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486 IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 | NOV-DEC 2011

A Review Note for Position Control of an Autonomous Underwater Vehicle

Ahmed Rhif Department of Electronics, High Institute of Applied Sciences and Technologies, Sousse, Tunisia

(Institut Supérieur des Sciences Appliquées et de Technologie de Sousse)

Abstract

A new autonomous underwater vehicle (AUV) called H160 is described in this article. The first prototype of this AUV has been realized through collaboration between two partners, which are the Laboratory of Data processing, Robotics and Micro electronic of Montpellier (LIRMM) and the ECA‑HYTEC (specialist in the de‑ sign and manufacture of remote controlled systems in “hostile” environments). This paper shows a general presentation of the vehicle, its hardware and software architecture including the process modeling and the control law used. Simulation results presented are based on the AUV mathematical model.

Keywords Autonomous underwater vehicle, Position control, Sliding mode control, Underwater vehicle.

1. Introduction

The concept of underwater vehicle is not a recent idea. The first proposal was designed by William Bourne in 1578. In 1664, Cornelis Van Drebbel proposed the first underwater vehicle advancing using 12 oarsmen equipped with special oars that could be actuated in order to carry out vertical movements. This ovoid boat was built of wood and had been tested experimentally. In 1776, David Bushnell and his brother introduced the first submarine “Turtle” built out of steel. Its principle operation was similar to that of the current submarines. This mobile used a propeller for its propulsion. The machine was immersed by actuating a valve, allowing the water admission in a tank which was used as bal- last. It went up thanks to a pump which expelled water. Oxygen autonomy was of 30 min (Pararas‑Carayannis, 1976). Nowadays, the submarines have strongly evolved from a technological point of view. A classification of the underwater vehicles in two groups is proposed: Manned vehicles and unmanned vehicles [1].

Under the manned vehicles, we can distinguish two categories of underwater vehicles: • The large‑sized submarines operated by a crew which

can reside on during long periods. This category belongs to the military submarines.

• The small‑sized submarines intended for the great depths’ exploration. The crew of this kind of machine is reduced (two to three persons) and the oxygen quan- tity is limited. For example, Nautile was conceived by Ifremer 1 in 1984 and can immerse up to 6000 m with three passengers. Its main missions were the search for hydrothermal sources in the Pacific Ocean.

The unmanned vehicle was specially the interest of the navy. In 1866, the Austrian navy asked Robert Whitehead to develop a new weapon for the warships. He showed the effectiveness of a system propelled at a speed of 3 m/s to a distance of 700 m transporting an explosive load: The torpedo was born. However, this machine did not have any monitoring system. Those underwater vehicles exist in three different technology: those con- nected to the surface by a cable, vehicle connected by an acoustic bond, and finally completely autonomous vehicles [2‑4].

Actually, the first autonomous underwater vehicles (AUVs) developed during 1960s–1970s were as fol- lows: • The Self‑propelled Underwater Research Vehicle

(SPURV, USA, 1977): It weighed 480 kg and could operate at a speed of 2.2 m/s during 5 hours until a depth of 3000 m. The vehicle was acoustically controlled from the surface. The researchers used it to make conductivity and temperature measures to perfect the theoretical wave modeling.

• Remotely Operated Vehicles (ROVs): Machines equipped by a camera operated by an operator, connected to surface via a cable, called umbilical, by which the orders, energy and/or measurement are provided. The principal disadvantage of these robots is the presence of the umbilical which makes their movements complicated and especially the extent of their fields of application.

• Unmanned Underwater Vehicles (UUVs): Uninhabited underwater machines which are equipped with sophisticated systems for their navigation and their work according to their degree of autonomy. The

487IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 | NOV-DEC 2011

principal constraint lies in the energy necessary to embark for mission realization. There exist two types of UUVs:

• The AUV can be defined as a machine knowing its position and which surfs toward an objective [ Figure 1]. For this, we have to draw an operation list to be carried out beforehand. The operators do not intervene under nominal operation; the machine is completely autonomous.[5]

• The Untethered Underwater Vehicle (UUV) func- tions like the AUV, but there exists an acoustic bond between the surface and the machine, allowing the verification and the data exchange. In the event of problems, the operator can order the system to be in an emergency situation implying its return to the surface. It is important to note that the redundancy of term UUV poses a problem. In fact, UUVs are also called AUVs.

2. Autonomous Underwater Vehicle Description

The AUVs can be classified into two types depending on the immersion depth, i.e. AUVs coastal and AUVs deep seas. From a few hundred meters of depth, the dimensions, structure and the characteristics of the AUVs change. This limit of depth makes difference between the deep seas vehicles from the coastal one [2].

Today, the underwater robots are an integral part of the scientific equipment for sea and ocean exploration. Many examples show that ROVs and AUVs are used in many fields and for various applications like the inspec- tion, the cartography or bathymetry [1]. However, we can distinguish a limiting depth for the various types of existing autonomous underwater machines. Indeed, starting from 300 m, the structure, dimensions and the characteristics of these vehicles change. We have, on one side, AUVs Hugin 3000 type of Kongsberg Simrad, the Sea Oracle of Bluefin Robotics or Alistar 3000 of ECA, which can reach depths of 3000 m, have a very great autonomy, considerable dimensions and a weight which requires important logistics. On the other side, AUVs of Remus Hydroid or Gavia Hyfmind types, with much less autonomy, but of reduced dimensions and logistics and with good modularity capacities, seem to be the per- fect tool for the exploration of not very deep water [2].

In this context, the Laboratory of Data processing, Robotics and Micro electronic of Montpellie (LIRMM) and the ECA‑HYTEC company became partners to develop the first prototype of the AUV H160. This prototype was developed to surf and position with the using a global positioning system (GPS). On the surface, the torpedo must be able to transmit the mission’s data. The applications concerned are the inspection, bathym- etry, the chemical data acquisition or sonar and video

images. The machine also has the possibility of surfing between 1 and 2 m of depth with no angle of immersion.

H160 is a torpedo type vehicle of small size and low cost, dedicated to the applications in not very deep water (up to 160 m). The vehicle measures 1.80 m in length with a diameter of 20 cm and a weight of 50 kg. Thanks to its small size, the tests on the sea require a logistics reduced to the minimum to two people and a motor boat. The prototype is able to accomplish a mission of at least 3 hours, maintaining its speed of 3 knots. Its positive floatability makes it possible for the torpedo to go back to surface after the end of each mission. H160 is fed by a battery 48 V/16 Ah of the NiMH type, has an actuator with DC current 230 W and 430 N cm servo‑motors for the riders control. The torpedo immersion capacity with no angle of pitching is due to its pair of surface riders that constitutes the main feature of this machine [2‑5].

The torpedo is a cylindrical vehicle form as shown in Figure 2. Its structure is mainly made up of aluminum. We can detail the prototype in seven parts: 1. The principal part is the electronic section, composed

of two stages. The first stage accommodates the battery, while the second one is composed of all the embarked charts (sensors, power, PC, etc.). This part is obviously tight.

2. Section made by the antennas for GPS, Radio and Wifi, also by the riders’ control of the front immersion.

3. The sensor Conductivity Temperature Depth (CTD) and sidescan sonar are in a wet part.

4. The Doppler Log is located in a tight part. 5. The nose of the vehicle composed of a CCD camera

and two sounders. 6. Behind the principal part, we find the pressure

Figure 1: Schematic of an AUV.

Figure 2: Different components of the H160.

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488 IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 | NOV-DEC 2011

pick‑ups and an emergency acoustic pinger in a wet part.

7. Finally, the propeller and the riders constitute the engine back part.

3. Autonomous Underwater Vehicle Modeling and Control

3.1 Mathematical Model

For the modeling of this system, two referentials are defined [Figure 3] [6]: One fixed referential related to the vehicle which is defined in an origin point: R

0 (x

0 , y

0 ,

z 0 ) and the second one related to the Earth R(x, y, z) [1].

The referential related to the mobile R0 could be formu- lated using the referential R as shown in Equation (1):

r r r

U U U

U U

x x z

y y x

z z

= +

cos sin

φ φ

θ θ

ψ ψ UUx



 

  

(1)

The kinematic model is represented as follows (Equa- tion (2)):

   

 

= = 

 



  =



 



  

 J v

J J

v vc

c x

x c ( )

( ) ( )

2 1

1 2 3 3

3 3 2 2

0 0 



 

(2)

where J c1

( 2 ) is the linear speed transformation matrix

and J c2

( 2 ) is the angular speed transformation matrix.

η η η

η η φ θ ψ

= 

 



  =





  





  

= 



  





  

= 

 



 

2 1 2

; ; x y z

v v v

;; ;

;

v u v w

v p q r

X Y Z

1 2

2 1

= 



  





  

= 



  





  

= 

 



  =





 Γ

Γ Γ

Γ 





  

= 



  





  

; Γ2

K M N

(3)

 Represents the robot position related to the R(x, y, z) reference, u represents the robot speed related to R

0 (x

0 , y

0 , z

0 ), and Γ is the forces vector applied to the

mobile.

The dynamic equation is represented by:

M C v D v gη η η η ηη η η η η η η τ( ) ( , ) (( , ) ( )&& & &+ + + = (4)

where M is the inertia matrix, C the Coriolis matrix, D

the rubbing forces matrix, g the hydrostatic effort vector and th is the input control vector.

In order to control the behavior of an underwater vehicle in the immersion phase, we must be able to vary its buoyancy. The buoyancy of a vehicle in immersion is the difference between the Archimedes pressure and the gravity. Buoyancy (denoted as Φ

1 ) depends on the

vehicle mass (m), its volume (V) and the density of water (). So, it can be defined as (Equation (5)):

Φ1 = V-m (5)

The AUV presents a strong nonlinear aspect that appears when we describe the system in three dimensions (3D), so the state function will present a new term of disturbances as shown in Equation (6).

&X AX Bu X u= + +( , ) (6)

where | |j (X, u)| | ≤ MX, M > 0.

As we consider only the linear movement in immer- sion phase, we need only four degrees of freedom. For this, we describe the system only in two dimensions (2D). With all the developments done, the result- ing state space describing the system is given by Equation (7):

X = AX + Bu (7)

where

w q





    





    

= −

 ,

. . . . .

0 47 0 3 0 0 0 69 0 79 0 36 0 0 1 0 0 1 0 1 00

0 05 0 14 0 0





   





   





   





   

andB

where ω is the linear velocity, q the angular velocity, θ the inclination and z is the depth.

Figure 3: AUV engine referentials.

u Xo

Origin referential

q r

v w

p Fix referential

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489IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 | NOV-DEC 2011

3.2 Autonomous Underwater Vehicle Controller Design

3.2.1 The Sliding Mode Control

The AUV position control is ensured by the sliding mode approach. The choice of such a controller is imposed by the strong nonlinear aspect of the AUV, thanks to the robustness of this approach [7].

The development of the sliding mode approach occurred in the Soviet Union in the sixties with the discovery of the discontinuous control and its effect on the system dynamics. This approach is classified in the monitoring with Variable System Structure (VSS) [8,9]. The sliding mode is strongly requested due to its facility of establishment, its robustness against the disturbances and model uncertainties [10]. The principle of the sliding mode control is to force the system to converge toward a selected surface and then to evolve there in spite of the uncertainties and the disturbances. The surface is defined by a set of rela- tions between the state variables of the system. The synthesis of a control law by sliding mode includes two phases: • The sliding surface is defined according to the control

objectives and to the wished performances in closed loop.

• The synthesis of the discontinuous control is carried out in order to force the trajectories of the system state to reach the sliding surface, and then to evolve in spite of uncertainties, of parametric variations, etc. The sliding mode exists when commutations take place in a continuous way between two extreme values u

max and u

min [11]. To ensure a good commutation,

we choose a relay type control and get the desired result when commutations are sufficiently high [12]. The sliding mode control [13] has largely proved its effectiveness in the reported theoretical studies. Its principal scopes of application are robotics [13‑17] and the electrical motors [12,18,19].

For any control device which has imperfections such as delay, hystereses, which impose a frequency of finished commutation, the state trajectory oscillates in the vicinity of the sliding surface. A phenomenon called chattering appears [20].

3.2.2 The High Order Sliding Mode Control

The high order sliding mode consists of the sliding variable system derivation [21,22]. This method allows the total rejection of the chattering phenomenon while maintaining the robustness of the approach. For this, two algorithms could be used: • The twisting algorithm: The system control is

increased by a nominal control ue; the system error,

on the phase plane, rotates around the origin until it has been canceled. If we derive the sliding surface (S) n times, we see that the convergence of S is even more accurate when n is higher [23].

• The super twisting algorithm: The system control is composed of two parts u1 and u2 with u1 being the equivalent control and u2 the discontinuous control used to reject disturbances. In this case, there is no need to derive the sliding surface [6]. To obtain a sliding mode of order n, in this method, we have to derive the error of the system n times.

In [24], a comparison between the two algorithms was achieved. In conclusion, we note that the super twisting algorithm is more reliable than the twisting algorithm, despite the approximate results, since it does not ensure the same robustness to perturbations. Indeed, in his arti cle [24], the author used the second‑order sliding mode to improve the performances of a turbine torque. Notice that the conventional control approaches of double‑fed asynchronous generator is incapable to make the torque convergence to the desired value, then, the choice. Then, the choice of the high order sliding mode approach was based on its robustness against disturbances. On the other hand, the use of linear surfaces in the control laws synthesis by sliding mode was considered satisfactory by the author in terms of stability. However, the dynamics imposed by this choice is relatively slow. To overcome this problem, we may use nonlinear sliding surfaces. In the same direction, to work on the speed and position regulation or power of asynchronous machines, we often limit the stator cur- rent (torque) that can damage the system. In this case, the author suggested the use of the high order sliding mode approach considering a nonlinear switching law that consists of two different sliding surfaces S1+ and S1− using two switched positions. Thus, we get two limits bands, a lower band and a higher one that reduces the chattering phenomenon.

In the literature, different approaches have been pro- posed for the synthesis of nonlinear surfaces [6,10,23‑ 27]. In [25], the proposed area consists of two terms, a linear term that is defined by the Herwitz stability criteria and a nonlinear term used to improve transient performance.

In [10], to measure the armature current of a DC motor, Zhang Li used the high order sliding mode since it is faster than the traditional methods such as vector control. To eliminate the static error that appears when measur- ing parameters, we use a Proportional Integrator (PI) con- troller [23,28‑30]. Thus, the authors have chosen to write the sliding surface in a transfer function of a proportional integral form while respecting the convergence proper- ties of the system to this surface. The same problem of

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490 IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 | NOV-DEC 2011

the static error was treated by adding an integrator block just after the sliding mode control [31‑34].

The tracking problem of an AUV is treated by using sliding mode control [Figure 4] with nonlinear sliding surface as shown in Equation (8). s(t)=k

1 e(t)+k

2 e . (t) (8)

where e(t) is the system error, k 1 > 0 and k

2 > 0.

To ensure the state convergence to the sliding hyper- plane, we have to verify the Lyaponov stability criterion (Equation (9)) [35‑37].

ss. ≤ ‑h|s| (9)

where h>0.

The control law can be then composed of two parts:

u=u 0 +u

1 (10)

• u 0 the nominal control

• u 1 the discontinuous control allowing to reject the

disturbances.

4. Simulation Results and Discussion

Simulation results were accomplished using the MATLAB software for both the first‑ and second‑order sliding modes of the state function (Equation (7)) that represent the process in the immersion phase using four degrees of freedom. In

Rhif A: AUV Position Control

2.5

2.0

1.5

1.0

0.5

-0.5

0.15

0.10

0.05

-0.05

-0.10

2.0

1.5

1.0

0.5

-0.5

-1.0

-1.5

-2.0

2.0

1.0

-1.0

-2.0

-3.0

-4.0

-5.0

-6.0

-7.0

0 5 10 15 20 25 30 35 40 45 50

0 2 4 6 8 10 12 14 16 18 20

0 5 10 15 20 25 30 35 40 45 50

Z (m

) ta

ta (d

eg )

w (d

eg /s

ec )

t(s) t(s) (a) (b)

Figure 4: Sliding mode control bloc representation.

Equivalent control

∑

∑ Switching control

Surface

Transducer

AUV

ueq

uc xd e+

u x

Figure 5: First‑order sliding mode control.

491IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 | NOV-DEC 2011

this simulation, we need to study the system output evolu- tion (the depth z), the linear control (u), the inclination θ and the angular velocity q that ensures this output.

The sliding surface parameters used are k 1 =1 and k

2 =3.

The desired immersion point was fixed on 2m. For the first‑order sliding mode, the simulation shows that the system output [Figure 5a] reaches its desired value in a short time (about 5 s) with good precision. But we notice the presence of the chattering phenomenon (oscilla- tions on the steady state). Moreover, the variations in the inclination θ [Figure 5c] and in the angular velocity q [Figure 5d] are due to this chattering phenomenon.

Other ways, the control level and the frequency of switching of this control [Figure 5b] are not very sharp that gives good operating conditions to actuators. By using high order sliding mode control, the chattering phenomenon has disappeared, the output evolution [Figure 6a] is more stable and the tracking process is more precise. The control level of the process is now less than the first solution but its commutation frequency is sharper [Figure 6b]. The inclination θ [Figure 6c] and

the angular velocity q [Figure 6d] are now very close to 0 which means that the system reaches the steady state.

5. Conclusion

An extensive review of the literature of AUVs and tracking process by sliding mode has been carried out. In this work, major components like actuators, sensors, amplifier, etc. have been listed. AUVs’ controllers have been presented, detailed and justified by the simulation results. This paper could be a ready study for those who want to start research with AUVs and sliding mode control.

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Figure 6: Second‑order sliding mode control.

2.5

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)

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492 IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 | NOV-DEC 2011

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Rhif A: AUV Position Control

AUTHOR Ahmed Rhif was born in Sousse, Tunisia, in August 1983. He received his Engineering diploma and Master degree, respectively, in Electrical Engineering in 2007 and in Automatic and Signal Processing in 2009 from the National School of Engineer of Tunis, Tunisia (L’Ecole Nationale d’Ingénieurs de Tunis E.N.I.T). He is currently pursuing his PhD degree. His research interest includes

control and nonlinear systems.

E‑mail: [email protected]

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