The Neural Control of a Robot in the Conditions of Movable Obstacles
The proposed concept of robot control assisting uses a neural network, whose operation relies on the activation of neurons delimiting a path from the source to the target with evading movable obstacles The complexity of the control algorithm is O (n). The proposed adjustment of neuron sensitivity us...
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| Опубліковано в: : | Электронное моделирование |
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| Дата: | 2007 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут проблем моделювання в енергетиці ім. Г.Є. Пухова НАН України
2007
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| Цитувати: | The Neural Control of a Robot in the Conditions of Movable Obstacles / H. Piech, M. Spiewak // Электронное моделирование. — 2007. — Т. 29, № 4. — С. 105-112. — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859669970933252096 |
|---|---|
| author | Piech, H. Spiewak, M. |
| author_facet | Piech, H. Spiewak, M. |
| citation_txt | The Neural Control of a Robot in the Conditions of Movable Obstacles / H. Piech, M. Spiewak // Электронное моделирование. — 2007. — Т. 29, № 4. — С. 105-112. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Электронное моделирование |
| description | The proposed concept of robot control assisting uses a neural network, whose operation relies on the activation of neurons delimiting a path from the source to the target with evading movable obstacles The complexity of the control algorithm is O (n). The proposed adjustment of neuron sensitivity using a two-element pencils of planes passing over the shortest path of the robot makes it possible to obtain a set of solutions with simultaneous classification in terms of a very important path length criterion.
Предложена концепция сопровождения управления роботом с использованием нейронной сети, работа которой основана на активизации нейронов, определяющих путь от исходной точки до цели с уклонением от подвижных препятствий. Сложность алгоритма управления составляет О (n). Предложенная настройка нейронной чувствительности с использованием двухэлементных пучков плоскостей, пересекающих кратчайший путь робота, позволяет получить множество решений с одновременной классификацией по критерию длины пути.
Запропоновано концепцію супроводу управління роботом з використанням нейронної мережі, робота якої базується на активізації нейронів, що визначають шлях від вихідної точки до цілі з відхиленням від рухомих перешкод. Складність алгоритму управління складає On(). Запропоноване настроювання нейронної чутливості з використанням двоелементних пучків площин, що перетинають найкоротший шлях робота, дозволяє отримати велику кількість рішень з одночасною класифікацією за критерієм довжини шляху.
|
| first_indexed | 2025-11-30T12:42:17Z |
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| fulltext |
H. Piech*, M. Spiewak**,
* Institute of Mathematics and Computer Science,
Czestochowa University of Technology
** Institute of Machines Technology and Production Automation,
Czestochowa University
The Neural Control of a Robot
in the Conditions of Movable Obstacles
The proposed concept of robot control assisting uses a neural network, whose operation relies on
the activation of neurons delimiting a path from the source to the target with evading movable ob-
stacles The complexity of the control algorithm is O (n). The proposed adjustment of neuron sen-
sitivity using a two-element pencils of planes passing over the shortest path of the robot makes it
possible to obtain a set of solutions with simultaneous classification in terms of a very important
path length criterion.
Ïðåäëîæåíà êîíöåïöèÿ ñîïðîâîæäåíèÿ óïðàâëåíèÿ ðîáîòîì ñ èñïîëüçîâàíèåì íåéðîí-
íîé ñåòè, ðàáîòà êîòîðîé îñíîâàíà íà àêòèâèçàöèè íåéðîíîâ, îïðåäåëÿþùèõ ïóòü îò
èñõîäíîé òî÷êè äî öåëè ñ óêëîíåíèåì îò ïîäâèæíûõ ïðåïÿòñòâèé. Ñëîæíîñòü àëãîðèòìà
óïðàâëåíèÿ ñîñòàâëÿåò Î (n). Ïðåäëîæåííàÿ íàñòðîéêà íåéðîííîé ÷óâñòâèòåëüíîñòè ñ
èñïîëüçîâàíèåì äâóõýëåìåíòíûõ ïó÷êîâ ïëîñêîñòåé, ïåðåñåêàþùèõ êðàò÷àéøèé ïóòü
ðîáîòà, ïîçâîëÿåò ïîëó÷èòü ìíîæåñòâî ðåøåíèé ñ îäíîâðåìåííîé êëàññèôèêàöèåé ïî
êðèòåðèþ äëèíû ïóòè.
K e y w o r d s: robot control, neural networks, neuron activation thresholds.
The utilization of the neural structure for control is a unified control system en-
abling the dynamic and easy determination of weights and thresholds. The effec-
tiveness of using different methods of aggregation can be analyzed. The model
for establishing the values of weights and activation thresholds of aggregating
neurons relies on the position of the robot and the location of the line connecting
the robot’s starting and target points (Fig. 1).
The prediction obstacle position at the moment of robot approach enables
this situation to be allowed for in the threshold forming planes (Fig.2). The pur-
pose of the study is to examine the algorithmic possibilities of the realization of
the control model with the use of a neural structure of adjustable neuron
activation levels.
The mechanism of formation of neuron activation thresholds. The value
of neuron activation can be defined using two planes, S1, S2, which form a pencil
(have the common edge PK). The equations of the two planes (Fig. 3) can be de-
fined in an intercept form:
x
a
y
b
z
c
� � �1. The calculation of the values of a, b, c
ISSN 0204–3572. Ýëåêòðîí. ìîäåëèðîâàíèå. 2007. Ò. 29. ¹ 4 105
H. Piech, M. Spiewak
106 ISSN 0204–3572. Electronic Modeling. 2007. V. 29. ¹ 4
Start
Stop
t i j( , )
(xi, yj)
h
z
x
y
D
Fig. 1. Graphical illustration of the method of determining the neuron activation threshold t(i,j):
h—quantity controlling the activation threshold levels; D — area available for robot peregrination
Start
Stop
Thresholds and obstacles
z
x
y
D
Maximum
Fig. 2. Taking account of obstacle prediction in the formation of thresholds (maximum)
z
x
y (0, , 0)b
( , 0, 0)a
(0, 0, )c
Fig. 3. Plane in an intercept form
will be carried out in the simplest possible way by using the equation of the
straight line connecting the starting and the end points, P, K, of the robot’s route.
The equation of this straight line is written as follows:
y y P
y K y P
x K x P
x x P� �
�
�
�( )
( ) ( )
( ) ( )
( ( )).
The determination of the value of the coefficient a only requires the substitution
of the value of y = 0
a x P
x K x P
y K y P
y P� �
�
�
( )
( ) ( )
( ) ( )
( ) ,
(1)
whereas for the calculation of b, we substitute x = 0 to obtain:
b y P
y K y P
x K x P
x P� �
�
�
( )
( ) ( )
( ) ( )
( ) ,
while the value c = h. Ultimately, the intercept equation of the plane passing
through two points, P and K, will have the form of
x
x P
x K x P
y K y P
y P
y
y P
y K y P
x K x
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
�
�
�
�
�
�
� ( )
( )
P
x P
z
h
� �1.
So, to calculate the threshold value, we can use the following equation:
z h
xh
x P
x K x P
y K y P
y P
yh
y P
y K y P
� �
�
�
�
�
�
�
( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
x K x P
x P
( ) ( )
( )
�
,
where x = i�d, y = j�d, d is a grid size.
The Neural Control of a Robot in the Conditions of Movable Obstacles
ISSN 0204–3572. Ýëåêòðîí. ìîäåëèðîâàíèå. 2007. Ò. 29. ¹ 4 107
D
Shortest
robot path
lm
ln d
x
y
Stop
Start
Fig. 4. Graphical illustration of the location of neurons for the determination of their activation
thresholds: x = i·d, 1� �i ln; y = j·d; 1� �i lm ; ln is a number of neurons in a layer; lm is a num-
ber of layers
Relating the neuron location to the coordinates x and y is not complicated,
i.e. it is sufficient to perform some simple recalculations that are related to the
situation shown in Fig. 4.
The simulation of neural structure operation requires the methods of aggrega-
tion of signals coming to each neuron to be specified more precisely. These can be
the operations of summation of input signals or mini-max operations (Fig. 5).
Inter-layer communication. The number of neural network layers lm de-
termines the number of iterations of inter-layer transfers, which will be equal to
lm – 1. The algorithm for the operation of the neural structure can be represented
in the form of a block diagram, as in Fig. 6.
A l g o r i t h m d e s c r i p t i o n:
0. — data input: number of layers (lm); number of neuron in a layer (ln); in-
put signals (s(i)); beginning and end of the route (coordinates x, y), respectively;
parameter of neuron response sensitivity (h);
1. 2. 3. — determination of the values of neuron activation thresholds (z (i,j),
where i is the number of the layer, j is the number of the node. We use equation (2);
4. 5. 6. — determination of (or correction to) the values of weights, for ex-
ample depending on the velocity of approach of obstacles (the proposal will be
presented in the next section);
7. 8. 9. 10. 11. 12. 13. — simulation of neural network operation:
7. — transition to subsequent layers;
8. — location of the neuron sending signals (the k-th layer);
9. — location of the neuron receiving signals (the k + 1 layer);
10. — aggregation of signals (summation is chosen);,
11. — condition for the activation of the neuron of the coordinates j, k + 1;
12. 13. — result of neuron activation;
14. 15. — transfer of the signal to the subsequent layer.
The algorithm can be implemented in either a static (one-off transition: for-
ward-propagation) or a dynamic (change in the robot and obstacles position with
H. Piech, M. Spiewak
108 ISSN 0204–3572. Electronic Modeling. 2007. V. 29. ¹ 4
s w i1 (1, ) s w i1 (1, )
s w i2 (2, ) s w i2 (2, )
... max
sn w n i( , ) sn w n i( , )
.
.
.
.
.
.
Fig. 5. Selected types of aggregation that can be employed to the «neural simulation» of the ro-
bot working space
each «turnaround»: back-propagation) variant. The variant with turnarounds
will also require correction to the weights prior to each return. In the static vari-
ant, we will use the algorithm of the prediction of obstacle position at the time of
the robot approaching to the obstacle.
Determination of the values of weights in respect to the relative position
and velocity of motion of the obstacle in relation to the robot. The basis for
the determination of the threat resulting from the possibility of a collision is the
The Neural Control of a Robot in the Conditions of Movable Obstacles
ISSN 0204–3572. Ýëåêòðîí. ìîäåëèðîâàíèå. 2007. Ò. 29. ¹ 4 109
Start_neuron_rob
0. lm,ln,s(i) 1�i�ln,x(P),y(P),x(K),y(K),h
A Stop_neuron_rob
1. k=1(1)lm 7. k=1(1)lm ��
C
2. i=1(1)ln 8. i=1(1)ln 14. i=1(1)ln B
3. pr g z(i,j)o 9. j=1(1)ln 15. s(i)=b(i)
10. a(j,k+1)=a(j,k+1)+s(i) w(i,j)�
4. i=1(1)ln A
T N
11.a(j,k+1)>z(j,k+1)
5. j=1(1)ln 12. b(j)=1 13. b(j)=0
6. w(i,j) B
4. i=1(1)ln C
5. j=1(1)ln
6. w(i,j)
Fig. 6. Algorithm of the inter-layer communication of the neural network indicating the robot
path: k is a number of the layer from which the transferred signal originates; i is a number of the
neuron transferring signals; j is a number of the neuron receiving signals; a (j, k) is a size of the
aggregated signal in the neuron of the number j of the k-th layer
relativization of the situation existing between the robot and the obstacle con-
cerning their relative position and the rate of its change (Fig. 7).
The safe distance between the robot and the obstacle results from the satis-
fying of the following condition:
dist Or Op Rr Rp� � � �( , ) 0,
where (Or, Op) is a distance between the robot and obstacle centres
( ( ) ( ) )xOr xOp yOr yOp� � �
2 2
); Rr — maximum size of the robot, as counted
from its center; Rp — maximum size of the obstacle, as counted from its centre.
The velocity of obstacle and robot approach can be estimated as follows:
vpr vr vr d vp vp d� � � � � �cos ( ) cos ( ) ;
tg d yOr yOp xOr xOp( ) ( ) / ( ) � � � .
The reduction of the weights of signals coming to the neurons lying within the
hazardous zone (between the robot and the obstacle) can be accomplished by
presetting the number of reduction thresholds (on condition of satisfying the re-
lationship vrp � vp < 0: the robot and the obstacle approach each other);
H. Piech, M. Spiewak
110 ISSN 0204–3572. Electronic Modeling. 2007. V. 29. ¹ 4
vr
dist
d
vr vp
vp
Fig. 7. Relative position of the robot and the obstacle
Robot
Fig. 8. Corrections to robot and obstacles positions associated with the change in the direction of
propagation
w i j dist x xOr y yOr( , ) ( ) ( )� � � � �
2 2
)/dist, provide that vrp � vp < 0,
� � � � �w i j dist x xOr y yOr( , ) [ ( ) ( )
2 2
)/dist � wsk] � sck,
provided that vrp � vp < 0,
where
w i j( , ) is a stepwise reduced weight of signals coming to the neuron (i, j);
wsk is a number of weight reduction thresholds; sck is a weigh correction scale,
vrp/wsk.
The effects of individual obstacles superimpose multiplicatively:
cw i j w i jk
k
lp
( , ) ( , )�
�
�
1
,
where k— obstacle number; lp — number of obstacles. In the back-propagation
algorithm, after reaching the end of the robot route, a turnaround takes place (the
output signals from the last layer lk y K d� ( ( ) / )change the transfer direction and
become input signals, and the layer numbers change in the reverse order,
k lk lp� �( )1 , lp y P d� ( ( ) / )). Simultaneously with the velocity set for a single ro-
bot pass (through all important layers) we change the positions of the robot and
the obstacles after each propagation (Fig. 8).
Conclusions. The neural control of a robot allows any changes in the robot
movement environment to be taken into account flexibly and in a unified and
easy-to-accomplish manner.
The proposals concerning threshold levels and weight values should be
tested for each neural structure and the configuration of robot and obstacle
movement parameters.
The neural solutions enable the implementation of a large number of con-
cepts related to establishing the threshold and weight parameters. They reduce,
at the same time, the complexity of geometrical-kinetic analysis.
The neural algorithm in the proposed form can be combined with the ant al-
gorithm by setting the thresholds at levels allowing several solutions to be ob-
tained.
Çàïðîïîíîâàíî êîíöåïö³þ ñóïðîâîäó óïðàâë³ííÿ ðîáîòîì ç âèêîðèñòàííÿì íåéðîííî¿
ìåðåæ³, ðîáîòà ÿêî¿ áàçóºòüñÿ íà àêòèâ³çàö³¿ íåéðîí³â, ùî âèçíà÷àþòü øëÿõ â³ä âèõ³äíî¿
òî÷êè äî ö³ë³ ç â³äõèëåííÿì â³ä ðóõîìèõ ïåðåøêîä. Ñêëàäí³ñòü àëãîðèòìó óïðàâë³ííÿ
ñêëàäຠO n( ). Çàïðîïîíîâàíå íàñòðîþâàííÿ íåéðîííî¿ ÷óòëèâîñò³ ç âèêîðèñòàííÿì äâî-
åëåìåíòíèõ ïó÷ê³â ïëîùèí, ùî ïåðåòèíàþòü íàéêîðîòøèé øëÿõ ðîáîòà, äîçâîëÿº îòðè-
ìàòè âåëèêó ê³ëüê³ñòü ð³øåíü ç îäíî÷àñíîþ êëàñèô³êàö³ºþ çà êðèòåð³ºì äîâæèíè øëÿõó.
The Neural Control of a Robot in the Conditions of Movable Obstacles
ISSN 0204–3572. Ýëåêòðîí. ìîäåëèðîâàíèå. 2007. Ò. 29. ¹ 4 111
1. Cormen T. H. Wprowadzenie do algorytmow.— Warsaw: WNT, 1997.— 624 s.
2. Dudeba I. Metody i algorytmy planowania ruchu robotow mobilnych i manipulacyjnych. —
Warsaw: Akademicka Oficyna Wydawnicza, EXIT, 2001.—311 s.
3. Galicki M. Wybrane metody planowania optymalnych trajektorii robotow manipulacyjnych. —
Warsaw : WNT, 2000.—185 s.
4. Goldberg D. Algorytmy genetyczne. — Warsaw : WNT, 1995. — 342 s.
5. Gwiazda T. D. Algorytmy genetyczne. Zastosowania w finansach. — Warsaw: Wydawnictwo
Wyzszej Szkoly Predsiebiorczosci i Zarzadzania im. L. Kozminski, 1998.—126 s.
6. Jog P., Van Gucht D. Parallelisation of probabilistic sequential search algorithms//Genetic
algorithms and their applications. — 1987.— N1. — P.170 —176.
7. Koziel S., Michalewicz Z. Evolutionary algorithms, homomorphous mappings, and con-
strained parameter optimization// Evolutionary computation. — 1999. —¹.7 — P. 19—44.
8. Osowski St. Sieci neuronowe do przetwarzania informacji. — Warsaw: OWPW, 2000.—
365 s.
9. Osowski St. Sieci neuronowe w ujeciu neuronowym. — Warsaw: WNT, 1996. — 287 s.
10. Siemiatkowska B. Rastrowa reprezentacja otoczenia dla celow nawigacji autonomicznego
robota mobilnego. — Warsaw : IPPT PAN, 1997. — 69 s.
11. Syslo M., Deo N., Kowalik J. Algorytmy optymalizacji dyskretnej. — Warsaw : PWN,
1995. — 426 s.
12. Tadeusiewicz R. Sieci neuronowe. — Warsaw: Akademicka Oficyna Wydawnicza, 1993. —
356 s.
13. Wasserman P. D. Neural Computing. Theory and Practice. — N. Y. : Von Nonstrand
Reinhold, 1989. — 266 p.
14. Zadeh L. A. Rachunek ograniczen rozmytych. Projektowanie i systemy: Zagadnienia
metodologiczne. — Warsaw: Ossolineum, 1980. — 345 s.
15. Handbook of genetic algorithms. Red. Davis Lawrence. — N. Y. : Van Nostrand Reinhold,
1991.— 412 s.
Ïîñòóïèëà 12.03.07
H. Piech, M. Spiewak
112 ISSN 0204–3572. Electronic Modeling. 2007. V. 29. ¹ 4
|
| id | nasplib_isofts_kiev_ua-123456789-101790 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0204-3572 |
| language | English |
| last_indexed | 2025-11-30T12:42:17Z |
| publishDate | 2007 |
| publisher | Інститут проблем моделювання в енергетиці ім. Г.Є. Пухова НАН України |
| record_format | dspace |
| spelling | Piech, H. Spiewak, M. 2016-06-07T09:13:14Z 2016-06-07T09:13:14Z 2007 The Neural Control of a Robot in the Conditions of Movable Obstacles / H. Piech, M. Spiewak // Электронное моделирование. — 2007. — Т. 29, № 4. — С. 105-112. — Бібліогр.: 15 назв. — англ. 0204-3572 https://nasplib.isofts.kiev.ua/handle/123456789/101790 The proposed concept of robot control assisting uses a neural network, whose operation relies on the activation of neurons delimiting a path from the source to the target with evading movable obstacles The complexity of the control algorithm is O (n). The proposed adjustment of neuron sensitivity using a two-element pencils of planes passing over the shortest path of the robot makes it possible to obtain a set of solutions with simultaneous classification in terms of a very important path length criterion. Предложена концепция сопровождения управления роботом с использованием нейронной сети, работа которой основана на активизации нейронов, определяющих путь от исходной точки до цели с уклонением от подвижных препятствий. Сложность алгоритма управления составляет О (n). Предложенная настройка нейронной чувствительности с использованием двухэлементных пучков плоскостей, пересекающих кратчайший путь робота, позволяет получить множество решений с одновременной классификацией по критерию длины пути. Запропоновано концепцію супроводу управління роботом з використанням нейронної мережі, робота якої базується на активізації нейронів, що визначають шлях від вихідної точки до цілі з відхиленням від рухомих перешкод. Складність алгоритму управління складає On(). Запропоноване настроювання нейронної чутливості з використанням двоелементних пучків площин, що перетинають найкоротший шлях робота, дозволяє отримати велику кількість рішень з одночасною класифікацією за критерієм довжини шляху. en Інститут проблем моделювання в енергетиці ім. Г.Є. Пухова НАН України Электронное моделирование The Neural Control of a Robot in the Conditions of Movable Obstacles Нейронное управление роботом в условиях движущихся препятствий Article published earlier |
| spellingShingle | The Neural Control of a Robot in the Conditions of Movable Obstacles Piech, H. Spiewak, M. |
| title | The Neural Control of a Robot in the Conditions of Movable Obstacles |
| title_alt | Нейронное управление роботом в условиях движущихся препятствий |
| title_full | The Neural Control of a Robot in the Conditions of Movable Obstacles |
| title_fullStr | The Neural Control of a Robot in the Conditions of Movable Obstacles |
| title_full_unstemmed | The Neural Control of a Robot in the Conditions of Movable Obstacles |
| title_short | The Neural Control of a Robot in the Conditions of Movable Obstacles |
| title_sort | neural control of a robot in the conditions of movable obstacles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/101790 |
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