**4. Simulation results and analysis**

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

Modeling and Motion Control Strategy for AUV 143

(a) Surge displacement (b) Surge velocity response

(c) Sway displacement (d) Yaw displacement

Fig. 8. Position control results of surge, sway and yaw

tests on its motion characteristics, stability and controllability. The states of the vehicle including positions, attitudes and velocities are obtained at each instant by solving the mathematical model equation by integration using a time step of 0.5s. Fig.6 shows the interface of AUV-XX simulation platform. Fig.7 shows the data flow of the simulation platform connecting with motion control system.

Figs.8–10 show the simulation results of capacitor plate model's S-surface control for separate position and speed control in surge, sway and yaw respectively, and also combined control of heave and pitch for diving of the vehicle. The roll is left uncontrolled. And all the vehicle states, including speed, are initialized to zero at the beginning of the each of the simulation. The solid lines denote the actual responses of the vehicle while the dashed denote the desired position or speed that the vehicle is commanded to achieve.

Fig. 7. Data flow of AUV-XX motion control in simulation platform

It can be seen from Fig.8 that, the vehicle is commanded to move to some specified positions in surge, sway and yaw, respectively. For the case of surge as shown in Fig.8(a) and Fig.8(b), the larger position deviation from the target position produces faster response of surge velocity. Compared with responses of surge and yaw, the sway is slower with a rise time of 150s for the desired position is 16m, which may result from that the lateral resistance is much larger longitudinally and the thrust of transverse tunnel thrusters can provide is smaller than the main aft thrusters.

Fig.9 shows the speed control results of surge with constant yaw and depth keeping. The desired velocity is 1m/s and once the vehicle is moving stably with such speed then the vehicle is commanded to track the specified depth (5m) and yaw (45o) commands. It can be seen that there is no overshoot in surge speed and system response is fast with the yaw experiencing an accepted overshoot of ± 2o, and the depth is stably maintained, hence the vehicle is able to move at a desired speed with a desired fixed heading and depth. The speed control simulation results prove the feasibility of the proposed speed control strategy.

142 Autonomous Underwater Vehicles

tests on its motion characteristics, stability and controllability. The states of the vehicle including positions, attitudes and velocities are obtained at each instant by solving the mathematical model equation by integration using a time step of 0.5s. Fig.6 shows the interface of AUV-XX simulation platform. Fig.7 shows the data flow of the simulation

Figs.8–10 show the simulation results of capacitor plate model's S-surface control for separate position and speed control in surge, sway and yaw respectively, and also combined control of heave and pitch for diving of the vehicle. The roll is left uncontrolled. And all the vehicle states, including speed, are initialized to zero at the beginning of the each of the simulation. The solid lines denote the actual responses of the vehicle while the dashed

denote the desired position or speed that the vehicle is commanded to achieve.

Fig. 7. Data flow of AUV-XX motion control in simulation platform

smaller than the main aft thrusters.

It can be seen from Fig.8 that, the vehicle is commanded to move to some specified positions in surge, sway and yaw, respectively. For the case of surge as shown in Fig.8(a) and Fig.8(b), the larger position deviation from the target position produces faster response of surge velocity. Compared with responses of surge and yaw, the sway is slower with a rise time of 150s for the desired position is 16m, which may result from that the lateral resistance is much larger longitudinally and the thrust of transverse tunnel thrusters can provide is

Fig.9 shows the speed control results of surge with constant yaw and depth keeping. The desired velocity is 1m/s and once the vehicle is moving stably with such speed then the vehicle is commanded to track the specified depth (5m) and yaw (45o) commands. It can be seen that there is no overshoot in surge speed and system response is fast with the yaw experiencing an accepted overshoot of ± 2o, and the depth is stably maintained, hence the vehicle is able to move at a desired speed with a desired fixed heading and depth. The speed control simulation results prove the feasibility of the proposed speed control strategy.

platform connecting with motion control system.

Fig. 8. Position control results of surge, sway and yaw

Modeling and Motion Control Strategy for AUV 145

(c) Depth keep response (d) Pitch response

In this chapter, the design of motion control system for Autonomous Underwater Vehicles is described, which includes both position and speed control in horizontal plane and combined control of heave and pitch in vertical plane. To construct the control system, a 6 DOF general mathematical model of underwater vehicles was derived, which is powerful enough to apply it to different kinds of underwater vehicles according to its own physical properties. Based on the general mathematical model, a simulation platform was established to test motion characteristics, stability and controllability of the vehicle. To demonstrate the performance of the designed controller, simulations have been carried out on AUV-XX simulation platform and the capacitor plate model S-surface control shows a good

Fossen T. I. (1991). *Nonlinear modeling and control of underwater vehicles*. Ph.D. thesis,

Fossen T. I. (2002). *Marine control system*: *guidance*, *navigation and control of ships*, *rigs and* 

Gan Yong, Sun Yushan, Wan Lei, Pang Yongjie (2006). Motion control system architecture of

Gan Yong, Sun Yushan, Wan Lei, Pang Yongjie (2006). Motion control system of underwater

Li Xuemin, Xu Yuru (2002). S-control of automatic underwater vehicles. *The Ocean* 

underwater robot. *Proceedings of the 6th World Congress on Intelligent Control and* 

robot without rudder and wing. *Proceeding of the 2006 IEEE International Conference* 

Norwegian Institute of Technology-NTH, Trondheim, Norway

*underwater vehicles*. Marine Cybernetics, Trondheim, 254-260

*on Intelligent Robotics and Systems*, Beijing, China, 3006-3011

*Automation*, Dalian, China, 8876-8880

*Engineering*, 19(3), 81-84

Fig. 10. Combined depth control of heave and pitch

**5. Conclusions** 

performance.

**6. References** 

Fig. 9. Speed control results of surge with yaw and depth keeping

Fig.10 shows the combined control of heave and pitch for diving in vertical plane. For this case, the velocity of surge that the vehicle is commanded to track is 1.5m/s, which is not very large so that the vertical tunnel thrusters will suffer thrust reduction to some extent but still can work to provide a portion of vertical thrust for diving. Hence when the vehicle is commanded to dive, the pitch will not experience a large change, which is reasonable design consideration in the case of large inertial vehicles.

Fig. 10. Combined depth control of heave and pitch
