=Paper=
{{Paper
|id=Vol-3734/invited13
|storemode=property
|title=The control of four-track underwater mining vehicle based
on NNPID
|pdfUrl=https://ceur-ws.org/Vol-3734/paper13.pdf
|volume=Vol-3734
|authors=Yixuan Tong,Yichun Tao,Mingyu Yang
|dblpUrl=https://dblp.org/rec/conf/iccic/TongTY24
}}
==The control of four-track underwater mining vehicle based
on NNPID==
https://ceur-ws.org/Vol-3734/paper13.pdf
The control of four-track underwater mining vehicle based
on NNPID
Yixuan, Tong1, ∗, Yichun Tao1 and Mingyu Yang1
1 Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, China
Abstract
The article introduces a novel control algorithm for an underwater four-track mining vehicle
utilizing NNPID, which effectively tackles the issue of unstable speed control in challenging
underwater conditions that traditional fixed parameter algorithms struggle to overcome. The
algorithm was evaluated through simulation utilizing RecurDyn software, showcasing its
effectiveness in achieving precise speed and directional control of the vehicle.
Keywords
control strategy, BP network, PID, underwater track vehicle
1. Introduction
The ocean floor abounds with valuable minerals, including cobalt-laden crusts and
manganese nodules [1], both of which serve as vital suppliers of rare earth elements
essential for contemporary technological applications, from smartphones to electric
vehicles. As the demand for these elements surges, driven by the rapid advancement of
technology and the push towards sustainable energy solutions, the exploration and
exploitation of underwater mineral resources have gained significant interest. The mining
of submarine metal resources is more difficult than that on land, which requires underwater
mining vehicles to complete the mining of submarine metal. However, the pursuit of these
resources is fraught with challenges. Unlike terrestrial mining operations, where heavy
machinery can operate with relative ease on stable ground, underwater mining presents a
unique set of difficulties. The harsh underwater environment, characterized by high
pressure, low visibility, and unpredictable seabed conditions, demands specialized vehicles
capable of navigating and working effectively in these conditions.
In the 1960s and early 1970s, the extraction of underwater minerals was primarily
conducted through the bucket mining system and the shuttle vessel mining system [2-4]. In
the late 1970s, several consortia, including OMI (Ocean Mining Inc), OMA (Ocean Mining
ICCIC 2024: International Conference on Computer and Intelligent Control, June 29–30, 2024, Kuala Lumpur,
Malaysia
∗ Corresponding author.
tongyixuan@sia.cn (Y. Tong); taoyichun@sia.cn (Y. Tao); yangmysia@163.com (M. Yang)
0009-0007-9293-9144 (Y. Tong); 0009-0001-5198-026X (Y. Tao); 0009-0000-4122-3727 (M. Yang)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Associates), and OMCO (Ocean Minerals Company-Lockheed), began the extraction of
underwater minerals for the first time using underwater mining vehicles [5]. Afterwards,
various countries have also conducted sea trials at different depths for key equipment such
as underwater mining vehicles. Japan conducted a 2,000-meter water depth mineral
collector test in 1997 [6], India carried out a 400-meter-class partial system sea trial in the
2000s [7] and a seabed walking test for a mining vehicle in 2021, South Korea conducted a
simulated polymetallic nodule collection test at 1,370 meters water depth in 2013 and a
mineral lift pump and intermediate storage test at 1,200 meters water depth in 2015 [8],
and the European Union performed an operational and disturbance test for a mining vehicle
at 300 meters water depth in 2022, among others. However, there is a current absence of a
well-defined and mature model for the development of marine mineral resources on a
global scale, and the commercial extraction of these resources has not yet been achieved.
To enhance the mobility of track vehicles over the challenging sea floor topography,
certain subsea mining machines are equipped with a four-track configuration, which
significantly bolsters their capability to overcome obstacles. The track design is
instrumental in optimizing the operational performance of these vehicles within the
demanding environment of deep-sea mining operations. However, due to the complex
condition of the seabed bottom [9], the four-track mining vehicle often cannot guarantee
that it can walk in accordance with the predetermined path, and it may be unable to walk in
a straight line due to skidding. The complex condition of the seabed, including its irregular
surfaces and varying consistencies, can lead to deviations from the predetermined path,
causing the vehicle to skid or veer off course. Moreover, maintaining a consistent speed is
crucial for the efficiency of ore collection, as fluctuations in speed can affect the overall yield
and success of the mining operation. At the same time, it is necessary to ensure that the
vehicle can travel at a constant speed, so as to ensure the ore collection rate control. The
conventional PID controllers are used widely in the field of underwater vehicle control.
However, the underwater conditions are changing, so PID with fixed parameters cannot
solve the control problem well [10].
The paper introduces a novel control method for an underwater four-track vehicle
utilizing Neural Network PID (NNPID), designed to address the instability issues
encountered when employing fixed-parameter control algorithms in the complex
underwater setting. This approach uses neural network adaptability to dynamically adjust
parameters, ensuring robust and reliable vehicle operation across varying underwater
conditions. The paper is organized as follows: Part 2 introduces the dynamics model of four-
track mining vehicle; Part 3 introduces a control algorithm for four-track mining vehicle. In
Part 4, the proposed algorithm is verified by using RecurDyn software. Part 5 presents the
conclusion.
2. Vehicle dynamic model
Underwater track vehicles mainly work on the two-dimensional plane of the seabed, thus
the vehicles only moves on the horizontal plane and have three degrees of freedom [11].
The dynamic model of track vehicles is shown as Figure 1.
B
y
ω1
ω2
ω0 x
O2' O2 O1
'
O1 O
C2 C1
RS
Figure 1: Dynamic model of track vehicles
𝑂𝑂 is the steady state steering center of the track vehicle, and the vehicle dynamic model
is established with 𝑂𝑂 point as the coordinate origin [12]. 𝑅𝑅𝑠𝑠 is the turning radius of the
mining vehicle, and 𝐵𝐵 is the distance between the left and right tracks. 𝜔𝜔0 is the angular
speed of the vehicle. 𝑂𝑂1 and 𝑂𝑂2 are the intersection points of 𝑥𝑥 axis with the center line
of the left and right tracks. 𝑂𝑂1 ′ and 𝑂𝑂2 ′ are the instantaneous rotation centers of the inner
and outer tracks respectively. The distance from 𝑂𝑂1 to 𝑂𝑂1 ′ is 𝐶𝐶1 , the distance from 𝑂𝑂2 to
𝑂𝑂2 ′ is 𝐶𝐶2 . The velocity of point 𝑂𝑂2 to the ground is
B
Voo2 ω0 (
= + Rs ) (1)
2
The projection of point O on the track junction with respect to the speed of the track
frame is
U=
o2 ωout ⋅ r (2)
𝜔𝜔𝑜𝑜𝑜𝑜𝑜𝑜 is the angular speed of the outer track motor, and 𝑟𝑟 is the radius of the track drive
wheel.
The speed of the track ground point relative to the ground is
Vo2o2 = −ω2 c2
Voo2 − U o2 = (3)
The steering radius of the track vehicle can be obtained from the above formulas [13]
B B
ωout ( + c2 ) + ωin ( + c1 )
2 2 (4)
RS =
ωout − ωin
3. Control strategy
Because it is difficult to establish the mechanical model of underwater vehicles, especially
for underwater tracked vehicles, the ground soil mechanical parameters are difficult to
measure. Thus, PID has become one of the most commonly used control algorithms in
underwater vehicle control [14]. To enhance adaptability to fluctuating soil environments,
this paper proposes the implementation of a Neural Network PID (NNPID) control strategy
for underwater vehicles.
The structure of NNPID controller is shown as Figure 2. On the basis of the basic PID, a
neural network module is added to adjust the three parameters, K p , K i , K d . The paper
adopts the incremental PID control algorithm, so
u (k=
) u (k − 1) + ∆u (k ) (5)
u (k ) K p (e(k ) − e(k − 1)) + K i e(k ) + K d (e(k ) − 2e(k − 1) + e(k − 2))
∆=
(6)
u (k=
) u (k − 1) + ∆u (k )
Neural
Network
Kp Ki Kd
r(k) E(k) Underwater y(k)
PID
Vehicle
Figure 2: The structure of NNPID controller
As shown in Figure 3, the network has 3 layers, and it has 4 input-layer nodes, 5 hidden-
layer nodes, 3 output-layer nodes. The input layer nodes include system states and error,
while the output layer nodes are three PID parameters, K p , K i , K d .
Input Layer i Hidden Layer j Output Layer k
y1
x1
x2
y2
x3
x4 y3
Figure 3: The structure of the network
The cost function is shown below:
1
E (k )
= (r (k ) − y (k )) 2 (7)
2
The network refreshed the weight coefficient of nodes by using the gradient descent
method [15].
∂E (k )
∆ωil(3) (k ) =
−η + αωil(3) (k − 1) (8)
∂ωil(3)
η is the learning rate and α is the momentum factor. And according to the chain rule,
there is
∂E (k ) ∂E (k ) ∂y (k ) ∂u (k ) ∂oi(3) ∂neti(3) (k )
= (9)
∂ωil(3) ∂y (k ) ∂u (k ) ∂oi(3) ∂neti(3) ∂ωil(3) (k )
And
∂neti(3) (k )
= oi(2) (k ) (10)
∂ωil (k )
(3)
∂E (k )
= − e( k ) (11)
∂y (k )
Finally, the weight coefficients of output layer can be derived as shown below [16].
∆ωli(3) (k ) =α∆ωli(3) (k − 1) + ηδ i(3)Oi(2) (k ) (12)
∂y (k ) ∂u (k )
δ i(3) = e(k )sgn( ) (3) g '(netl(3) (k )) (13)
∂u (k ) Ol (k )
And, the weight coefficients of hidden layer are
∂y (k ) ∂u (k )
δ i(3) = e(k )sgn( ) (3) g '(netl(3) (k )) (14)
∂u (k ) Ol (k )
∆ωij(2) (k ) =α∆ωij(2) (k − 1) + ηδ i(2)O (1) (15)
j (k )
3
δ i(2) = f '(neti(2) (k ))∑ δ l(3) wli(3) (k ) (16)
l =1
Where
2
g '( x) = (17)
(e + e − x ) 2
x
4
f '( x) = x − x 2 (18)
(e + e )
4. Simulation
The paper uses RecurDyn to build the dynamic model of the track vehicle to verify the
control algorithm. The model built in the RecurDyn is shown as Figure 4, and main
parameters of the vehicle are shown as table 1 [17].
Figure 4: The model of the track vehicle built in RecurDyn
Table 1
Main Parameters of Vehicle
Parameter Data
Vehicle mass in water(kg) 1000
Ground length of the front track(m) 0.6
Distance between front and rear tracks(m) 1.7
Ground length of the rear track(m) 0.6
Track guage(m) 1.5
Track width(m) 0.46
The walking of track vehicle on soft ground are closely related to the parameters of the
seabed soil [18], such as cohesion, shearing resistance angle, etc. In this paper, the
parameters of the real seabed soil are selected as the simulation parameters in RecurDyn,
as shown in table 2.
Table 2
The Parameters of The Real Seabed Soil
Parameter Data Parameter Data
Shearing Resistance
Terrain Stiffness 1.27×10-2 1
Angle(°)
Shearing Deformation
Exponential Number 0.7 25
Modulus
Cohesion(c) 10-3 Sinkage Ration 0.05
The control system is built using Simulink as shown in Figure 5, and co-simulation is
performed on Simulink and RecurDyn [19]. The RecurDyn model has 4 inputs, including
motor speed of four tracks, and 2 outputs, including the speed and heading of the vehicle.
After comparing the output speed and the set speed, the output heading and the set heading,
the control system calculates the track motor speed that the vehicle needs according to the
error of the speed and heading [20].
Figure 5: The model of the control system built in Simulink
Table 3
Parameters of NNPID
Parameter Data
Learning rate 0.5
Momentum factor 0.1
Sample time(S) 0.001
The model of neural network PID is shown as Figure 6, which has 2 inputs including
r (k ) and y (k ) , and 4 outputs including the k p , ki , kd and the output of the PID.
Figure 6: The model of the neural network PID in Simulink
The simulation time is set to 10 seconds, and the sample time is set to 0.001 seconds. As
shown in Table 3, the learning rate and the momentum factor of the neural network are set
to 0.5 and 0.1. By employing the dynamic vehicle model and control system, simulations
yield data on vehicle speed and heading, which are depicted in Figure 7 through a co-
simulation process. The proposed control technique is evaluated against both traditional
PID control and an uncontrolled direct drive approach.
0.03 1000
Direct Direct
NNPID 800 NNPID
0.025
PID PID
600
0.02
400
0.015
200
Speed(m/s)
Heading(°)
0.01 0
-200
0.005
-400
0
-600
-0.005
-800
-0.01 -1000
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
Time(s) Time(s)
(a)The heading of the vehicle (b)The speed of the vehicle
30
Kp
Ki
25 Kd
20
15
10
5
0
0 1 2 3 4 5 6 7 8 9 10
Time(s)
(c)The evolutions of the parameters of NNPID controller
Figure 7: The simulation data through co-simulation on Simulink and RecurDyn
As shown in Figure 6(a) and Figure 6(b), the newly introduced NNPID control algorithm
demonstrates superior performance in managing both speed and heading in comparison to
traditional PID and uncontrolled direct drive approach. Figure 6(c) illustrates how the
NNPID parameters, namely K p , K i and K d , have the capacity to self-adjust in response
to changes in the desired signal and converge towards a stable set of values.
5. Conclusions
The research presented in this paper successfully demonstrates the feasibility and
effectiveness of the NNPID algorithm for controlling underwater tracked vehicles. The
proposed control method has the potential to enhance the performance and operational
capabilities of underwater tracked vehicles, thereby expanding the possibilities for
underwater exploration, resource collection, and environmental monitoring. Furthermore,
the research opens up opportunities for future studies to explore the application of the
NNPID algorithm in other domains of unmanned underwater vehicles and robotics. The
significance of the NNPID algorithm lies in its ability to adapt to the complex and dynamic
underwater environment, which is a key advantage over traditional PID control methods.
By incorporating neural networks, the NNPID algorithm can learn from the changing
conditions and adjust the control parameters accordingly, resulting in improved speed and
heading control. This adaptability makes the NNPID algorithm particularly well-suited for
underwater operations where the environment is unpredictable and constantly changing.
The research also highlights the importance of using collaborative simulation tools like
RecurDyn and Simulink to evaluate the performance of control algorithms. By integrating
the multi-body dynamics simulation capabilities of RecurDyn with the control system
design features of Simulink, the research was able to provide a comprehensive assessment
of the NNPID algorithm’s effectiveness. This approach allows for a more realistic
representation of the underwater vehicle’s behavior and its interaction with the
environment, leading to more accurate and reliable results.
In conclusion, the research presented in this paper makes a significant contribution to
the field of underwater vehicle control. The introduction of the NNPID algorithm and its
successful evaluation through collaborative simulation provide a valuable framework for
future research and development in this area. As underwater operations continue to grow
in importance, the enhanced control capabilities offered by the NNPID algorithm have the
potential to drive advancements in underwater exploration, resource extraction, and
environmental monitoring.
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