2003; Wachs et al., 2002), we used the cri-

terion known as the sum of squared errors within a

class, which uses the Euclidean norm to describe the

distance between vectors d

3 presented in (Devy-

atkov and Alﬁmtsev, 2007). This criterion is denoted

J(u, v), where u is a partition of all points in clusters,

and v is a vector of cluster centers, which corresponds

to the partition u. The formula of the criterion (the

objective function) would be the following:

J(u, v) =

∑

k=1

∑

i=1

(2)

where d

- is a measure in Euclidean n-dimensional

feature space between the k-th m-dimensional vector

and the i-th cluster center v

, which is calculated

by using the formula:

= |p

− v

| =



∑

k=1

k j

− v

i j

)



1/2

(3)

The coordinates of the cluster centers v

,...,v

} are calculated by the formula:

i j

∑

k=1

k j

∑

k=1

(4)

where u

- the characteristic function, A

- i-th cluster,

i = 1, 2, ...,C:



1, i f p

∈ A

0, i f p

/∈ A

(5)

Figure 4: Graph of the gesture in the form of letter "N".

It is required to ﬁnd the optimal partition u

∗

into

clusters with centers v

∗

, for which the objective func-

tion value is minimal:

J(u

∗

) = min

u,v

J(u, v)



u∈M

(6)

where M

- the set of all different partitions into C

clusters.

We use a strategy of c-means clustering algorithm,

which is known as iterative optimization that includes

the following steps (Devyatkov and Alﬁmtsev, 2007):

1. Fix the number of clusters C(2 < C < N) and se-

lect the primary partition for the set of trajectories

of points on the A

clusters. Then, perform the

following steps for r = 0, 1, 2, ...

2. Compute the centers v

(r)

of all clusters deﬁned by

partition u

(r)

3. Calculate the new features for all i and then k:

(r+1)







1, i f argmin



i=1,N

0, otherwise.

(7)

4. Build a new partition of u

(r+1)

5. If u

(r+1)

= u

(r)

then stop the process, considering

the partition of u

(r+1)

as optimal. Otherwise, sup-

pose r = r + 1 and go to the step 2.

This strategy (Devyatkov and Alﬁmtsev, 2007) al-

lows to determine models of all reference gestures,

which can be presented with graphs, where points of

trajectories (x

(t),y

(t)) can be assigned to each ver-

tex of the graph for dynamic gestures. It gives pattern

gestures, where graph vertices correspond to clusters

with their centers and edges relate to trajectory direc-

tion. The example of gesture graph, which has the

shape of letter ”N”, is shown in Fig. 4, where vertices

correspond to cluster A

and A

. The coordi-

nates of the cluster centers are shown on the axes.

The Hand-gesture-based Control Interface with Wearable Glove System

451

Figure 5: Gesture graph projections of the graph shown in

the Fig. 4.

4 GESTURE RECOGNITION

WITH FUZZY FINITE

AUTOMATA AND GRAMMARS

Gesture graph in Fig. 4 does not contain information

about the movement of the centers of clusters over

time. To consider gesture over time, a model of dy-

namic gestures based on fuzzy ﬁnite automata should

be build (Devyatkov and Alﬁmtsev, 2007). To do this,

according to the gesture graph shown in Fig. 4, two

graphs shown in Fig. 5 can be constructed. These

graphs are obtained by moving the projection trajec-

tories hands on time axis and the abscissa axis and

also on the ordinate axis and the time axis.

The basic principles of automation grammar gen-

eration for gesture recognition is well presented in

(Alﬁmtsev, 2008). Since it was published in Rus-

sian, let us describe the main statements. When

considering one sample of a gesture projections

(t), the sequence of n + 1 samples Y

] =

),y

),...,y

)} of i-th projection of

the same graph gesture for several consecutive

time points t

,...,t

(for the time interval [t

]))

is called a signal. The set of samples K(t) =

(t),y

(t),..,y

(t)}, where m - number of differ-

ent projections of the same gesture graph at time

t is called the reaction. The reaction sequence

K(t

),K(t

),...,K(t

), obtained by m projections of

same gesture for several consecutive moments of time

,...,t

(for a time interval [t

]) is called a

ﬂow of reactions. Each sample y

) of the same

signal corresponds the condition b

) of the ﬁnite

automaton M

. Then it can be introduced a func-

tion of outputs ϕ(b

)) = y

) and the function

of automaton transitions f (b

),t

i+1

) = b j(t

i+1

) for

a ﬁnite automaton M

. Thus, each sample is a

value of output function y

(t) = ϕ(b

(t)) of automa-

ton M

; each signal is a sequence of values of out-

put functions y

(t) = {y

),y

),...,y

)} of the

same automaton M

; each reaction is the set y(t) =

(t),...,y

(t)} values of output functions of differ-

ent automaton M

,...,M

, and reaction ﬂux is a

sequence of y(t

),y(t

),...,y(t

). Therefore, any au-

tomaton M

corresponding to a projection of a ges-

ture graph can be represented by its transition graph,

where each graph vertex is marked with the symbol

, each pair of adjacent vertices (b

i+1

), and edge

directed from vertex i to vertex i + 1 is marked with

the symbol t

in the alphabet T = {t

,...,t

m−1

If write down all edges, the result will conclude a

sequence of characters t

...t

m−1

Λ (where Λ is an

empty symbol, which may be omitted). This sequence

can be considered as a word or a sentence of the lan-

guage L = L(G), generated by an automaton grammar

G = {V, T,P,S = b

}, where V = {b

...b

m−1

}, T =

...t

m−1

Λ}, P = {b

→ t

, b

→ t

,... b

m−2

→

m−1

, b

m−1

→ t

, b

→ Λ }.

In the ideal case for gesture recognition a set of

automatons M

,...,M

can be constructed such

way that each automaton corresponds to one of the

distinct grammars. Then the language correspond-

ing to this automation could be unambiguously de-

tected by the automaton grammar. However, in re-

ality such an ideal situation is unattainable, because

the person can not perform every new gesture in ab-

solutely same way. Therefore, to cope with the uncer-

tainty that arises when performing gestures, we need

to move from deterministic to fuzzy automata. To do

this, we construct for each distinct grammar G the cor-

responding fuzzy grammar G

, based on the princi-

ples described in (Alﬁmtsev, 2008).

Each edge of the ﬁnite deterministic automaton

corresponds two incident vertices b

and b

i+1

with

the vertices’ coordinates [t

,ϕ(b

)) = y

)] and

i+1

,ϕ(b

i+1

)) = y

i+1

)] respectively. Follow-

ing (Alﬁmtsev, 2008), we will assume that the sam-

ples y

) of the same cluster corresponding to l dif-

ferent trajectories of the same gesture may vary within

the standard deviation of the projection from the clus-

ter center v

∑

l=1



) − v

)



, (8)

where N – number of samples belonging to the clus-

ter, v

– the coordinate of the center of the i-th cluster,

) – sample, belonging to i-th cluster. For sim-

plicity, assume that s

is the same for all i and equal

to s. For each set of samples y

) we set the trian-

gular membership function µ

(y), deﬁned by points

−

= v

− s, y

= v

, y

= v

+ s, where µ

−

) =

0,µ

) = 1 and µ

) = 0.

The vertex b

with coordinates (t

) is replaced

by set of vertex b

∈ B(b

) with coordinates, chang-

ing within the interval (y

−

= y

−s, y

= y

−s). Each

vertex b

corresponds to a speciﬁc coordinate, and

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

452

the set B(b

) is calculated as a set of vertices of all the

coordinates for which y

) > 0. Then, instead of ver-

tex b

i+1

with the coordinates (t

i+1

) we will have

a set of vertices b

r(i+1)

∈ B(b

i+1

) with coordinates,

changing within the interval (y

−

i+1

), and instead

of one edge t

i+1

(from vertex b

to vertex b

i+1

) we

will have a plurality of all edges {(b

r(i+1)

)|b

∈

B(b

),b

r(i+l)

∈ B(b

i+1

)} joining each vertex of the set

B(b

) to each vertex of the set B(b

i+1

More detailed description about how to generate

grammars for both ﬁnite deterministic automa-

ton and fuzzy ﬁnite automata for hand gesture

recognition is presented in (Alﬁmtsev, 2008).

Thus, two triangular membership functions: µ

(y)

and µ

i+1

(y) are deﬁned by triplets at the points

−

}and{y

−

i+1

} correspondingly.

Each of these functions is determined by the

following expression:

µ(y) =







y−y

−

−y

−

, i f y

−

≤ y ≤ y

−y

, i f y

< y ≤ y

(9)

where, k ∈ (i, i + 1). These functions deﬁne the mea-

sure of closeness to vertex coordinates to the "ideal

coordinates", which correspond to the value of the

membership function, equal to 1. It is assumed that

the membership function of each edge (b

r(i+1)

) of

incident vertices b

∈ B(b

) and b

r(i+l)

∈ B(b

i+1

) is

deﬁned as:

r(i+1)

)

i+1

) = min{µ

),µ

i+1

r(i+1)

)}. (10)

Fuzzy grammar G

obtained from the regular

grammar G (Alﬁmtsev, 2008). The set of the rules

for the fuzzy grammar G

will be the following:

= {b

→ t

i+1

r(i+1)

µ(t

i+1

r(i+1)

) = µ

r(i+1)

)

i = 0, ..., n − 1}.

(11)

According to (Alﬁmtsev, 2008), the grammar G

with rules {b

→ t

i+1

r(i+1)

, i = 0,...,n − 1} is com-

parable to the fuzzy grammar G

, if there is a se-

quence of fuzzy rules {µ

r(i+1)

)

, i = 0,...,n − 1},

which takes place b

= b

for all i = 0, ..., n − 1.

Thus, the dynamic gesture recognition algorithm,

which uses a model based on fuzzy ﬁnite automata

and the corresponding set of reference fuzzy gram-

mars G

,...,G

will contain the following

steps (Alﬁmtsev, 2008):

1. A gesture is treated with the same sampling

steps along the time axis as the reference ges-

tures, and with construction of a set of grammar

,...,G

Figure 6: Gestures to control a quadcopter in V-Rep simu-

lator: (a) move forward, (b) move backward, (c) move up,

(d) move down, (e) turn right, (f) turn left.

2. The grammars G

,...,G

correspond-

ing recognizable gesture with each correspond-

ing fuzzy reference grammar G

,...,G

where k ∈ {1, ..., K}, and K is a number of rec-

ognizable gestures, are compared.

3. For the sets of fuzzy reference grammars

,...,G

, where comparison was

successful, it is calculated the correspond-

ing set of values for membership functions

,µ

,...,µ

according to the

formula 10, and then the value of the measure

, which characterizes the similarity of the

recognizable gesture to the reference gestures k,

by the formula:

A(G,G

) = A

max{µ

,µ

,...,µ

(12)

4. The recognizable gesture is considered coincident

with the pattern gesture k, for which the measure

value A

was maximal. If there is no successful

comparison of grammars, then recognition of this

gesture fails (i.e. the gesture was not recognized).

The Hand-gesture-based Control Interface with Wearable Glove System

453

(a) The quadcopter in V-Rep environment.

(b) Control with a glove system (exp, ).

Figure 7: Experiments with hand-gesture control of the

quadcopter with the glove system in V-Rep simulator.

5 TESTS OF THE

HAND-GESTURE CONTROL

INTERFACE WITH THE

GLOVE SYSTEM

After glove-based system hardware and software im-

plementation, it was conducted experiments to un-

derstand the recognition ability. To test the system’s

recognition rate and demonstrate the advantages of

gesture-based control, we decided to provide exper-

iments to control UAV (in our case, the simulated

quadcopter, Fig. 7a) with this glove system. To con-

trol position and orientation of the quadcopter in V-

Rep simulator environment we selected 6 gestures

(Fig. 6): move forward and backward, move up and

down, turn left and right. The Fig. 7b shows an op-

erator at the moment of the quadcopter control by

the hand gestures during its ﬂight in a V-Rep maze.

The video with this experiment with the gesture con-

trol of the quadcopter with the wearable glove-based

system in V-Rep simulator is achievable on YouTube

(exp, ). Before the UAV ﬂight, the operator calibrates

the glove system, recording in software the main ges-

tures, which will be used for the control. By using

only a set of predeﬁned motions user could easily nav-

igate UAV through the V-Rep maze. But it should

be noticed that in this scenario the operator can only

control the desired drone navigation points, whereas

the built-in algorithms of V-Rep quadcopter control

ﬁnds an optimal way to reach them. The tests show

that the implemented wearable glove system for hand-

gesture-based control is intuitive, easily adjustable

and customizable through personal gesture library.

6 CONCLUSIONS AND FUTURE

WORK

In this paper, we present glove-based system hard-

ware and software implementation, which organize

the user-friendly hand-gesture-based control interface

based on fuzzy ﬁnite state automata gesture recogni-

tion methods. These wearable glove system (with in-

ertial IMU and ﬂex sensors) and gesture recognition

methodology were used to manipulate a quadcopter

model in V-Rep simulator, demonstrating successful

real-time gesture-based control of the quadcopter po-

sition and orientation with 6 different dynamic ges-

tures. This methodology is based on fuzzy c-means

(FCM) clustering algorithm with the sum of squared

errors measure criterion (Devyatkov and Alﬁmtsev,

2007), which minimizes a distance between a clus-

ter’s point and the cluster center, and maximizes a dis-

tance between clusters’ centers. These glove-based

system’ hardware and software can also be used in

various applications to create human-computer inter-

faces. The software solution can be of interest in the

situations, for instance in a teaching environment, to

check the correctness of gestures, in case where ges-

tures are many and the trajectory is important as much

as the ﬁnal position.

The methodology for gesture recognition based on

fuzzy ﬁnite automata and grammars has many advan-

tages and capabilities, for example: (1) Automatic

creation of a pattern gesture model for each dynamic

gesture. (2) Dynamic gesture model training with a

small training set (only a few examples). (3) Re-

liable recognition of dynamic gesture trajectories in

real-time, including occlusions and intersections. (4)

Computational efﬁciency for such models. Fuzzy

model has the computational complexity of O(mn),

where m - the number of fuzzy automata used for

recognition, the n - the maximum number of states

fuzzy ﬁnite automaton.

The future work may include extension of control

interface capabilities to manipulation of larger num-

ber of robots, additional testing with a real quadcopter

and comparison with alternative methods to clarify

the learning time, control accuracy, etc.

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

454

ACKNOWLEDGEMENTS

This research has been supported by the grant of Rus-

sian Ministry of Education and Science, agreement:

No14.606.21.0007, ID: RFMEFI60617X0007, "An-

droid Technics" company and Innopolis University.

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