Coordinate Control, Motion Optimization and Sea Experiment of a Fleet of Petrel-II Gliders
Xue et al. Chin. J. Mech. Eng.
Coordinate Control, Motion Optimization and Sea Experiment of a Fleet of Petrel-II Gliders
DongY‑ang Xue 0 2
Zhi‑Liang Wu 0 2
Yan‑Hui Wang 0 1 2
ShuX‑in Wang 0 1 2
0 Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University , Tianjin 300072 , China
1 The Joint Laboratory of Ocean Observing and Detecting, Qingdao National Laboratory for Marine Science and Technology , Qingdao 266237 , China
2 School of Mechanical Engineering, Tianjin University , Tianjin 300072 , China
The formation of hybrid underwater gliders has advantages in sustained ocean observation with high resolution and more adaptation for complicated ocean tasks. However, the current work mostly focused on the traditional gliders and AUVs. The research on control strategy and energy consumption minimization for the hybrid gliders is necessary both in methodology and experiment. A multi‑ layer coordinate control strategy is developed for the fleet of hybrid underwater gliders to control the gliders' motion and formation geometry with optimized energy consumption. The inner layer integrated in the onboard controller and the outer layer integrated in the ground control center or the deck controller are designed. A coordinate control model is proposed based on multibody theory through adoption of artificial potential fields. Considering the existence of ocean flow, a hybrid motion energy consumption model is constructed and an optimization method is designed to obtain the heading angle, net buoyancy, gliding angle and the rotate speed of screw propeller to minimize the motion energy with consideration of the ocean flow. The feasibility of the coordinate control system and motion optimization method has been verified both by simulation and sea trials. Simulation results show the regularity of energy consumption with the control variables. The fleet of three Petrel‑ II gliders developed by Tianjin University is deployed in the South China Sea. The trajectory error of each glider is less than 2.5 km, the formation shape error between each glider is less than 2 km, and the difference between actual energy consumption and the simulated energy consumption is less than 24% actual energy. The results of simulation and the sea trial prove the feasibility of the proposed coordinate control strategy and energy optimization method. In conclusion, a coordinate control system and a motion optimization method is studied, which can be used for reference in theoretical research and practical fleet operation for both the traditional gliders and hybrid gliders.
Underwater glider; Petrel‑ II; Coordinate control; Path planning; Artificial potential fields (APFs); Energy consumption
Nowadays, deployment of autonomous mobile
vehicles or platforms has become the mainstream method
in ocean observation. Autonomous underwater glider
] (AUG) is a type of autonomous underwater
vehicle (AUV), which is distinguished from scientists by its
unique gliding mode. AUG shows more competitiveness
than other unmanned vehicles (e.g., typical AUVs [
], and Mobile Buoy [
]) in ocean observing and
monitoring tasks due to its high endurance and low cost.
On the basis of traditional AUG, the hybrid underwater
] (HUG) is developed with the combination
of AUG’s gliding motion and AUV’s propulsion motion,
and thus has more advantages in maneuverability and
adaptation under severe ocean conditions. Cooperation
and coordination of multiple gliders can improve task
quality both in providing more complete
spatiotemporal data  of the object and minimizing observer error
by adaptive task control strategy. Advantages of multiple
gliders have been proved in several sea trails including
ASAP field experiment [
], bloom tracking [
ocean currents mapping [
Coordinate control of the fleet both in real-time
operation and theoretical research has become a hot topic
as the application of the formation increases. Paley
et al. [
] designed a glider coordinated control system
(GCCS) which is an automated control system that
performs feedback control at the level of the fleet designed
for AOSN [
]. Leonard et al. [
] presented a
coordinated adaptive sampling method for ASAP experiment
based on GCCS. The experiment in Monterey Bay,
California proved the coordinate adaptive motion control
capability for ocean sampling. Das et al. [
the coordination of a AUVs’ team with communication
constrains based on the leader-follower method and
the CLONAL selection algorithm is applied to plan the
formation leader motion utilizing the triangular
sensorbased grid coverage technique. A distributed control
] based on artificial potential fields (APFs)
and virtual leaders was introduced for a group of
underwater vehicles to coordinate motion and construct
geometry. Combination of the APFs method and the Kane’s
method was researched by Yang et al. [
] to achieve
coordinate motion planning for Multi-HUG formation
in an environment with obstacles. Ren et al. [
proposed an approach based on fuzzy concept to solve
coordination problems of multiple gliders, which considers
influence of the surrounding environment. Qi et al. [
developed a practical design method for path following
and coordinated control of AUVs by modeling each AUV
as a system with time-varying parameters, unknown
nonlinear dynamics and unknown disturbance. It is
necessary to make efforts on the coordinate control of HUG
formation for its superiority in operation and control,
while most researches on coordinate control strategy of
fleet focused on the traditional gliders and AUVs.
Energy saving, utilization and recycling are always
concerned in practical engineering technology, especially
in remoted mobile vehicles [
]. Since the glider is
required long voyage in most task, the endurance which
is mainly determined by the onboard battery capacity,
motion control strategy and ocean environment plays
an important role in the glider operation. The
questionnaire survey  carried out among the GROOM
(Gliders for Research, Ocean Observation and Management)
members shows that the battery and power failure is the
second highest reason leading to the failure of glider
mission. Several researches to achieve energy saving and
optimal control have been reported in literature. The
Rapidly-Exploring Random Trees (RRTs) method was
utilized in the glider path planning for lower energy
consumption in ocean current [
]. Yu et al. [
a computational method to extend glider endurance by
optimizing gliding motion parameters and sensor
scheduling based on an energy consumption model. Zhou et al.
] presented an optimal energy consumption method
with adjustable speed of glider to achieve path planning.
The energy consumption model and analysis focused on
traditional glider form literature, the model of HUG is
urge to research.
To meet the objective of coordinate motion, energy
efficiency with consideration of the ocean environment, this
paper develops a multi-layer coordinate control strategy
to control the fleet of gliders. The control strategy within
each control layer is integrated in the off-board controller
and on-board controller respectively. Compared with the
method in GCCS, different types of APFs are constructed
in the path planning model and an energy consumption
model of hybrid underwater glider is established based
on the concept of Refs. [
] to optimize motion
efficiency. The existence of ocean flow is taken into
consideration in the coordinate control system.
In this research, a hybrid underwater glider (HUG), the
Petrel-II glider is taken as the object of study.
Nonetheless, the methods might be used in the coordinate control
of Multi-HUG formation or Multi-AUG formation with
other types of underwater gliders. The paper is organized
as follows. In Section 2, the specifications and the
working principle of Petrel-II glider are introduced as
background of the research. Then in Section 3, a coordinate
control system for multi-HUG formation is described.
Consequently, the primary sea trail is deployed in the
South China Sea to test the method and experiment
results are presented in Section 4, followed by
conclusions in Section 5.
2 Background of Petrel‑II Glider
2.1 Structure and Main Parameters of Petrel‑II
Petrel-II glider, shown in Figure 1, is a hybrid
underwater glider (HUG) developed by Tianjin University, China
]. It expands the capability of traditional
underwater glider by the combination of gliding mode and screw
propeller driven mode, which is more adaptive in harsh
ocean environment and more suitable for complex task.
Petrel-II glider has successfully completed numerous sea
trials in the South China Sea and has been proved reliable
for ocean observation. It has achieved high performance
of 1108.4 km for non-stop sailing without any fault and
1514.2 m diving depth in the project acceptance of 863
High-tech Program. The main specifications of Petrel-II
are listed in Table 1.
Petrel-II glider is constructed by the following main
parts: the buoyancy driven part (regulating the net
buoyancy to control glider’s diving or rising), attitude
adjusting and battery package (adjusting the yaw, pitch and
roll angles by the movement and rotation of the battery
package, meanwhile supplying power for glider),
electronic part (glider on-board controller for motion
control, state monitoring and data obtaining), payload part
(scientific sensors), GPS and communication module
(wireless modem and Iridium satellite/Beidou
satellite modem) and screw propeller. More details can be
obtained in Refs. [
2.2 Motion Control of Single Glider
A typical glider motion is shown in Figure 2, where the
dash line represents the actual glider trajectory and the
black arrow line represents the trajectory in the
horizontal plane. In general, the underwater glider is always
required to move along a preset trajectory or an adaptive
reset local trajectory in the horizontal plane, meanwhile
diving to the desired depth during the motion. A series
of waypoints can be chosen along the required trajectory
(horizontal plane) as a series of desired local positions.
A simple PID controller [
] can be used to control the
related subsystems to reach the desired motion
parameters which can further control the glider to move to the
waypoint by calculating the distance between the current
position and the preset waypoint.
The heading angle of the glider is adjusted during the
gliding to minimize the moving distance. As shown in
Figure 3, the direction of dash glider represents the current
attitude when the glider surfaces. The heading angle of the
glider is required in the same direction with the connection
between the current position and the waypoint, i.e., the
direction of yellow glider in Figure 3. A PID controller [
is also used to control the rotation of the battery package to
regulate the heading angle during glider motion.
3 Coordinate Control System of Multi‑HUG
The coordinate control system introduced here can fulfill
three goals: (1) to plan the optimal trajectory and
meanwhile shape the formation under preset configuration
with given the desired position of the task, even when
obstacles exiting. (2) to control each glider to move to
Figure 3 Heading angle adjustment of glider
the desired position with optimized parameters to save
energy. (3) to estimate the interference velocity of ocean
current and make decision to move to the desired goal.
3.1 Overall Architecture
The coordinate of the HUG formation can be achieved
by a multi-layer coordinate control system as shown in
Figure 4. There are totally two control layers which are
under control loop with different time scales. This
control system is not based on the dynamics of the glider.
The outer layer with long-time scale loop is integrated
in the ground control center or the deck controller which
can only work during communication when the glider
surfaces. The function of outer layer is to plan the fleet
trajectory and generate waypoints for each glider. The
control software of Petrel-II can manipulate up to 10
gliders at the same time in one computer. Since each glider
has sailing error and may be influenced by the ocean
environment, the trajectory is re-planned every time loop
for about 48/72 h by updating the current glider positions
and the fresh task requirement (for adaptive glider
sampling based on ocean model, the forecast period is 48/72
]). The waypoints are updated to each glider by
surfacing communication. On the outer control layer,
gliders update working status every profile and receive new
command every long-time loop.
The inner layer with short time scale loop is integrated
in the onboard controller inside each glider. This layer
receives the command waypoints from the outer layer
and control the glider to move to the desired waypoints.
Since endurance of the glider is very important for the
long-term marine observation, a LEC (least energy
consumption) algorithm is designed to minimize the energy
cost in the glider motion. The distance between neighbor
waypoints is calculated as the input of LEC and the
optimal control variables are generated as the optimization
output. The influence of ocean flow is considered by the
controller. The glider gets its position every time it
surfaces and estimates the flow velocity by comparing the
position with the dead-reckoned position (DK position)
or that of the desired waypoint. The controller makes
decision to decrease the influence of the flow by
determining the heading angle of the glider and outputs the
flow speed into the LEC to obtain optimal control
variables. The onboard subsystem controller based on PID
control will achieve the motion control under the optimal
command. This control cycle loops every profile, so the
inner layer is under a short-time loop by profiles.
3.2 Fleet Trajectory Planner
3.2.1 Multibody System Model Based on Kane’s Equation
The goal of the trajectory planning of multi-HUG is to
generate optimal trajectories for each glider and
meanwhile shape the whole formation under given motion
conditions (initial position, motion goal and obstacle
location) and desired formation configuration (formation
geometry). Artificial potential fields (APFs) method is
adopted in the planner for its capabilities in steering the
motion along the trajectory of global minimum potential
energy. The multi-HUG formation is regarded as a
virtual multibody system and for simplicity, the individual
agent in the fleet is treated as a particle and is virtually
connected with other agents in the multibody system.
Motion simulation results of a three-glider fleet motion
controlled by this method has been achieved in our early
work (more details see Refs. [
Kinematics: this study assumes it as a two-dimensional
question since the desired trajectories of the gliders are
only in horizontal plane. As an N-body system shown in
Figure 5, the gliders are regarded as particles with full
actuation. Bk represents the kth agent and all the
bodies are fixed in the Cartesian reference frame which is
denoted by the unit vector (N1, N2). Each body has two
degrees of freedom and the system has 2 N degrees of
The position coordinates of the bodies can be chosen as
the generalized coordinate, which is given by
ql = (x11, x12, . . . , xk1, xk2, . . .),
where xkn (k = 1,…, N, n = 1, 2) represents the position
coordinates of the kth body with respect to the inertial
Diving depth: d
Formation shape: d jk
Ocean flow: f
x2 y2 (k = 1, 2,3...N)
Figure 4 Architecture of coordinate control system
Long-time scale control loop
Land control center
Surfacing positioning and communication
Current position wij
On board controller
DR position estimate
& control f
B,ζ , nP
Subsystem controller for
Short-time scale control loop
frame and n denotes the two axes of reference frame. The
generalized speed can be expressed by
q˙ l = (x˙11, x˙12, . . . , x˙k1, x˙k2, . . .),
where x˙kn is the time derivative of xkn.
The partial velocity array is adopted to describe the
kinematic characteristics of the multibody system, which
can be obtained by
vklm = ∂∂vq˙kl =
where vk is the velocity of the kth body in the inertial
system, l = 1,…, 2 N represents the number of elements in
the generalized coordinate, n, m = 1, 2 represent the two
axes of the coordinate system, and is the velocity
component of the agents.
Kinetics: The APFs are constructed for particular
mission requirement, ocean environment, and formation
geometry. Attractive potential field [
] between the
gliders and the task target can guide the formation to the goal
area. Interactive potential field [
] between gliders can
shape and maintain the formation geometry by pulling
together or pushing away the neighboring vehicles when
they are apart from each other or toward each other by
a control distance. Repulsive potential field [
gliders and ocean obstacles is also necessary to avoid
collision in the ocean environment. The three types of APFs
are expressed by the following equations:
21 kr ( R1ok − do1bs )2 0 < Rok ≤ dobs,
0 Rok > dobs,
where i, j, k are the ith, jth, kth bodies, i, j, k = 1…N, N is
the total number of bodies, ka is the scalar attractive
control gain, kI is the scaling interactive control gain, kr is the
scalar repulsive control gain, Rgk is the distance between the
kth body and goal, Rok is the distance between the kth body
and the effective obstacle, rij is the distance between the ith
and jth bodies, d0 is the constant denoting the critical point
between attraction and repulsion, d1 is the limited distance
of interaction, dgoal is the equivalent radius of the attractive
area, dobs is the distance of influence by the obstacles.
The potential forces generated by APFs are the negative
gradients of potential fields:
FAPF = −∇U ,
where FAPF is the potential force and U is the artificial
potential field. More derivation process of formulas can
be obtained in Ref. [
]. Dissipative force is applied to
individuals of the formation to achieve asymptotic
stability at desired velocity:
FdKiss = −kdiss(vk − vd ),
where FdKiss is the dissipative force on the kth body, kdiss is
the scalar control gain, vd is the desired velocity of each
Kane’s equation: The Kane’s equation has advantages
in the construction of the dynamic equation with
minimal sets of coordinates and complexity. The principle of
Kane’s equation is that the sum of the generalized active
force and the generalized inertia force equals to zero:
Fl + Fl∗ = 0, l = 1, 2, . . . , 2N ,
where Fl is the generalized active force and Fl∗ is the
generalized inertia force. Fl in the multi-HUG formation is
the sum of the generalized active force corresponding to
APFs force and dissipative force:
Fl = Fal + Frl + FIl + Fdisl , l = 1, 2, . . . , 2N ,
where Fal, Frl, FIl, and Fdisl is the generalized active force
constructed by the attractive potential field, the
repulsion potential field, the interaction potential field and
the dissipative control term, expressed in Eqs. (4)‒(8),
respectively. See Ref. [
] for more details about the
construction of Kane’s equation.
3.2.2 Waypoints Generator
The waypoints are chosen to steer each glider’s motion
to the trajectory planned by the method presented in
Section 3.2.1. There are two principles for converting
trajectory to waypoints [
]. One is to space waypoints
uniformly in time and the other is to let the waypoints
subject to a maximum spacing constrain. Considering
the practical operation, the second method is adopted to
set a maximum space between two waypoints, which is
an optimization problem obtaining optimal points on the
curve to minimize the distance function.
Let wki denotes the ith waypoint position of the kth
body, k = 1,…, N and i = 1,…, p, p is the total number of
the waypoints. The problem can be express as
min f (xkj) = ||xkj − wk(i−1)||2
− dr ,
where xkj is the jth calculated position on the planned
trajectory of the kth body, j = 1,…, q, q is the number of
the calculated position which is much larger than p, and
dr is the required distance between neighbor waypoints.
3.3 Optimal Onboard Control Based on LEC
3.3.1 Least Energy Consumption Algorithm (LEC)
Model: since the Petrel-II glider is an under actuated
system with the compound motion in horizontal plane,
it is difficult to analyze the energy consumption of the
system based on the motion dynamic model [
29, 30, 38
] that finds the relationship between
the motion parameters (gliding angle, diving depth, etc.)
and the energy cost of the subsystem by analyzing the
glider operation principle and control flow, can simplify
the complication of the question and give a practical
expression. In this article, based on the main concept in
the Refs. [
29, 30, 38
], an energy consumption model of
the screw propeller driven hybrid underwater glider is
established under the following assumptions:
(1) The question is assumed only in the vertical plane
for the vertical motion (diving and rising) of glider cost
the major power.
(2) The energy cost is considered under the steady
gliding motion. It is assumed under the force balance
condition with drag force D, lift force L, net buoyancy force B
and screw propeller driven force P (exiting under hybrid
motion condition) acted on the glider.
The force diagram of the glider under steady gliding
balance is shown in Figure 6. Let the scalars D, L, B and
P represent the magnitude of the force D, L, B and P,
respectively. When considering the propulsion force P,
the attack angle α is simplified to be zero, and the balance
equations of the system can be given by
L = Bcos ζ ,
D = Bsinζ + εP,
where α and ζ are the attack angle and the gliding angle of
the glider, respectively, and ε is the condition coefficient
0, under gliding mode,
1, under hybird mode.
The drag force and lift force are related to the gliding
speed V and the attack angle α. The propulsion of screw
V cos ζ
propeller is related to its rotate speed nP, its diameter DP and
the seawater density ρ. The three forces can be expressed by
D = KD0 + KDα2 V 2,
L = (KL0 + KLα)V 2,
P = KP ρDP4 nP ,
where the KD0, KD, KL0, and KL, are the coefficients of drag
force and lift force, respectively. KP is coefficient of the
propulsion which can be obtained by the screw propeller atlas.
The gliding speed is a function of the variables B, nP and ζ.
And the motion time of the distance S between neighbor
waypoints can be obtained by
The energy consumed during the glider motion can be
divided into two classes [
]: the energy cost by the
continuous working units (the control unit, part of sensors
and screw propeller), which is related to gliding time,
symbolled by Et and the energy consumed by motion
driven units which is related to the number of working
profiles, symbolled by En.
E = Et + En ,
where Et = Pt·t, En = n · (Eh + Em), Pt is the total power
of the continuous working units, n is the number of the
And Eh is energy cost by buoyancy driven unit, which
is considered as the consumption of the hydraulic system
when glider dives and rises. Em is the energy cost by the
attitude adjusting unit, which is considered as the
consumption of the motor driving the battery movement.
2B · ( Pv + Pp0 + kpd ), (17)
ρg qv qp
Eh = n · VB · Ph = n ·
Em = n · 4Pmr ,
where Pv is the power of the magnetic valve, Pp0 and kp
are coefficients of the hydraulic pump which are related
to its working depth (i.e., diving depth) d, g is the
acceleration of gravity, qv and qp are the fluxes of the magnetic
valve and hydraulic pump, respectively. ρ is the seawater
density which is related to the temperature, pressure and
salinity at the related position and depth undersea, and it
is taken as a constant for simplicity in this study. Pm is the
power of the attitude adjusting motor, vm is the speed of
the moving package and r is the movement of the
package from the equilibrium position, which is determined
by the pitch angle:
M · h
· tan ζ ,
where pitch angle is assumed to be equal to the gliding
angle for the attack angle is small. M and m are masses
of glider and moving package respectively, and h is the
Algorithm: the total energy consumption is obtained by
Eqs. (16)‒(19), from which we can analyze the
relationship between the energy, the motion parameters and the
control variables. The time-related energy is determined
by the required distance between neighbor waypoints S,
the gliding angle ζ and the gliding speed V which is
further determined by the net buoyancy B and the rotate
rate of the screw propeller nP. The profile-related energy
is determined by the gliding angle ζ, the number of
profiles n, the diving depth d and the net buoyancy B. Thus,
the total energy consumption function can be expressed
E = f (S, d, B, nP , n, ζ ).
Endurance is important for the glider to achieve long
term ocean observation. The question is how to make
the battery on the glider sustain as long as possible. A
low energy cost optimization can be designed to choose
the optimal variables to minimize the total energy cost
based on the energy consumption function when given
the required conditions S and d. Thus, the optimization
problem can be expressed by
min f (S, d, B, nP , n, ζ ),
s.t. Bmin ≤ B ≤ Bmax,
ζmin ≤ ζ ≤ ζmax,
nnP=min ≤S·t2adnnPζ ≤, nPmax ,
where Bo, ζo and nPo are the optimal variables, Bmin and
Bmax represent the ability of the net buoyancy
determined by the design volume of oil tank, and ζmin, and
ζmax are the minimum value and maximum value of the
gliding angle which is determined by the intersection of
the design attitude adjusting range and the stable gliding
condition. nPmin and nPmax are the rotate speed extreme
values of normally glider operation. ⌈•⌉ is to round up
the value to make sure that the glider can arrive at the
desired surfacing position.
As the problem described by Eq. (21) is complicated
nonlinear question, it is difficult to obtain the optimal
control variables by analytic method. An iterative
optimization algorithm can solve the problem, which is
designed as follows:
3.3.2 Flow Estimate and Motion Correction
The existence of ocean flow (ocean current) always
influences the trajectory of the glider since the speed of the
glider in horizontal plane is generally less than 0.4 m/s
which has the same magnitude with the speed of the
flow. A control scenario is designed to control the glider
motion with the existence of ocean flow, shown in
The controller first estimates the velocity of ocean flow
by the actual position and the desired position during
every time the glider surfaces. Then the controller makes
decision to determine the heading angle of the next
motion and outputs the estimated speed into the LEC
module. The optimal control variables can be obtained
with the existence of ocean flow.
Flow estimate: The actual and the desired horizontal
positions of glider at current surfacing time t are denoted
by r(t) and r′(t), respectively. The average flow velocity of
the last profile can be estimated by
r(t) − r(t)
where t is the motion period of the last profile and the
surfacing time is assumed to be contained in the period.
Compared with the ocean model based forecast, this
method is much easier and does not need larger amount
of precise sensor data. It is suitable to integrate into the
onboard control system.
Heading angle determination: In order to keep the
glider moving to the next waypoint, the direction of the
resultant velocity of the desired glider velocity and the
flow velocity should be on the connection of the current
position and the next waypoint. When the glider is
capable to move along the desired direction, the heading angle
should be set same with the angle of the desired glider
velocity. Otherwise, when the ocean flow is too strong for
the glider to move on the resultant velocity direction, the
heading angle should be set opposite to that of the ocean
Figure 7 Control flow chart with the existence of ocean flow
V ′ = f + Vglider .
||V ′|| cos ζ
flow velocity. The criteria that tests whether the glider
can move along desired direction is presented in Ref.
LEC with ocean flow: Since ocean flow influences the
speed of the glider, the motion time in the energy
consumption model is changed by flow speed. The glider
velocity relative to ground is the vector sum of the flow
velocity and the water–referenced velocity [
The motion time of the distance S between neighbor
waypoints can be obtained by
4 Simulation and Primary Sea Experiment
In order to verify the availability of the coordinate control
algorithm, an actual deployment of three Petrel-II
gliders has been carried out in the South China Sea. In this
section, a simulation test of optimal control base on LEC
(see Section 3.3.1) is also presented to show the necessity
of the method.
4.1 Simulation Test of Optimal Control Based on LEC
The Petrel-II glider is taken as the simulation object. The
energy consumption model expressed by Eqs. (16)‒(19)
is programmed in MATLAB to implement the
simulation. The hydrodynamic coefficients and the subsystem
parameters of Petrel-II involving in the model are listed
in Table 2. For simplicity, the depth density value of
1000 m is taken as a constant seawater density, which is
obtained by fitting the experiments data [
] of Petrel-II
deployed in the South China Sea.
The distance between neighbor waypoints is set to be
6 km in the simulation. Figure 8 shows the regularity of
the energy consumption with the net buoyancy B,
diving depth d and the number of profiles n. The energy cost
increases along with the increase of the diving depth as
shown in Figure 8. The energy cost by one-profile
gliding is lower than two-profile gliding, and the one-profile
energy cost increases faster than the two-profiles energy
cost with the increase of the diving depth, which
illustrates that the number of the profiles should be less in the
practical glider operation. And the energy cost decreases
to a minimum value then increases along with the
increase of the net buoyancy. This implies that the LEC
method is necessary to obtain an optimal net buoyancy
which minimize the energy consumption.
There are maximally five profiles calculated by the LEC
constrained by the gliding angle range by setting the
desired diving depth to 1000 m and the waypoints
distance to 6 km. The results are shown in Figure 9, and the
comparison of five different numbers of gliding profiles
based on LEC
| f |
Heading angle ϕ
shows the optimal net buoyancy locating on the curve of
Figure 10 shows the energy consumed without and
with the existence of the ocean flow by setting the
distance to 6 km and the diving depth 1000 m under
oneprofile gliding, respectively. The blue solid line represents
the regulation without ocean flow and the blue dash line
represents the result with a flow at speed of 0.1 m/s. It
shows that the optimal net buoyancy value and the
energy value get bigger when ocean flow exists. The value
of the optimal net buoyancy and minimum energy can be
obtained by the Algorithm 1. The optimal net buoyancy
et buoyancy B / N
Figure 8 Regularity of the energy consumption with the net buoy‑
ancy B, diving depth d and the number of profiles n
1 2 3 4 5 6
Net buoyancy B / N
Figure 9 Regularity of the energy consumption of 1000 m diving
is 4.0 N and 5.4 N respectively. And the corresponding
minimum energy is 6.5440 × 104 J and 7.6193 × 104 J.
This illustrates that it costs more for glider to move to
the desired waypoint when ocean flow existing and it also
implies that the high net buoyancy regulating ability is
important in the glider system designed to operate under
Figure 11 shows the energy consumption under the
hybrid motion mode with the same motion conditions
of S and d. The result shows that one-profile motion
costs more energy than two-profile motion. The
regulation is influenced by the existence of the propeller
propulsion compared with Figures 8‒10. The energy cost by
hybrid motion is much larger than in the unmixed
gliding, which illustrates that the major energy is consumed
by the motor of screw propeller and in order to ensure
long term task, the hybrid mode should be applied only
when fast motion is necessary. Based on LEC, the
optimal rotate speed is 1000 r/min, the optimal net buoyancy
is 7 N and the minimum energy is 3.2877 × 105 J .
4.2 Actual Deployment in the South China Sea
A fleet of three Petrel gliders, referred to as EG03, EG04
and EG05, was deployed in the South China Sea in
September 2014. The goal of the experiment was to test the
coordinate control algorithms delivered in Section 3.
Figure 12 shows the mission area where the three
gliders move as a triangle to two targets in order. The yellow
dash line around targets is the effective area with a radius
of 5 km. The two target positions of EG03, as a leader of
the fleet, are:
The start position of EG03, EG04 and EG05 are:
P1 18◦18′59′′N , 111◦35′26′′E ,
P2 18◦23′19′′N , 111◦31′55′′E ,
P3 18◦18′54′′N , 111◦31′42′′E .
The geometry of the formation is constrained by the
interactive distance between EG03 and EG04, EG03 and
EG05, EG04 and EG05 which are 10 km, 7 km and 10 km,
The trajectories of the gliders were generated by the
fleet trajectory planner which shaped the desire
formation geometry and achieved the sailing goals. Generally,
560 570 580 590
Position coordinate x / km
Figure 13 Trajectory of the formation generated by the fleet trajec‑
Figure 12 Mission area of the sea trial
The ordinal of profiles n
The ordinal of profiles n
The ordinal of profiles n
the trajectories are renewed every two or three days by
updating current position of the glider, the environment
information and current task arrangement. As this
experiment was a short-term test for only three days, the
trajectories were calculated once when the task began. The
planned trajectories are shown in Figure 13, in which
the coordinates of the gliders are converted to the earth
coordinates from the latitude–longitude coordinates. The
glider was commanded to dive to average depth of 800 m
every profile. The waypoints of the leader glider EG03
were chosen by the waypoints generator by giving the
desired distance d equal to 3 km with a truncation error
of 0.3 km. The waypoints of EG04 and EG05 were set
by the position related to the corresponding moment of
every EG03 waypoint. The waypoints near the two desire
positions were alternated by the latter. The small red
cycle, red * and red × in Figure 13 represent the planned
waypoints of EG03, EG04 and EG05, respectively.
The total number of profiles, the net buoyancy of
every profile and the heading angle after every surfacing
was determined by the onboard controller considering
the energy consumption and the ocean flow
environment. In this case, each glider was desired to run 15
profiles during the mission. Specifically, an addition profile
before the desired motion is necessary to test the status
of each components onboard and calibrate the control
coefficients referenced by the sea environment, which is
always set to dive less than 100 m. The actual fleet
trajectory is shown in Figure 14. Compared with the planned
trajectory shown in Figure 13, the actual fleet trajectory
keeps the path shape and formation geometry basically.
The surface locations of each glider float around the
preset waypoints. The position errors are mainly caused by
the uncertainties of ocean environment, the errors of the
flow estimation, the errors of the GPS location, the
latencies of communication and the errors of control system.
Figure 15 records the moving process of each glider in
vertical plane. The diving depth of each glider is detected
by the onboard pressure sensor. The total number of
The ordinal of profiles n
The ordinal of profiles n
The ordinal of profiles n
Figure 19 Trajectory error of each glider
The ordinal of profiles n
The ordinal of profiles n
The ordinal of profiles n
diving profiles is 16 with an additional test profile at the
depth of 50 m. And the depth of other profiles is mainly
800 m with an error range of [− 10, 10] m. The average
net buoyancy of each profile is calculated by the records
of the residual oil volume in the inner ballast, as shown in
Figure 16, which is larger than the optimal value shown
in Figures 9, 10. This is caused by the existence of ocean
flow and the errors of the onboard control system. The
actual control heading angle is shown in Figure 17. The
sharp changes of the heading angle happened in the
inflection points of the trajectory and the area that the
flow speed might be higher than the through-water speed
of the glider.
The minimum energy consumption of each profile was
calculated by choosing optimal control variables before
each diving. The actual energy consumption was obtained
by the real-time onboard records of the battery
voltage and current. Figure 18 gives a comparison between
the simulation results and actual energy consumption.
In Figures 18(a)‒(c), the yellow bar and blue bar
represent the actual profile energy cost Ea and the simulated
energy cost Es. The average simulated energy cost of
EG03, EG04 and EG05 is 6.6852 × 104 J, 6.6880 × 104 J
and 6.6862 × 104 J. The corresponding actual energy
consumption of each glider is 8.6718 × 104 J, 8.6716 × 104 J
and 8.6525 × 104 J.
Figures 18(d)‒(f ) shows the percentage difference
between the two quantities, which is in the range of
[22%, 24%] basically. The difference in Figure 18 is mainly
caused by the limitation of calculation model which
considered only vertical motion consumption and the errors
of onboard control.
Trajectory error of each glider and the distance
between gliders are adopted to evaluate the performance
of the fleet controlled by the method presented in this
paper. The results are shown in Figures 19, 20. The
trajectory error of each profile is defined by the distance
between the desired position and the actual surfacing
position. The maximum error of each glider is 2.41 km,
1.3 km, 1.9 km respectively, as shown in Figure 19. The
distance between gliders at each surfacing can help to
evaluate the geometry maintaining performance of the
formation. As shown in Figure 20, the distance fluctuates
around the desired distance with a floating range of less
than 2 km. The results prove that the fleet can basically
move along the desire trajectory and keep the desired
formation shape during the sea experiment. The higher
trajectory error might be caused by the low estimate
precision of the ocean flow, low control accuracy and
uncertainty error. This implies that the regional ocean model
which can forecast the ocean environment might be
necessary in the coordinate control of multi-HUG formation.
(1) A multi-layer coordinate control strategy is
proposed to achieve the coordinate control, motion
optimization of Multi–HUG formation.
(2) An energy consumption model is constructed for
HUGs with the consideration of hybrid motion.
The Least Energy Consumption (LEC) algorithm is
proposed to minimize the motion energy cost with
consideration of ocean flow existence.
(3) The regularities of HUG energy consumption with
motion variables is studied by simulation. The
results show that the number of profiles is better
to be less to extant endurance and the energy
consumption under ocean flow is larger than the
situation without flow existence, which need larger
net buoyancy. It also suggests the propeller costs
much more energy than other components under
hybrid motion which need the largest net
buoyancy to save energy.
(4) A primary sea experiment of three Petrel-II gliders
is achieved in the South China Sea. The actual fleet
trajectory is similar with the planned path and the
formation geometry fits the shape request. The
trajectory error is less than 2.5 km and the formation
shape error is less than 2 km which meet the preset
task request. The results verify the feasibility of the
multi-layer control strategy and the effect of LEC
(5) The modeled energy consumption is about
76%‒78% of the actual energy consumption of each
glider. This implies the model can basically describe
the energy cost of HUG. The future work could be
drawn in more precise model considering
DYX carried out the dynamic modeling studies, and drafted the manuscript.
ZLW carried out the control system design. YHW carried out the sea trials of
the Petrel underwater gliders, participated in the analyzing of the test data
and the design of the Petrel underwater glider. SXW carried out the design of
the Petrel underwater glider, participated in the analyzing of the test data. All
authors read and approved the final manuscript.
Dong‑ Yang Xue, born in 1987, is currently a PhD candidate at School of
Mechanical Engineering, Tianjin University, China. She received her master
degree from Northeastern University, China, in 2011. She received her bachelor
degree from Northeastern University, China, in 2009. Her research interests
include autonomous underwater vehicle and multiple agents control.
Zhi‑Liang Wu is currently an associate professor at School of Mechanical
Engineering, Tianjin University, China. Her research interests focus on coordina‑
tion of mobile autonomous agents.
Yan‑Hui Wang born in 1979, received his bachelor, master and PhD
degrees on mechanical engineering from Tianjin University, China, where he is
currently a professor at School of Mechanical Engineering. He has been involved
in the research of various underwater vehicles.
Shu‑ Xin Wang born in 1966, received his bachelor degree on mechanical
engineering from Hebei University of Technology, China, in 1987 and master and
PhD degrees on mechanical engineering from Tianjin University, China. He is
currently a professor at Tianjin University, China and has been active in various
aspects of the research and design of ocean vehicles since 2000.
Supported by National Key R&D Plan of China (Grant No. 2016YFC0301100),
National Natural Science Foundation of China (Grant Nos. 51475319,
51575736, 41527901), and Aoshan Talents Program of Qingdao National Labo‑
ratory for Marine Science and Technology, China.
The authors declare that they have no competing interests.
Ethics approval and consent to participate
Springer Nature remains neutral with regard to jurisdictional claims in pub‑
lished maps and institutional affiliations.
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