Synthesis of the Decentralized Control System for Robot-Manipulator with Input Saturations

IT in Industry, vol. 6, 2018 Published online 17-Feb-2018
Copyright © Eugenie, Evgeniy 2018 27 ISSN (Print): 2204-0595
ISSN (Online): 2203-1731
Synthesis of the Decentralized Control System for
Robot-Manipulator with Input Saturations
Eugenie L. Eremin
Information and Control Systems Department
Amur State University
Blagoveshchensk, Russia
Evgeniy A. Shelenok
Automation and System Engineering Department
Pacific National University
Khabarovsk, Russia
Abstract—It is discussed the problem of synthesis of the
decentralized adaptive-periodic control system for two degrees of
freedom robotic manipulator which have an input limitations.
The solution of the problem is based on the use of hyperstability
criterion, L-dissipativity conditions and dynamic filter-corrector.
Keywords—adaptive control; combined regulator; serial dynamic
corrector; hyperstability criterion; input saturation
INTRODUCTION
Control systems for robotic manipulators of various
purposes have a special place among the variety of modern
automatic system. The relevance of the design and
development problems of this class of the control systems is
due to a very wide application of robots-manipulators. These
devices are used in the metallurgical industry, aviation and
automotive industry, chemical manufacturing and other areas
[1 – 4]. As a rule, the role of the manipulators is to implement a
large number of cyclically repeating process steps and
problems of the development of robot control systems are to
ensure the high precision tracking of a given movement
trajectory. At that in practice the desired movement often has a
complicated shape, which is typical for automatic arc welding
of the complex compounds, laser or plasma cutting, gluing of
the various component products and other. From this point of
view manipulators control systems are assumed to be the class
of so-called periodic control systems From this point of view
manipulator control systems is assumed to be the class of so-
called periodic control systems, the construction of which is
expedient to use a specialized block –periodic signals generator
[5 – 10].
It should be note that the robotic manipulators as a control
plants are multidimensional (multiply connected) systems with
set of input and output signals (each input and output signal
corresponds to a single degree of freedom). In several articles
which devotes to the development of complicated multiply
connected dynamic plants control systems, it is proposed to use
the principle of the decentralized control [11 – 13]. This
approach lies in the partition of the original multi-dimensional
system into several independent or interrelated local
subsystems, and the stability analysis of each of them.
It is well known that the development of automatic control
systems is associate with a number difficulties. During the
operation of practically any control system some of the control
plant parameters are subject to change (for example, because of
wear of its components or the external influence: changes in
temperature, pressure and humidity. These parametric changes
could lead to reduce of the system performance. In this context,
the control algorithms development should always be carried
out considering the level (or the class) of a priori uncertainty of
the controlled plant. Moreover, in practice operation of the
control objects takes place in the conditions of the continuous
action external disturbances, which also must be considered in
order to reduce their negative impact on the functioning
process of the control system.
One more important peculiarity is what in almost all actual
systems there is a so-called input saturation, caused by the
necessity of limiting the actuators input signals levels. As
applied to the manipulation robots, the need to limit the input
signals arises in situations when manipulator links are moved
in a closed space and thus the amplitude of the control
moments must have the prescribed limits which exclude
undesirable robot elements displacement (for example, hitting
the manipulator of the constructs that are limit the scope of its
movement). It should be noted that taking account of the input
limitations when developing of the control systems is a very
important requirement, because in the systems which designed
without considering of the input saturation in some cases there
may be observed the deterioration in quality of their
functioning or even loss of working capacity [14].
One of the design techniques of control systems for
dynamic plants which operate in the conditions of a priori
uncertainty, an external perturbations and input saturation is
the use of adaptive regulators. By now it is known quite a wide
spectrum of adaptive control systems schemes which are
designed taking into account the input saturation [15 – 19]. In
particular, in [17 – 19] for single channel plants in the
assumption of complete measurement of the state vector and
the absence of external noise have been proposed a variety of
adaptive control schemes in the circuit with the reference
model. The obtained results allowed to achieve the
convergence of control error to zero, and boundedness of all
signals of the closed system. The main feature of the developed
control systems is the introduction of a special regulator switch
which is responsible for changing the adaptive coefficients
The work was supported by the Russian Foundation for Basic Research
(project 17-08-00871).

adjustment speed, whereby the input saturation is partically or
completely compensated. In [20] with the help of hyperstability
criterion and L-dissipativity conditions for the scalar plant with
the input saturation and the relative order greater than one has
been proposed a modification of the adaptive regulator, which
allowed to implement effective compensation of limitations on
the entry in a non-zero initial conditions, constant external
disturbances and unavailability of internal states. In the present
article by using the results of [7 – 10, 13, 20 – 24] we discussed
the possibility of using a combined regulator structure, as well
as proposed in [20] modified adaptive algorithms for the
construction of control system for two degrees of freedom
robot-manipulator with input saturation.
INITIAL DESCRIPTION OF THE CONTROL SYSTEM
The dynamics of the manipulator, which consist of n-links
and having an input saturation, according to [4], is described by
),()(),()( τSfqGqqqCqqM dis =+++ &&&& (1)
where q ∈ Rn
is the vector of coordinates (angular
displacement) of the robot links; τ ∈ Rn
is the input control
signal (vector of the control torques of each link);
nn
RqqC ×
∈),( & is the matrix describing the centrifugal and
Coriolis forces; n
RqG ∈)( is the vector determining the
influence of gravitational forces; n
dis Rf ∈ is the vector
external constantly operating bounded disturbances acting on
the manipulator links; S(τ) is the non-linear function of the
input signal saturation which describes as follows:





−<−
≤
>
=
,,
,||,
,,
)(
00
0
00
SS
S
SS
S
τ
ττ
τ
τ (2)
where S0 > 0 is the known constant corresponding to limit
level.
Let us consider more detail the dynamic properties of the
robot manipulator, which includes two degrees of freedom. In
accordance with [4] and equation (1) the dynamics of similar
object may be presented as follows
.
)(
)(
2,
1,
2
1
2
1
2221
1211
2
1
2221
1211
2
1






+





+





⋅





+
+





⋅





=





dis
dis
f
f
G
G
q
q
CC
CC
q
q
MM
MM
S
S
&
&
&&
&&
τ
τ
(3)
The elements of the inertia matrix and matrix of the
Coriolis forces have the form
);cos(
);cos()cos(
;0);sin(
);sin()();sin(
;);cos(
);cos();cos(2
2152
215141
2221321
22131222311
22223221
23212232111
qqgpG
qqgpqgpG
CqqpC
qqqpCqqpC
pMqppM
qppMqpppM
+=
++=
==
+−=−=
=+=
+=++=
&
&&&
(4)
where
.;;
;;
225122142123
2
2
2221
2
12
2
111
ccc
cc
lmplmlmpllmp
IlmpIlmlmp
=+==
+=++=
(5)
In equations (3) – (5) are introduced the following
notations: 2,1,,, =iqqq iii
&&& are the angular displacement,
velocity and acceleration of each link; mi is the mass of the first
and the second link of the manipulator [kg]; li is the length of
the i-th link [m]; Ii – the moment of inertia of each link
[kg·m2
]; lci is the distance from (i – 1)-th connection to the
center of mass of the i-th link [m].
We represent the a mathematical description of the system
in vector-matrix form, considering the manipulator, as a
multidimensional dynamic plant [13, 22], where each link of
the manipulator is assigned its own local subsystem.
Introducing the notations: τi = ui, qi = xi, ,ii xq && = ,ii xq &&&& = fdis,i
= fi, i = 1, 2; and performing a number of obvious mathematical
transformations we write the model (3) – c(5) in the state
space:
,2,1),()()(
,))(,()())(())(,(
)(
1
1
===
+++= ∑
=
itxtxLty
txtbtftuSbtxtA
dt
tdx
ii
T
i
k
j
ijiiiiii
i
λ
(6)
where T
i txtxtxtx iii
)](),(),([)( 321= is the state variables
vector of the local subsystems; Rtui ∈)( are the local control
signals; Rtyi ∈)( is the angular displacement of the robot
links (output of the i-th local subsystem); =))(,( txtA ii
))(()())(),(( 2211 txAtxtxtxA ii ii
+= is the nonlinear vector
function; ))(),(())(),(( 211211 txtxbAtxtxA T
iiii
α+= is the
matrix whose elements are the nonlinear functions; i
A1 is the
some stationary matrix; ))(())((2 txbtxA iiiii
β= is the some
nonlinear vector; ))(),(( 21 txtxT
iα и )( ii xβ are the vector and
scalar non-linear functions respectively; ))(,( txtijλ are the
nonlinear functions describing the dynamic interconnection of
the robot links; 3
)( Rtfi ∈ is the external permanent
disturbances vector, which satisfies the condition

.0,|)(|,
)(
0
0
)()( 003
3
3 >=≤










== constfftf
tf
tfbtf iii
i
ii
T
i
(7)
In accordance with (3) – (5) nonlinear functions that are
part of the model (6) and (7) have the form:
for the first degree of freedom
));(cos())((
));(cos(2))(),((
));(sin()())(),((
;0))(),((
;
))(),((
))(),((
))(),((
))(),((
1
21
221
1
1
1
1
1411
13213
113212
211
213
212
211
211
txgptx
txptxtx
txtxptxtx
txtx
txtx
txtx
txtx
txtx
=
=
=
=










=
β
α
α
α
α
α
α
α
& (8)
for the second degree of freedom
.0))((
;0))(),((;0))(),((
;0))(),((
;
))(),((
))(),((
))(),((
))(),((
22
213212
211
213
212
211
212
11
2
2
2
2
=
==
=










=
tx
txtxtxtx
txtx
txtx
txtx
txtx
txtxT
β
αα
α
α
α
α
α
(9)
the dynamic cross-connections
)).()(cos(
)()))(sin()((
)()))(cos(())(,(
));()(cos(
)()))(sin())()(((
)()))(cos(())(,(
21
121
12
21
2221
22
115
2123
313221
115
21223
313212
txtxgp
txtxtxp
txtxpptxt
txtxgp
txtxtxtxp
txtxpptxt
++
++
++=
++
++−
−+=
λ
λ
(10)
To specify the required movement of the robot links,
similar to [20], we use the local reference models with two
outputs:
,2,1),()(),()(
),()(
)(
1 ===
+=
itxgtztxty
trBtxA
dt
tdx
iiii
iii
i
M
T
iMMM
iMMM
M
(11)
where T
MMMM iiii
xxxtx ],,[)( 321= is the state vector of the
local reference models; ,],0,0[ 3
T
MM ii
bB = ;03 >= constb iM
RTtrtr ii ∈+= )()( is the scalar periodic command signal;
,)( Rty iM ∈ Rtz iM ∈)( are the main and auxiliary outputs of
the reference model; gi is the given vector;
)( T
MMiM iii
cBAA −= is the Hurwitz matrix in the Frobenius
form; ],,[ 210 iiii MMMM cccc = is the vector with given
numbers.
The regulator structure we will be given as the following
adaptive-periodic combination
;2,1),()()()( =−= itxtctktu i
T
iiii θ (12)
where ki = const > 0; θi(t) is the periodic signals generator
output (regulator periodic setting); ci(t) is the vector of self-
tuning coefficients (regulator adaptive setting).
THE PROBLEM STATEMENT
For multidimensional dynamic plant (3) – (10) with using
the reference model (11) it is necessary to synthesize the
explicit form of the self-tuning algorithms for vector of
bootstrapping coefficients ci(t), providing for any initial
condition x(0) and any changes of the functions αi(x1(t),x2(t)),
λij(t,x(t)) an implementation of limit target conditions
,0,||)(||lim 00 >=≤
∞→
constcctc iii
t
(13)
.2,1,0,|)()(|lim 00 =>=≤−
∞→
iconstyytyty iiiM
t i
(14)
where ,0ic iy0 are sufficiently small numbers.
SOLUTION METHOD, ALGORITHMS OF THE CONTROL LOOP
AND L-DISSIPATIVITY CONDITIONS OF THE CONTROL SYSTEM
To solve this problem we use the same method proposed in
[20, 21], namely:
Under the assumption of the availability of all state
variables xi(t) using hyperstability criterion we will
determine the explicit form of the self-tuning
algorithms for coefficients θi(t) and ci(t) of the
combined regulator (12).
For the technical implementation of synthesized at the
previous step control algorithms, we will introduce in
each subsystem filter-corrector to obtain estimates of
the state vectors xi(t) and define the specific conditions
to ensure the operability and L-dissipativity of the
developed system.
According to [7 – 10, 20], in the case of availability of the
internal states of local subsystems (6) – (10) by using the
hyperstability criterion we can show that the synthesis of the
regulator (12) algorithms in the form
,0
],0;[,0)(),()()(
>=
−∈=+−=
constT
TsstvTtt
i
iiiii θθθ
(15)

.2,1;3,2,1;0)0(,0
,|)(|,0
,|)(|),(
~
)()()(
===>=




≤∀
>∀−
=
ikcconsth
tv
tvttvtxh
dt
tdc
ii
iii
kk
ii
iiiikkk
φ
φδ
(16)
where )()()( tztztv iMi i
−= are the mismatch signals of the
auxiliary outputs of the local reference models (11) and the
control plant subsystems (6) – (10) formed by using the
vectors gi; 0>= constiφ are values of the dead zones; )(
~
tiδ
are outputs of the local dynamic switches
,10
,0)()]())(([,
,0)()]())(([,1
)(
,0),()(
~)(
~
0
0
<=<




<−∀
≥−∀
=
>==+
const
tvtutuS
tvtutuS
t
constdtt
dt
td
d
i
i iii
iii
i
iii
i
i
δ
δ
δ
δδ
δ
(17)
will ensure the hyperstability and adaptability of the system
(6) – (12), (15) – (17) and perform for it the targets (13), (14).
Since local variables of the dynamic plant (6) – (10) is not
available for measuring we connected to the output of each
local subsystem a filter-corrector, which is described by
equations
;
)1(
)(
)det(
)(
)(
)(
)(
);()()(
),()(
)(
2
+
=
=+
−
−
==
+=
+=
+
sT
sg
D
AsE
BAsEg
sy
sz
sW
tyDtxgtz
tyBtxA
dt
tdx
i
i
F
Fi
FFi
T
F
i
F
F
FF
T
FF
iFFF
F
i
i
iiii
i
iiii
iii
i
(18)
where Rtz iF ∈)( and T
FFF txtxtx iii
)](),([)( 21= are the scalar
outputs and filters state vectors respectively; Ti are the small
time constants; )(sW iF are filter transfer functions; s is the
complex variable.
In this case, we can show [20, 21] that, when considering a
certain steady state of the multiply connected system (6) –
(12), (15) – (18) local contours while setting the value of the
parameter Ti, based on the conditions
;
2
465.0
;
93.0
2
1
2
1
1
i
i
i M
M
i
M
i
c
c
TT
c
TT =<=<
it is possible to ensure L-dissipativity of the system, which
losing a hyperstability will retain operability and adaptability
in a given class. Herewith the local adaptive regulators are
transformed to the form
;2,1),()()()( =−= itxtctktu iF
T
iiii θ (19)
,0
],0;[,0)(),(~)()(
>=
−∈=+−=
constT
TsstvTtt
i
iiiii θθθ
(20)
);()())()(()(~
;2,1;3,2,1;0)0(,0
,|)(~|,0
,|)(~|),(
~
)(~)()(
tztztxtxgtv
ikcconsth
tv
tvttvtxh
dt
tdc
iiii
ii
iii
FMFM
T
ii
kk
ii
iiiikkk
−=−=
===>=




≤∀
>∀−
=
φ
φδ
(21)
where T
FFFF iiii
xxxtx ],,[)( 221
&= are estimates of the local
subsystems (6) state variables.
COMPUTATIONAL EXPERIMENT
Let us consider control problem of the two degrees of
freedom manipulator with input saturations and dynamics,
which describes by equations
.
)(
)(
2,
1,
2
1
2
1
2221
1211
2
1
2221
1211
2
1






+





+





⋅





+
+





⋅





=





dis
dis
f
f
G
G
q
q
CC
CC
q
q
MM
MM
S
S
&
&
&&
&&
τ
τ
(22)
);cos(
);cos()cos(
;0);sin(
);sin()();sin(
;);cos(
);cos();cos(2
2152
215141
2221321
22131222311
22223221
23212232111
qqgpG
qqgpqgpG
CqqpC
qqqpCqqpC
pMqppM
qppMqpppM
+=
++=
==
+−=−=
=+=
+=++=
&
&&&
(23)
.;;
;;
225122142123
2
2
2221
2
12
2
111
ccc
cc
lmplmlmpllmp
IlmpIlmlmp
=+==
+=++=
(24)
where 2,1,,, =iqqq iii
&&& are the angular displacement, velocity
and acceleration of each link; mi is the mass of the first and the
second link of the manipulator [kg]; li is the length of the i-th
link [m]; Ii – the moment of inertia of each link [kg·m2
]; lci is
the distance from (i – 1)-th connection to the center of mass of
the i-th link [m].
For the experiment we take the robot parameters as follows:
m1 = 1.2 kg; m2 = 0.8 kg; l1 = 0.35 m; l2 = 0.31 m; I1 =
= 61.25·10-3
kg·m2
; I2 = 20.42·10-3
kg·m2
.
External disturbances acting on the considered control
plant are described as follows:
( )
.2,1
,)3sin(3)2sin(2)sin(1.0)(3
=
++⋅=
i
ttttf i
πππ

To the outputs of local subsystems we connect the filter
correctors
;0)0()0();(25.0)()()(
);(10)(2000)(10)(
);()(
21221
6
21
6
2
21
==++=
+−−=
=
iiiiii
iii
ii
FFFFFF
iFFF
FF
xxtxtxtxtz
tytxtxtx
txtx
&
&
&
and their desired dynamics and the dynamics of the
decentralized system local main circuits we specify by explicit
etalons
).sin(25.1)(;0)0()0()0(
);(25.0)()()(),()(
);(86)(12)(8)(
);()(
);()(
321
3211
3213
32
21
ttrxxx
txtxtxtztxty
trxtxtxtx
txtx
txtx
iMMM
MMMMMM
iMMMM
MM
MM
iii
iiiiii
iiii
ii
i
====
++==
+−−−=
=
=
&
&
&
During the simulation input constraints of the robot links
actuators were set with the values 1.710 =S and .520 =S
Parameters of the combined control circuit (9) – (12) in order
to increase system performance were selected as follows:
.5.2;2
;5;0006.0;5;0007.0
;001.0;10;500;750;1000
;001.0;1;20;100;300
21
2010
23212
13211
21
222
111
==
====
=====
=====
TT
dd
hhhk
hhhk
δδ
φ
φ
(25)
In Fig. 1 – 3 are presented the results of system operation
when the initial positions of the manipulator links are y1(0) =
= -1.2 and y2(0) = 1.2.
Fig. 1. Position tracking.
Fig. 2. Tracking errors of the control system.
Fig. 3. System control signals.
Presented results are indicate a sufficiently good quality of
functioning of the developed system.
CONCLUSION
It is presented the solution of the control problem of a robot
manipulator with two degrees of freedom with input saturation.
By using the hyperstability criterion, L-dissipativity conditions
and dynamic filter-corrector it is constructed the decentralized
control system with combined adaptive-periodic local control
circuits.
REFERENCES
[1] Spong M.W., Thorp J.S., Kleinwaks J.M. The Control of Robot
Manipulators with Bounded Input // IEEE Transactions on Automatic
Control, 1986, Vol. AC-31, No. 6, pp. 483-490.
[2] Purwar S., Kar I.N., Jha A.N. Adaptive Control of Robot Manipulators
Using Fuzzy Logic Systems Under Actuator Constraints // Fuzzy Sets
and Systems, 2005, No. 152, pp. 651-664.
[3] Dixon W.E., De Queiroz M.S., Zhang F., Dawson D.M. Tracking
Control of Robot Manipulators with Bounded Torque Inputs //
Robotica,1999, Vol. 17, pp. 121-129.

[4] He W., Xiao S., Yu S. Learning Control for a Robotic Manipulator with
Input Saturation // 3rd IFAC International Conference on Intelligent
Control and Automation Science, 2013, Chengdu, China, pp. 74-79.
[5] Zaks V.S. Ob odnoy vozmozhnosti povysheniya tochnosti
regulirovaniya v sledyashchikh sistemakh tsiklicheskogo deystviya //
Avtomatika i telemekhanika, 1981, №1, pp. 170 – 174.
[6] Shinji Hara, Yutaka Yamamoto, Tohru Omara, Micho Nakato.
Repetitive Control System: A New Type Servo System for Periodic
Exogenous Signals // IEEE Transactions on automatic control, 1988,
Vol. 33, №7, pp. 659 – 668.
[7] Eremin E.L., Telichenko D.A., SHelenok E.A. Kombinirovannye
algoritmy sistemy robastno-periodicheskogo upravleniya nelineynym
ob"ektom s zapazdyvaniem // Informatika i sistemy upravleniya, 2009,
№ 3(21), pp. 125-135.
[8] Eremin E.L., Lelyanov B.N., SHelenok E.A. Sistema kombinirovannogo
adaptivnogo upravleniya mnogorezhimnym nelineynym dinamicheskim
ob"ektom periodicheskogo deystviya // Informatika i sistemy
upravleniya, 2015, № 4(46), pp. 125-135.
[9] Eremin, E.L., Shelenok, E.A. Adaptive periodic servo-system for
nonlinear control-affine objects // Optoelectronics, Instrumentation and
Data Processing, 2015, No. 51(5), pp. 523-529.
[10] Eremin, E.L., Shelenok, E.A. Adaptive-periodic control for nonlinear
dynamic object with delays on state set of functioning // 2016
International Siberian Conference on Control and Communications,
SIBCON 2016, Proceedings, Moscow, 2016.
[11] Ortega R., Herrera A. A solution to the decentralized adaptive
stabilization problem // Syst. Contr. Letters, 1993, No. 2, pp. 299-306.
[12] Jain S. Khorrami F. Decentralized adaptive control of a class of Large-
Scale interconnected nonlinear systems // IEEE Trans. Aut. Contr, 1997,
V. 42, No. 2, pp. 1618- 1624.
[13] Telichenko D.A. Gibridnaya adaptivnaya sistema s etalonnym
upreditelem v skhemakh detsentralizovannogo upravleniya s
zapazdyvaniem // Informatika i sistemy upravleniya, 2006, № 1(11), pp.
212-223.
[14] Andrievskiy B.R., Kuznetsov N.V., Leonov G.A. Skrytye kolebaniya i
vozbuzhdenie integratora pri nasyshchenii v konture upravleniya
letal'nykh apparatov // Trudy XII Vse-rossiyskogo soveshchaniya po
problemam upravleniya. (E'lektronnyy resurs), M.: IPU RAN, 2014, pp.
482-990. (CD-ROM).
[15] Monopoli R.V. Adaptive control for system with hard saturation // Proc.
of IEEE 14th Conf. on Decision and Control, 1975, pp. 841-842.
[16] Yang B-J., Calise A.J., Craig, J.I. Adaptive output feedback control with
input saturation // Proc. of 2003 American Control Conference, 2003,
pp. 1572-1577.
[17] Takagi N., Nishida T., Kobayashi T. A Design of Adaptive Control
Systems with Input Saturation // SICE-ICASE International Joint
Conference, 2006, pp. 984-987.
[18] Takagi N., Oya M., Wang Q., Kobayashi T. Adaptive control scheme
achieving smooth control input in the presence of input saturation // Int.
J. Advanced Mechatronic Systems, 2010, Vol. 2, No. 4, pp. 225-235.
[19] Takagi N., Sato K., Oya M. A modified adaptive control scheme in the
presence of input saturation // Int. J. Advanced Mechatronic Systems,
2011, Vol. 3, No. 3, pp. 168-180.
[20] Eremin E.L. Modifikatsiya adaptivnoy sistemy dlya upravleniya
odnokanal'nym ob"ektom s vkhodnym nasyshcheniem // Informatika i
sistemy upravleniya, 2016, №3(49), pp. 119-131.
[21] Eremin E.L. L-dissipativnost' giperustoychivoy sistemy upravleniya pri
strukturnom vozmushchenii. IV // Informatika i sistemy upravleniya,
2013, №2(36), pp. 100-106.
[22] Eremin E.L., Telichenko D.A., SHelenok E.A. TSiklicheskiy rezhim v
sisteme robastnogo upravleniya manipulyatorom Barretta // Vestnik
Tikhookeanskogo gosudarstvennogo universiteta, 2010, № 3(18), pp. 23
– 32.
[23] Eremin E.L., Chepak L.V., Shelenok E.A. Combined Adaptive Control
System for Nonlinear Periodic Action Plant // 2015 International
Siberian Conference on Control and Communications, SIBCON 2015,
Proceedings, Omsk, 2015.
[24] Eremin E.L., Shelenok E.A. Digital algorithms of the cycle operation
manipulator control system // First Russia and Pacific Conference on
Computer Technology and Applications (Russia Pacific Computer –
2010) 6 – 9 September, 2010 Russian Academy of Sciences, Far Eastern
Branch, Vladivostok, 2010, pp. 306 – 310.

Synthesis of the Decentralized Control System for Robot-Manipulator with Input Saturations

More Related Content

What's hot (19)

Similar to Synthesis of the Decentralized Control System for Robot-Manipulator with Input Saturations (20)

More from ITIIIndustries (20)

Recently uploaded (20)

Synthesis of the Decentralized Control System for Robot-Manipulator with Input Saturations