**3.2 Speed and position control in horizontal plane**

Since AUV-XX is equipped with two transverse tunnel thrusters in the vehicle fore and aft respectively and two main thrusters (starboard and port) aft in horizontal plane, which can produce a force in the *x*-direction needed for transit and a force in the *y*-direction for maneuvering, respectively. So both speed and position controllers are designed in horizontal plane.

Speed control is to track the desired surge velocity with fixed yaw angle and depth, which is usually used in long distance transfer of underwater vehicles. Before completing certain kind of undersea tasks, the vehicle needs to experience long traveling to achieve the destination. In this chapter, speed control is referred to a forward speed controller in surge based on the control algorithm we introduced in above section, its objective is to make the vehicle transmit at a desired velocity with good and stable attitudes such as fixed yaw and depth.

Fig. 4. Position and speed control loop

Position control enables the vehicle to perform various position-keeping functions, such as maintaining a steady position to perform a particular task, following a prescribed trajectory to search for missing or seek after objects. Accurate position control is highly desirable when the vehicle is performing underwater tasks such as cable laying, dam security inspection and mine clearing. To ensure AUV-XX to complete work assignments of obstacles avoiding, target recognition, and mine countermeasures, we design position controllers for surge, sway, yaw and depth respectively for equipping the vehicle with abilities of diving at fixed deepness, navigating at desired direction, sailing to given points and following the given track, *etc*.

As for the desired or target position or speed in the control system, it is the path planning system who decides when to adopt and switch control scheme between position and speed, the desired position that the vehicle is supposed to reach, and the velocity at which the

Modeling and Motion Control Strategy for AUV 141

 β

To verify the feasibility and effectiveness of the motion control system for the vehicle AUV-XX, simulations are carried out in the AUV-XX simulation platform. The vehicle researched in this chapter named by AUV-XX, AUV-XX's configuration is basically a long cylinder of 0.5m in diameter and 5m in length with crossed type wings near its rear end. On each edge of the wings, a thruster is mounted, which is used for both turn and dive. AUV-XX is also equipped with a couple of lateral tunnel thrusters for sway and a couple of vertical tunnel thrusters fore and aft of the vehicle, respectively. Based on the modeling method described in above section, we established the AUV-XX simulation platform to carry out fundamental

exp( /10) *u u u*

can be manually adjusted based on experiences. The block diagram of

=⋅ ⋅ (14)

1 1 2 2

εα

=

ε α

⎧⎪ ⎨ ⎪⎩

combined control of pitch and depth in vertical plane can be in Fig.5.

Fig. 5. Combined control of pitch and depth in vertical plane

Fig. 6. AUV-XX simulation platform

**4. Simulation results and analysis** 

/

with

where

α1 ,α2 , β

vehicle should navigate with respect to the present tasks and motion states of the vehicle as well as operation environment.

Fig.4 shows both position and speed control procedures. It can be seen that it is easier to realize the control algorithm. For position control of *i* th DOF, the control inputs are the position error and the change rate of position error, that is the velocity obtained from motion sensors; while for speed control, the velocity error and acceleration are control inputs, since AUV-XX is not equipped with IGS to acquire the acceleration of the vehicle, acceleration is calculated differential the velocity in each control step.

#### **3.3 Combined control of pitch and heave in vertical plane**

Since when the vehicle is moving at a high speed, the thrust that tunnel thrusters can provide will strongly degrade, it is difficult to control the depth merely using tunnel thrusters. Considering that once the depth or height of the vehicle changes, the pitch will change with it, and vice versa, so we combine pitch with heave control for diving when the vehicle is moving at some high speed to compensate for the thrust reduction of tunnel thrusters. In that case, the desired pitch angle can be designed as a function of the surge velocity of the vehicle:

$$\theta\_T = \begin{cases} -\frac{k\_\theta \cdot \Delta z}{\sqrt{\mu}} - \theta\_0 & \mu \ge 0.8m/s \\ 0 & \mu < 0.8m/s \end{cases} \tag{11}$$

where θ*T* is the target pitch angle, *k*θ is a positive parameter to be adjusted, Δ*z* is the depth deviation, *u* is the surge velocity of vehicle, θ0 is the pitch angle when the vehicle is in static equilibrium. Since the change of pitch angle is usually associated with depth change and they affect each other, the target pitch is the output of the proportional control with respect to depth change with the proportional parameters *k*θ , the velocity threshold of 0.8m/s is chosen based on the engineering experience of the sea trial and the capability of the thruster system of the vehicle.

When the vehicle is moving at a low speed( *u ms* < 0.8 / ), tunnel thrusters can normally provide the needed force, so the command of target pitch will not be sent to motion control. According to control law (9), we can get the output of the heave controller. Since the vehicle is usually designed with positive buoyancy, the final output of control of heave can be obtained by

$$f\_3 = K\_3 \cdot \mu\_3 + \Delta P \tag{12}$$

where Δ*P* is the positive buoyancy.

And as the surge velocity grows, the thrust of vertical tunnel will experience worse reduction and degradation, so the role it plays in the depth control will be greatly abridged, as a result, the output of pitch control of the main vertical thrusters aft of the vehicle should compensate for that, so the output of control will finally yields as

$$f\_5 = \begin{cases} K\_5 \mu\_5 & \mu \le 0.8\\ K\_5(\varepsilon\_1 \cdot \mu\_3 + \varepsilon\_2 \cdot \mu\_5) & \mu > 0.8 \end{cases} \tag{13}$$

with

140 Autonomous Underwater Vehicles

vehicle should navigate with respect to the present tasks and motion states of the vehicle as

Fig.4 shows both position and speed control procedures. It can be seen that it is easier to realize the control algorithm. For position control of *i* th DOF, the control inputs are the position error and the change rate of position error, that is the velocity obtained from motion sensors; while for speed control, the velocity error and acceleration are control inputs, since AUV-XX is not equipped with IGS to acquire the acceleration of the vehicle,

Since when the vehicle is moving at a high speed, the thrust that tunnel thrusters can provide will strongly degrade, it is difficult to control the depth merely using tunnel thrusters. Considering that once the depth or height of the vehicle changes, the pitch will change with it, and vice versa, so we combine pitch with heave control for diving when the vehicle is moving at some high speed to compensate for the thrust reduction of tunnel thrusters. In that case, the desired pitch angle can be designed as a function of the surge

0 0.8 /

<

θ

*u ms*

(11)

, the velocity threshold of

*u ms*

is a positive parameter to be adjusted, Δ*z* is the

θ

3 33 *f Ku P* = ⋅ +Δ (12)

<sup>≤</sup> <sup>=</sup> ⋅+⋅ > (13)

0 is the pitch angle when the vehicle is

0 0.8 /

in static equilibrium. Since the change of pitch angle is usually associated with depth change and they affect each other, the target pitch is the output of the proportional control with

0.8m/s is chosen based on the engineering experience of the sea trial and the capability of

When the vehicle is moving at a low speed( *u ms* < 0.8 / ), tunnel thrusters can normally provide the needed force, so the command of target pitch will not be sent to motion control. According to control law (9), we can get the output of the heave controller. Since the vehicle is usually designed with positive buoyancy, the final output of control of heave can be

And as the surge velocity grows, the thrust of vertical tunnel will experience worse reduction and degradation, so the role it plays in the depth control will be greatly abridged, as a result, the output of pitch control of the main vertical thrusters aft of the vehicle should

> 0.8 ( ) 0.8

θ

⋅ Δ −− ≥ <sup>=</sup>

acceleration is calculated differential the velocity in each control step.

**3.3 Combined control of pitch and heave in vertical plane** 

*T*

respect to depth change with the proportional parameters *k*

compensate for that, so the output of control will finally yields as

⎧⎪ ⎨ ⎪⎩

5

5 5

ε

51 3 2 5

*K u <sup>u</sup> <sup>f</sup> Ku u u*

 ε

θ

*T* is the target pitch angle, *k*

the thruster system of the vehicle.

where Δ*P* is the positive buoyancy.

depth deviation, *u* is the surge velocity of vehicle,

*k z*

θ

⎧ ⎪ ⎨ ⎪ ⎩

*u*

θ

well as operation environment.

velocity of the vehicle:

where

θ

obtained by

$$\begin{cases} \varepsilon\_1 = \alpha\_1 / \sqrt{\beta \mu} \\ \varepsilon\_2 = \alpha\_2 \cdot \exp(u \cdot u / 10) \end{cases} \tag{14}$$

where α1 ,α2 , β can be manually adjusted based on experiences. The block diagram of combined control of pitch and depth in vertical plane can be in Fig.5.

Fig. 5. Combined control of pitch and depth in vertical plane


Fig. 6. AUV-XX simulation platform
