Hybrid Control Approach to Multi-AUV System in a Surveillance Mission

IT in Industry, vol. 6, 2018 Published online 09-Feb-2018
Copyright © Bychkov, Davydov, Nagul, 20 ISSN (Print): 2204-0595
Ul’yanov 2018 ISSN (Online): 2203-1731
Hybrid Control Approach to Multi-AUV System
in a Surveillance Mission
Bychkov Igor, Davydov Artem, Nagul Nadezhda, and Ul’yanov Sergey
Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Science,
Irkutsk, Russia
Abstract—Surveillance missions for multiple autonomous
underwater vehicle (AUV) system suggest the use of different
modes of operation including organizing and keeping a
predefined formation, avoiding obstacles, reaching static and
tracking dynamic targets. While exploiting a leader-follower
strategy to formation control and the vector Lyapunov function
method to controller design, we use discrete-event approach and
supervisory control theory to switch between operational modes.
Keywords—underwater vehicle; formation control; vector
Lyapunov function; discrete-event system
I. INTRODUCTION
Nowadays autonomous underwater vehicles (AUV) have
become the main tool for environmental monitoring of water
space, seafloor mapping, and surveillance, or scanning,
operations. It is traditional for scanning missions that a human
operator generates a lawn-mowing pattern that covers an area
under survey and AUV moves along the generated path at a
constant altitude making forth and back movements as if it is
mowing a lawn. The pattern is represented as a sequence of
waypoints or as a smooth curve passing through them.
The application of coordinated groups (formations) in
underwater works may significantly decrease mission duration
and improve the operational reliability and robustness against
unexpected events. However, the behavior of multi-AUV
system is much more complicated and includes the number of
elementary behaviors, or modes of operations. The following
modes can be distinguished for surveillance missions:
formation-keeping mode, formation-gathering mode, obstacle
avoidance mode. In the formation-keeping mode AUVs try to
maintain a desired configuration as accurately as possible. The
formation-gathering mode is switched on when AUVs are
comparatively far from each other and it is necessary to bring
them together to start or continue survey in formation, and
also when there is a need to change the formation structure,
for example, after bypassing obstacles or reaching the border
of the survey area, in order to continue the execution of the
surveillance mission more efficiently. AUV activates the
obstacle avoidance mode if it encounters an obstacle during
the motion. The first two modes determine collective behavior
of the group and they are initiated by the leader AUV while
the obstacle avoidance mode is activated independently by
each AUV.
When implementing the elementary behaviors of AUVs,
the following basic problems arise: path generation problem
[1] including real-time path correction [2], path-following
problem [3], [4], and formation control problem [5], [6]. In
this paper, on the basis of a 6-DOF nonlinear dynamic model
of AUV, we design a path-following controller based on the
conception of virtual target [3] moving along the path to be
followed and a formation-keeping controller based on the
leader-follower approach [7], [8]. The design of controllers is
performed with the use of the numerical technology for
analysis and synthesis of nonlinear control systems based on
the reduction method [9] and sublinear vector Lyapunov
functions [10]. Unlike most of the control design methods
exploited in references, this technique allows one to build
more practical sampled-data controllers taking into account
uncertainties of the AUV’s parameters, measurement errors,
and constraints on the control actions (control force and
torque). The designed controllers form the low level of the
designed hybrid control system.
As far as continuous dynamics of the leader and follower
AUVs defines their predefined modes of movement, switching
between different modes of operation may be described in
terms of a discrete-event model. Widely used, discrete-event
systems (DES) represent systems evolution by considering the
occurrence of some event sequences. Supervisory control
theory (SCT), developed in 1980s to regulate DES behavior,
nowadays becomes powerful instrument in many real life
applications including robotics. Recent implementations in
this area concern single robot [11], robot groups [12], [13] and
robots formation control [14], swarm robotics [15], [16], robot
fights [17], etc. However, most of the listed works employ the
simplest supervisors constructed on the base of the finite-state
automaton model of a system to be controlled, by eliminating
unwanted transitions. A popular way of supervisory control
design consists in constructing automatons for turning on and
off elementary behaviors, building parallel composition of
these automatons and analyzing states of the resulting
automaton, which represent all possible combinations of
elementary behaviors. Transitions that lead to undesired
combinations are the subject of disablement by a supervisor.
Being rather effective, this approach only partly use the results
of SCT, developed in the first place to deal with formal
languages describing a system behavior and constraints on it.
Important properties of DES, such as controllability of a
specification language and non-blockness of a supervisor, are
not usually discussed, as well as specifications are often not
explicitly defined. We propose a discrete-event model for the
leader AUV operational modes switching as a reaction on
environment changes, previous and current modes, and
designa supervisor providing language-based specification on
an AUVs formation movement.

Fig. 1. Reference frames
The rest of the paper is organized as follows. Section II
explains the development of low level controllers for AUVs.
DES-based top level control algorithms are designed in
Section III. Section IV provides simulation results for the
designed hybrid control system. Section V contains the
conclusions and explanations of future work.
II. LOW LEVEL CONTROL ALGORITHMS
A. AUV model
In this paper we use the dynamic model of an AUV
borrowed from [3]. The kinematic and dynamics equations of
the vehicle can be defined using a global coordinate frame
{ }U and a body-fixed coordinate frame { }B (Fig. 1).
The kinematic equation of the AUV can be written
= cos( ) sin( ),
= sin( ) cos( ),
= ,
B B
B B
B
x u v
y u v
r
ψ ψ
ψ ψ
ψ
−
+
&
&
&
(1)
where x , y are the coordinates of the center of mass of the
vehicle, Bψ denotes the yaw angle, u and v are the surge and
sway velocities expressed in { }B , respectively, and r is the
angular yaw rate.
Neglecting the equations in heave, roll and pitch, the
equations for surge, sway and yaw can be presented as
= ,
0 = ,
= ,
u u
v ur v
r r
m u d
m v m ur d
m r d
+
+ +
+
&
&
&
F
G
(2)
where = ,u um m X− &
2 2
= ,u uu vvd X u X v− − = ,v vm m Y− &
| |= | |,v v v vd Y uv Y v v− − = ,r z rm I N− & | | ,r v v v rd N uv N N ur− − −
= ,ur rm m Y− m is the mass of the AUV, zI is the moment of
inertia around AUV’s vertical axis, { }X ⋅ , { }Y⋅ , { }N ⋅ are
classical hydrodynamic derivatives, and [ ]T
F G is the vector
of force and torque applied to AUV.
B. Path-following controller
To design path-following controller for a AUV, the
conception of virtual target is exploited. Define the virtual
target as a point P that moves along the path to be followed
by the AUV. Associated with P , consider the corresponding
Serret-Frenet frame { }F (see Fig. 1). As shown in [3], the
dynamics of the virtual target in { }F can be described by
1 1
1 1
= cos ,
= sin ,
= ,
t a F
t F
F
s v s y
y v s
r
ψ ψ
ψ ψ
ψ β ψ
− +
−
+ −
&& &
&&
&& &
where 1s , 1y are the coordinates of the vehicle in { }F , s is
the signed curvilinear abscissa of P along the path,
= arctan( / )v uβ is the side-slip angle, 2 2 1/2
= ( )tv u v+ is the
absolute value of the total velocity vector; Fψ is an angle that
defines the orientation of F with respect to U
( = ( )F c a ac s sψ& & ), cc is the path curvature, B Fψ ψ β ψ+ −@ .
We suppose that the virtual target moves along the path with a
desired speed du and there is a restriction on the curvature of
the path ( | |c cc c≤ ).
The path-following control problem can be formulated as
follows. Given the AUV model (1) and a path to be followed,
derive control laws for the force F and torque G that
minimize the steady-state errors in variables 1y , 1s , and ψ .
To solve the problem, the sampled-data control law is
proposed as:
1
1 1 2
3 1 4 5
( ) = , ( ) = , [ , ),
ˆ
= , = ( ),
ˆ ˆ= sat( , ),
ˆˆ ˆ= sat( , ),
c s c s k k k
c u c r r c a c a
ss k k
ss k k k
t t t T t t
d d m c s c s
k s k u
k y k k r
β
ψ
++ + ∈ ≡
+ + −
+ ∆
+ + ∆
&&& & &&
F F F G G G
F G
F F
G G
(4)
where =kt kh , = 0,1,2k K , h is the control step; cF , cG are
feedforward control terms aimed to cancel terms ud , rd in
equations (2) and terms c ac s& & , c ac s&& , β&& in the equation for
variable Fr r β ψ∆ + −& &@ ; ˆ
β&& is an estimate of acceleration β&&
obtained using the dynamic model of the AUV (see [3] for
details), =F c a c ac s c sψ +&& & & && ; sF , sG are feedback control terms,
sF , sG are the shares of maximum control force and torque
reserved for stabilization, 1
ˆ ks , 1
ˆ ky , ˆkψ , ˆku∆ , ˆkr∆ are
measurements of variables 1s , 1y , ψ , du u u∆ −@ , r∆
sampled at time moment kt with some additive bounded

errors; sat( , ) = sign( )min(| |, )σ σ σ σ σ is the saturation
function; ik are feedback coefficients ( = 1,5i ).
C. Formation controller
Formation control algorithm employed in the scanning
mode is based on the leader-follower approach which suggests
that each vehicle as a follower tries to maintain a desired
position with respect to its leader.
Assume that each AUV is equipped with sensors capable
of measuring the relative distance 2 2
= ( ) ( )l f l fs x x y y− + −
and the bearing angle = arctan
f l
Wf
f l
y y
x x
θ ψ
−
−
−
1
. Dynamics of
the leader-follower pair in terms of these variables can be
described by
= cos( ) cos ,
= sin sin( ).
tl Wl Wf tf
f tf tl Wl Wf
s v v
s s v v
ψ ψ θ θ
θ ω θ ψ ψ θ
− + −
+ − − +
&
&
Let a desired relative position of a follower AUV be
defined by constants s∗
and θ∗
. To achieve posture
stabilization for the follower AUV, we use the following
control law:
1 2 3 4
( ) = , ( ) = , ,
ˆˆ= sat( , ), = sat( , ),
s u s r k
s ss k k s k k
t d t d t T
k s k z k k zθ
θ
+ + ∈
∆ + ∆ +
F F G G
F F G G
(4) (5)
where ˆks∆ , ˆ
kθ∆ are estimates of stabilization errors in
distance =s s s∗
∆ − and in the bearing angle =θ θ θ∗
∆ −
respectively computed at kt with the use of discrete filters as
* *
1, 1,
=1 =1
ˆˆ = ( ), = ( ),k k k ks s s
µ µ
θ
ν ν ν ν
ν ν
λ θ λ θ θ− −∆ − −∑ ∑
1, 1, 1,( ) ( )k k ks s t s tν ν ν− − −+ %@ , 1, 1, 1,( ) ( )k k kt tν ν νθ θ θ− − −+ %@ are
measurements of the distance and bearing angle sampled at
1, 1=k kt tν ντ− − + , 0 hντ≤ ≤ , = 1,ν µ ( µ is the memory
depth) with some bounded errors s% , θ% ; νλ , θ
νλ are
parameters of the filters; kz , kzφ
are the outputs of discrete
observers of variables s∆& and θ∆ & given by difference
equations
*
1 , 0 0
=1
= ( ) ( ) = 0,k k kz a s s bz z z t
µ
ν ν
ν
+ − + ≡∑
1
Subscript index l ( f ) refers to the leader (follower).
*
1 , 0 0 0
=1
= ( ) ( ) = 0.k k kz a b z z z t
µ
θ θ θ θ θ θ
ν ν
ν
θ θ+ − + ≡∑
For modes of operation that require keeping accurately a
desired geometrical shape (when scanning), the controller
design problem consists in finding the parameters of the
control algorithm (feedback and observer’s coefficients) that
provide robust dissipativity of the formation [18] and
minimize its steady state error in variables s and θ . For
transient modes (the gathering mode), the parameters of the
controller have to be synthesized in such a way that they
provide decreasing some given errors in distance s and
bearing angle θ in oder to hit the admissible set of initial
states of the accurate stabilization modes. The conception of
practical stability [18] describes the desired behavior of the
formation in this case.
D. Controllers for obstacle avoidance
Assume that, using data obtained from range sensors,
AUV can generate a path that allows it to bypass obstacles
encountered during the scanning. The problem of real-time
path generation in unstructured environment is not considered
here and we refer the reader to [19, 2]. Under the assumption
above, the problem of bypassing obstacles by the leader AUV
can be solved using controller (4). The AUV activates the
obstacle avoidance mode when it detects an obstacle. Once the
AUV reaches the scanning path (tack), it switches the obstacle
avoidance mode to the gathering mode. After bypassing
maneuver, the leader of the group can also send control
commands to other vehicles to rearrange formation in order to
reduce energy consumption (for reasons of efficiency).
The followers of the team keeps a rigid formation with the
leader by using control law (4). But once obstacles are
encountered it is not possible to meet all of the formation
constraints at the same time. Hence we require the follower to
keep only a desired distance from the leader when bypassing
obstacles. A controller for obstacle avoidance with formation
is designed as in (4) except for
1 1 2 6
ˆ ˆ ˆ= sat( , ).ss k k kk s k u k s+ ∆ + ∆F F
E. Control design method
The parameters of the proposed sampled-data control
algorithms (4) and (5) are synthesized with the use of a
technique for rigorous analysis and design of nonlinear control
systems based on sublinear vector Lyapunov functions (see,
e.g., [20, 10]). When designing controllers, we take into
account uncertainties of the AUV’s parameters, measurement
errors, constraints on the control force and torque.
III. TOP LEVEL CONTROL ALGORITHMS
A. Discrete-event systems
Considered as discrete-event system, system functioning is
described with sequences of events, or words of some formal
language. Let 0= ( , , , , )mG Q q QδΣ be a discrete event system

modeled as a generator of a formal language [19]. Here Q is
the set of states ;q Σ the set of events; : Q Qδ Σ× → the
transition function; 0q Q∈ the initial state; mQ Q⊂ the set of
marker states. Unlike finite state automaton, which recognizes
a formal language, i.e. whether or not a word belongs to the
language, generator produces words of some language. As
usual, let *
Σ denote the set of all strings over ,Σ including the
empty string .ε The closure of L is the set of all strings that
are prefixes of words of ,L i.e.
* *
= { | : }.L s s and t s t L∈Σ ∃ ∈ Σ ⋅ ∈ Symbol ⋅ denotes string
concatenation and is often omitted. A language L is closed if
= .L L If G is any generator then ( )L G is closed.
Language generated by G is *
( ) = { :L G w w∈Σ and
0( , )w qδ is defined}, while language marked by G is
( ) = { : ( )mL G w w L G∈ and 0( , ) }.mw q Qδ ∈ Marked words
may be interpreted as completed tasks performed by the
system, for example, a finished sequence of actions, which
AUV should perform to inspect an objective of interest.
In this paper we suppose that G is fully observable,
although SCT for partially observed DES is an interesting and
challenging theory, which is indispensable in study of real life
systems. Dealing with partial observation in considered AUV
group control problem is left for further investigations.
B. The notion of controlled DES
The supervisory control theory (SCT) assumes that some
events of G may be prevented from occurring and there exists
a means of control presented by a supervisor [19]. Let cΣ be a
controllable event set, = ,uc cΣ Σ Σ = .c ucΣ ∩Σ ∅ The
supervisor switches control patterns so that the supervised
DES achieve a control objective described by some regular
language K called a specification on DES behavior.
Formally, a supervisor is a pair = ( , )J S φ where
0= ( , , , , )mS X x XξΣ is a deterministic automaton with input
alphabet Σ . S is considered to be driven externally by the
stream of event symbols (words) generated by G (i.e. words
from ( )),L G while : Xφ → Γ is a function that maps
supervisor states x into control patterns 2 .γ Σ
∈ If S is in
state ,x the events cσ ∈Σ of G are subject to control by
( ).xφ If ( ),xσ φ∈ then σ is enabled, while if ( )xσ φ∉ then
σ is disabled (prohibited from occurring). Note that, unlike
DES models with forced events, enabled events should not
necessary occur. It is obvious that φ is the state feedback
map. Because uncontrollable events cannot be disabled, it is
required = ( ).uc xγ φΣ ⊆ The function δ is now extended to
the function :c Q Qδ Γ×Σ× → accounting control patterns as
( , ), ( , ) ;
( , , ) =
, .
c
q if q is defined and
q
undefined otherwise
δ σ δ σ σ γ
δ γ σ
∈


Construct the function : ,c X Q X Qξ δ× Σ× × → × where
( )( , , ) = ( ( , ), ( ( ), , ))c cx q x x qξ δ σ ξ σ δ φ σ× is defined iff
( , )qδ σ is defined, ( )xσ φ∈ and ( , )xξ σ is defined. Denote
( / )L J G a language generated by the closed-looped behavior
of the plant and the supervisor: *
( / ) = { :L J G w w∈Σ and
( )( , , )c w x qξ δ× is defined}. Let ( / )mL J G denote the
language marked by the supervisor:
0 0( / ) = { : ( / ) ( )( , , ) }.m c m mL J G w w L J G and w x q X Qξ δ∈ × ∈ ×
The main goal of supervisory control is to construct such
supervisor that ( / ) = .mL J G K The notion of controllable
language is essential in solving this problem.
Definition 1 [21]. K is controllable (with respect to ( )L G
and ucΣ ) if ( ) .ucK L G KΣ ∩ ⊆
Thinking that K is the admissible behavior of the system,
it is controllable if occurring of any uncontrolled event after
prefix of the word from K leads to a word from ,K i.e. still
admissible. Checking for controllability is a necessary stage of
a supervisor design. For this the product H G× should be
constructed where H is a recognizer of the specification
language. Next for all ( , )H G H Gq q Q ×∈ inclusion
( ) ( , )G uc H GE q E E q q∩ ⊆ is checked, where ( )E q denotes a
set of events that are possible is the state .q
Definition 2 [21]. K is ( )mL G closed− if
= ( ).mK K L G∩
Supervisor existence criterion sounds as follows: given
( ),K L G⊆ there exists supervisor J such that
= ( / )mK L J G iff K is controllable and ( )mL G closed−
w.r.t. ( ).L G
C. Discrete-event model for AUVs formation control
From the point of view of the scanning width and
maneuverability of the group, it is reasonable for surveillance
missions to use in-line formations where the follower is
shifted backward with respect to its leader along the driving
direction. For reasons of efficiency, it also makes sense to
provide possibility of changing positions of the leader in the
line formation during the mission, thus distinguishing two
types of formations: with the follower on the left from the
leader (left formation) and with the follower on the right (right
formation).

Fig. 2. Leader’ generator lG
Fig. 3. Automaton H for specification on leader’s behavior
Fig. 4. The automaton S of the supervisor for ( )lL G and K
TABLE I. MAPPING φ:Χ→Γ
MFL MFR FL wait ROA LOA ML MR
1 1 0 0 0 - - - -
2 - - - - - - - -
3 0 0 0 - 1 1 0 0
4 0 1 0 0 − − − −
5 − − 0 − − − − −
6 − − 0 − − − − −
7 0 0 0 − 1 1 0 0
8 − − − − − − − −
9 1 0 0 − 0 0 0 0
10 0 0 0 − 0 0 0 1
11 − − 0 − − − − −
12 − − 0 − − − − −
13 0 0 0 − 0 0 1 0
14 0 1 0 − 0 0 0 0
To implement SCT for AUVs formation control, first we
construct a generator describing switching of a leader’s
operational modes. Let the set of leader’s generator states be
= {lQ PFR (path following in right formation), PFL (path
following in left formation), OA (obstacle avoidance mode), W
(waiting), S (surfacing), PC (path computing), G (formation-
gathering mode)}, 0, ,= = ,l m lq Q G and the set of leader
events be = {lΣ MFR (make right formation), MFL (make left
formation), OD (obstacle detected), LOA (obstacle avoidance
on the right), LOA (obstacle avoidance on the left), FSD (free
space detected), BR (border reached), FL (follower lost), FF
(follower found), ML/MR (send message to form left/right
formation), timeout, wait}. Function δ is defined according
to Fig. 2.
Assume , = { , , , }.l uc OD BR FSD FFΣ The model does not
claim to be exhaustive but presents key points of AUV
operation as a leader in scanning mission. Note that treating
FL as a controllable event allows one to manage leader’s
behavior aspects relative to the followers. Indeed, being
enabled, this event makes the leader AUV to wait for the lost
followers and in case of their absence for a certain time period
(timeout event), surface. This may be important to get to know
a human operator where the lost followers may be found.
Recall that enabled events should not necessary occur so
enabling controllable LOA and ROA does not imply their
concurrent occurring. Choosing between LOA and ROA is
made on board of AUV according to the obstacle detected
since a supervisor is just the means of restriction of system
functioning due to some constraints. Let a specification on the
leader AUV actions is as described by the language
= ( ),K L H where H is the automaton on Fig. 3.
This specification implies that AUV group starts scanning
mission in the left formation, and after reaching a border of
the scanned area, change the formation to the right one. Also,
bypassing an obstacle on the left (right) while moving in the
left (right) formation, formation is not changed. But after
bypassing an obstacle on the left (right) while moving in the
right (left) formation, there is not only the need to change a
formation but also to compute a new path and gather
following AUVs to achieve a new formation. The
specification does not suppose awaiting in gathering mode and
forbid waiting for the lost followers AUVs. Since event FL is
controllable, these do not affect controllability of ,K which is
easily checked. States of H are named in the the similar way
to lG states for convenience only, for there may be no
coincidence in the names of these states. K may be described
by any automaton since we are interested only in the language
itself but not the way it generated. By marking the states G1
and G2 ( )mL G - closeness of K is achieved.
Fig. 4 shows the automaton of a supervisor
= ( , ),J S φ such that ( / ) = ,mL J G K constructed with the help
of DESUMA2 software, and its mapping φ is presented in
Table 1. In the table enabling of an event corresponds to 1
while disabling of an event corresponds to 0. Dashes mean

Fig. 5. Simulation results
that it does not matter if an event enabled or disabled.
Uncontrolled events are not included in the table since they
are always enabled. The event timeout is not included as well
because FL is never enabled and the system never reaches the
state .W
Due to the space limitaion we just mention that the
follower AUV’s generator states set would be = {fQ KRF
(keeping right formation), KLF (keeping left formation), OFA
(obstacle avoiding in formation), OA (obstacle avoiding), W
(waiting), S (surfacing), G (formation gathering)} and the set
of follower events would be = {fΣ MFR (make right
formation), MFL (make left formation), OD (obstacle
detected), FSD (free space detected), LL (leader lost), LF
(leader found), ML/MR (receive message to form left/right
formation), timeout} . Thus the leader and the follower AUVs
share events ,MFR ,MFL ,ML and ,MR and this fact will be
used to construct decentralized supervisor in our future work.
IV. SIMULATION
To demonstrate the effectiveness of the developed
approach to hybrid control of multi-AUV systems, numerical
computations and simulations were conducted for a group of
three identical large-sized AUV with mass 2200m ≈ kg and
moment of inertia 2000zI ≈ N m 2
. These and other
parameters of the AUV are borrowed from [3]. For each
follower we take = 11.66s∗
m and = 1.03δ ∗
− rad in the left
formation = 11.66s∗
m and = 1.03δ∗
rad in the right
formation. Cubic splines are used to represent predefined and
real time generated curved paths for different operational
modes.
When designing path-following and formation-keeping
controllers and carrying out simulations, we set h = 0.2 s
(sampling period, common for all AUVs), sF = 320 N and
sG = 160 N m (maximum force and torque reserved for
stabilization), cc = 0.12 (constraints on the path curvature). It
is worth mentioning that controllers are synthesized off-line
and resulting control algorithms can be implemented in AUVs
with law computational capacities.
Fig. 5 shows the trajectory of the group in the following
simulation scenario. AUVs start moving along the first line in
the left formation, where AUV0 is the leader for AUV1 and
AUV1 is the leader for AUV2, until they encounter an
obstacle and asynchronously activate the obstacle avoidance
modes. After bypassing the obstacle, the group tries to
reorganize into the right formation and continue scanning.
Once the leader AUV reaches the border of the survey area, it
makes U-turn and gathers the group in the left formation for
the next line. In square brackets in Fig. 5 we list operation
modes of all AUVs at five different time instants.
V. CONCLUSION
In this paper we generally focused on the continuous
dynamics of the AUV formations and briefly discussed the
event-driven top-level control. Some results were omitted and
lots of questions are left for future work, including the partial
observability of system functioning, modular approach to DES
construction, and decentralized supervision. The case when a
robot in the group shares the functions of a follower for one
robot and a leader for another is our immediate research line.
Results from [22] will be used to provide supervisor
properties.
During surveillance or other complex missions, there may
be a situation when several variants of further actions are
possible. For example, if a vehicle detects an obstacle, it needs
to choose the side to bypass it. The problem of choice cannot
be solved using DES framework and therefore it is desirable to
have a subsystem, which is responsible for making strategic
decision and planning actions using knowledge about
underwater environment and AUV’s state. In future studies,
we are planning to use original logical calculus of positively
constructed formulas (PCF) and PCF-based automated
theorem proving method [23] for representing and processing
this knowledge.
ACKNOWLEDGMENT
The research is supported by the Russian Science
Foundation (project no. 16-11-00053).
REFERENCES
[1] C. Petres, Y. Pailhas, P. Patron, Y. Petillot, J. Evans,and D. Lane, “Path
planning for autonomous underwater vehicles,” IEEE Transactions on
Robotics, vol. 23, no 2, pp. 331–341, April 2007.
[2] A. Bagnitckii, A. Inzartsev, and A. Pavin, “Planning and correction of
the auv coverage path in real time,” in 2017 IEEE Underwater
Technology (UT), Feb 2017, pp. 1–6.
[3] L. Lapierre and D. Soetanto, “Nonlinear path-following control of an
AUV,” Ocean Engineering, vol. 34, no. 1112, pp. 1734–1744, 2007.
[4] D. W. Kim, “Tracking of remus autonomous underwater vehicles with
actuator saturations,” Automatica, vol. 58, pp. 15–21, 2015.
[5] X. Li, D. Zhu, and Y. Qiun, “A survey on formation control algorithms
for multi-auv system,” Unmanned Systems, vol. 2, no. 4, pp. 351–359,
2014.
[6] B. Das, B. Subudhi, and B. B. Pati, “Cooperative formation control of
autonomous underwater vehicles: An overview,” International Journal
of Automation and Computing, vol. 13, no. 3, pp. 199–225, 2016.
[7] R. Cui, S. S. Ge, B. V. E. How, and Y. S. Choo, “Leader-follower
formation control of underactuated autonomous underwater vehicles,”
Ocean Eng., vol. 37, pp. 1491–1502, 2010.

[8] P. Millan, L. Orihuela, I. Jurado, and F. R. Rubio, “Formation control of
autonomous underwater vehicles subject to communication delays,”
IEEE Transactions on Control Systems Technology, vol. 22, no. 2, pp.
770–777, 2014.
[9] S. N. Vassilyev, “Method of reduction and qualitative analysis of
dynamic systems: I, II,” Journal of Computer and Systems Sciences
International, vol. 45, no. 1, pp. 17–25; no. 2, pp. 167–179, 2006.
[10] I. V. Bychkov, V. A. Voronov, E. I. Druzhinin, R. I. Kozlov, S. A.
Ul’yanov, B. B. Belyaev, P. P. Telepnev, and A. I. Ul’yashin, “Synthesis
of a combined system for precise stabilization of the spektr-uf
observatory: II,” Cosmic Research, vol. 52, no. 2, pp. 145–152, 2014.
[11] A. Jayasiri, G.K. Mann, and R.G. Gosine, “Behavior coordination of
mobile robotics using supervisory control of fuzzy discrete event
systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B
(Cybernetics), vol. 41, no. 5, pp. 1224–1238, 2011.
[12] X. Dai, L. Jiang, and Y. Zhao, “Cooperative exploration based on
supervisory control of multi-robot systems,” Applied Intelligence, vol.
45, no. 1, pp. 18–29, 2016.
[13] A. Tsalatsanis, A. Yalcin, and K. P. Valavanis, “Dynamic task allocation
in cooperative robot teams,” Robotica, vol. 30, no. 5, pp. 721–730, 2012.
[14] G. W. Gamage, G. K. I. Mann, and R. G. Gosine, “Discrete event
systems based formation control framework to coordinate multiple
nonholonomic mobile robots,” in Proceedings of the 2009 IEEE RSJ
International Conference on Intelligent Robots and Systems, IROS 09,
2009, pp. 4831–4836.
[15] Y. K. Lopes, S. M. Trenkwalder, A. B. Leal, T. J. Dodd, and R. Groß,
“Supervisory control theory applied to swarm robotics,” Swarm
Intelligence, vol. 10, no. 1, pp. 65–97, 2016.
[16] F. J. Mendiburu, M. R. A. Morais, and A.M.N. Lima, “Behavior
coordination in multi-robot systems,” IEEE International Conference on
Automatica (ICA-ACCA), Oct. 2016, no. 32, pp. 1–7, 2016.
[17] C. R. Torrico, A. B. Leal, and A. T. Watanabe, “Modeling and
supervisory control of mobile robots: A case of a sumo robot,” IFAC-
Papers OnLine, vol. 49, no. 32, pp. 240–245, 2016.
[18] S. N. Vassilyev, R. I. Kozlov, and S. A. Ul’yanov, “Multimode
formation stability,” Doklady Mathematics, vol. 89, no. 2, pp. 257–262,
2014.
[19] E. Galceran, R. Campos, N. Palomeras, M. Carreras, and P. Ridao,
“Coverage path planning with realtime replanning for inspection of 3d
underwater structures,” in 2014 IEEE International Conference on
Robotics and Automation (ICRA), pp. 6586–6591, May 2014.
[20] S. V. Burnosov and R. I. Kozlov. “Investigation of the dynamics of
nonlinear systems with uncertainty and perturbations on the basis of the
vector lyapunov functions II,” Journal of Computer and Systems
Sciences International, vol. 53, pp. 82–90, 1996.
[21] P. J. Ramadge and W. M. Wonham, “Supervisory control of class of
discrete event processes,” SIAM J. Control and Optimisation, vol. 25,
no. 1, pp. 206–230, 1987.
[22] N. V. Nagul, “Generating conditions for preserving the properties of
controlled discrete event systems,” Autom. Remote Control, vol. 77, no.
4, 2016.
[23] A. Larionov, A. Davydov, and E. Cherkashin, “The calculus of
positively constructed formulas, its features, strategies and
implementation,” in 2013 36th International Convention on Information
and Communication Technology, Electronics and Microelectronics
(MIPRO), pp. 1023–1028, May 2013.

Hybrid Control Approach to Multi-AUV System in a Surveillance Mission

More Related Content

What's hot (20)

Similar to Hybrid Control Approach to Multi-AUV System in a Surveillance Mission (20)

More from ITIIIndustries (20)

Recently uploaded (20)

Hybrid Control Approach to Multi-AUV System in a Surveillance Mission