The Simulation for Autonomous Navigation of water-jet-propelled Unmanned Surface Vehicle Qi Xiaowei, Renguang,Yuejin Dalian Maritime University of Marine Engineering, Dalian, LiaoNing, 110, China xiaowei0735@13.com Abstract According to the motion characteristic and hydrodynamics of high-speed deep-v planning, a real-time DOF mathematical motion model for the USV was built and the performance was simulated in Matlab/Simulink software tool. Then a fuzzy logic system for autonomous navigation of unmanned surface vehicles is presented. The control system intelligently controls the vehicle to go from origin to destination avoiding the obstacles in its path. Depending on the anticipated danger of the obstacle, the vehicle chooses an angle of divergence which avoids the obstacles and keeps the speed of the vehicle. The proposed control system of the vehicle has two main controllers. The first one is speed controller and the second one is nozzle controller. Compared with the actual sea trial data, the results show that the proposed model and fuzzy controller can better reflect and simulate the maneuverability of the USV under ocean environment. Keywords-Unmanned surface vehicle (USV; ship motion mathematical model; water-jet propulsion; fuzzy logic control; autonomous navigation. DYNAMCS ANALYSS OF THE USV n order to discuss and analyze the motion and the stress of marine vehicles in DOF, we defined two coordinate frames: a body-fixed reference coordinate and an earth-fixed reference coordinate, as indicated in Fig.1. n the earth-fixed reference frame, the origin point O o is fixed at a certain point at sea surface, whereas xo axis, yo axis and zo axis point to the north, the east and the earth center respectively. However, the body-fixed coordinate is fixed to the USV for convenience, and the origin point O is chosen to coincide with the center of gravity of the USV, whereas x axis, y axis and z axis point to the stem, starboard and baseline respectively... NTRODUCTON The unmanned surface vehicle (USV refers to any vehicle that operates on the surface of the water without a crew. Since World War, they have been developed and tested in many countries. Nowadays, the need of counterterrorism and national defense paves the way for a new wave of USVs. There have been some classic cases, such as Spartan Scout by US Navy, Piranha by US Meggitt PLC, host uard by US irobot PLC, Protector and Stingray by srael and so on.they are reliable, fast, highly maneuverable, allowing them to conduct a wide range of missions, including patrols of the coast, without endangering navy personnel. With the development of the water-jet propulsion technology, more and more vessels including military and civilian field are propelled by water-jet engine. So in this paper, a water-jet-propelled USV will be introduced. Firstly, base on hydrodynamics and kinematics theory, the forces and moments acting on USVs hull are analyzed. Secondly, the water jet thrust-vector model is studied. Finally, the real-time degrees of freedom(dof motion mathematical model of the USV is obtained in the idea of MM model. So we could predict and simulate USVs movement including surge, sway, heave, roll, pitch and yaw under ocean environment. Figure 1. Body-fixed and earth-fixed reference frame n the model, the type of USV is deep-v planing with high-speed. According to the motion characteristics of highspeed planing, the forces and moments acting on the boat are divided into gravity, static buoyancy, hydrodynamic force, propulsion and environmental force. ravity is the vertical force acted on the center of gravity of the USV, consequently we can get the gravity projection in body-fixed reference frame as below. X Y Z = mg sin θ = = mg sin φ cos θ mg cos φ sin θ
Where is the mass of USV, g is acceleration of gravity, while φ and θ are respectively, rolling angle and pitching angle of USV. Hull Static Buoyancy is the force due to displacement of the USV, according to the reference[1], we can get the static buoyancy projection in body-fixed reference frame as below. X U X 1 X X 3 θ X φ X 5 φ X YU ZU Z1 Z Z3 θ Z φ Z5 φ Z KU K1 φ K φ φ K3 φθ K φt M U M 1 M M 3 θ M φ M 5 φ M NU Where ρ is seawater density, T is the draft of USV, while coefficient X n, Z n, K n and M n are obtained from regression analysis using the experimental values of the static buoyancy forces and moments testing as following: X n =( -0.037,0.39595,1.0, 0.05,0.00, 0.80.0058 Z n = (-3.0753,-.888,-59.81,- 0.13,5.5077,7.98,0.139 K n = (-0.398,0.08705,-1.5905,-0.599 M n = (-0.387,-9.9,-3.1337,- 0.01913,.333,.17,0.107 The hydrodynamics force of the USV changes with closely to the USV s navigation state and velocity. According to the reference[], the hydrodynamics force mainly consisted of inertia hydrodynamics force, viscous hydrodynamics force and hydrodynamics lift. Although there were already many relevant theories and empirical formulas, such as Murry theory, Savisky theory, Shuford theory and so on, it has its limitations. So the hydrodynamics force are obtained mainly base on the work of Serge Toxopeus in Delft University of Technology [3]. The vehicle is equipped with water jet system made by Hamilton company. t consists of deflector and nozzle that are used to propel and manipulate the USV. Being different from propeller, the USV astern sailing and yaw are controlled by astern deflector other than rudder. The force produced by water jet is reduced by the law of conservation of energy and momentum as below: T = ρq vj αvs = ρav j j vj αv s ( ( For convenience,the propulsion T is projected on coordinate x,y,z Tx = ρ Q v cos( δ - u α N j J ρv cos( ϕu α( Q Q j DL Ty = ρ Q v sin( δ - v α N j J ρv cos(r sin( ϕ v a ( Q -Q j J DL Tz ρ Q v sin( γ j J Where Q is the water flow, vj is the velocity of flow ejecting from the nozzle, is the flow from the nozzle, Q N Q is the flow into the right deflector, Q DL is the flow into the left deflector, γ J is the angle of astern deflector, δ J is the angle of steering nozzle,ϕ is the angle between astern deflector centre line and x axis. The environmental factor includes wave, wind and current whose random interference on vehicle cannot be ignored. There are so many relevant work on this field that we directly make use of the result which has been done by others.. THE DOF USV MOTON MATHEMATCAL MADOEL Based on the above work, the equations of motion of USV in body-fixed reference frame are deduced in some assumptions: (1 the vehicle is rigid and ( the earth-fixed reference frame is inertial. The first assumption eliminates the consideration of forces acting between individual elements of mass while the second eliminates forces due to the Earth s motion relative to a star-fixed reference frame. Then we can derive the general DOF motion equations of USV by applying the Newtonian and Lagrangian formalism. Equations are usually showed in component form according to the SNAME (1950 notation system, that is:. u& vr wq x ( q r y ( pq r& z ( pr q& ] = X v& wp ur y ( p r z ( qr p& x ( pq r& ] = Y w & uq vp z (p q x (pr q & y (rq p] & = Z p& ( zz qr ( r& pq xz ( r q yz ( pr q& y ( w& uq vp z ( v& wp ur] = K q& ( zz rp ( p& rq ( p r xz ( qp r& zy z ( u& vr wq x ( w& uq vp] = M zzr& ( qp ( q& rp zy ( q p ( rq p& zx x ( v& wp ur y ( u& vr wq] = N Where vector [ X ] X Z is the body-fixed resultant forces vector acted on USV, [ K M N ] is the bodyfixed resultant moments vector about the center of gravity of USV, [ u v w] is the body-fixed linear velocities vector of USV, [ p q r] is the body-fixed angular velocities vector of USV, [ x y z ] is the position coordinate of the center of gravity of USV, and [ K zz ] is the USV s bodyfixed moments of inertia vector.
V. MODEL SMULATON Base on the work in the previous sector, we construct a ship model and then we will compare the model with the sea trial report to see how close to the real ship the model perform. There are two control inputs: throttle and nozzle angle and the main hull parameters of a USV are as followings: the length is 9.0, the max breadth is.5 m, the depth is 1.35 m, the dead-rise angle is 5 deg, the draft is 0.7 m, the total mass is 5500 kg, the longitudinal moment of inertia is 58. kg m, the transverse moment of inertia is 35.95 kg m.. and the vertical moment of inertia is 778.5 kg m. n order to validate results of the USV motion, we will take turning test and zig-zag test. The turning test is completed with a series of nozzle angle respectively at10 deg, 0 deg and 30 deg nozzle angles at 70% of max speed.. The turning circle figures are the followings Figure 3. Zig-Zag track at 10 deg Figure. Zig-Zag track at 10 deg Figure. Turning circle at 10,0,30 deg From the above track charts, we were able to observe that the bigger nozzle angle was the smaller turning diameter was at a certain navigation velocity. Furthermore, the results of simulation matched with the data of real ship sea trial that turn radius at 30kts is 0-0m. Zig-zag test is the manoeuvre where a known amount of helm is applied alternately to either side when a known heading deviation from the original heading is reached. A series of zig-zag tests of which given nozzle angle and change of heading angle are respectively 10 deg, 0 deg and 30 deg were completed, and the track charts are the followings (Fig.3~Fig.5: Figure 5. Zig-Zag track at 10 deg From the above track charts, the results of simulation matched with the data of real ship sea trial, so the model could simulate the helm effect of the real USV rightly. V. CONTROL SYSTEM Appraently,there is a need to guide the cehicel without human for USV.So the control system for autonomous navigation [-7]which intelligently controls the vehicle to go from origin to destination avoiding the obstacles in its path or at designated heading must be taken into the model. n our ship model, there two controllers: throttle and nozzle. we first give a assumption that there is no ship or other obstacles on the sea and then we will add some obstacles on the course of the ship to check the control system. The control system intelligently controls the vehicle to go from origin to destination avoiding the obstacles in its
path.the block diagram of the control system are shown in figure. The main inputs to the navigation system are target poison, obstacles, current location, current speed, and nozzle angular velocity. These five inputs are used to calculate the next coordinate of the position vector (a,b,the velocity (u,v,and the nozzle angle that are required in order to reach a particular coordinate. The nozzle angle and the velocity provide the next position. nitially, the control system starts to navigate the vehicle at constant velocity in a line from origin towards a target with assumption of no obstacles in its linear path. However, if an obstacle is encountered in the course of travel,it then becomes an input,and the control system diverts the vessel from its default path to travel in an alternate path to avoid the obstacle. Then, when the obstacle has successfully been avoided, the vessel will be returned to its original path. n the chain of events,the navigator is the central component which makes the ultimate decision of the required deviation. Figure 7. Ship heading control Although there is some good result in heading control using PD, the track control is not so simple. So the fuzzy logic control which was proposed by professor Zodeh was taken into the system. t is convenient to use the fuzzy logic control in Matlab environment. n the navigation controller of the system, the fuzzy membership function is as figure 8, it characterizes and resembles a course of a ship s avoidance of an obstacle. This particular membership function has been implemented mainly because of the fact that it has a sudden deviation from the path, although not at a right-angel, which in practice is impossible to create. Therefore, the deviation in path is quite logical in terms of an actual surface vessel. Figure. Structure of the Control System n the control system, there are two kinds of navigation that includes ship heading control and the ship track control. The heading control is only in consideration that the ship heading points the set direction.the track control is more complicated and there are so much factors affecting the ship. Here the fuzzy control and PD control are used in the control system. The two methods are used alternatively according to environment. n the situation that the vehicle is sailing on the sea without any obstacles or at a certain heading, the PD will be implemented and in the other complicated situations the advanced fuzzy control would be implemented. The figure 7shows that the ship heading control using PD in the condition that the wind speed is.5m/s,sea state 1and the control system s performance is not bad. Figure 8. Fuzzy Membership Function To verify the fuzzy controller, two different conditions are presented. The first condition is shown in figure9. The point A,B,C is the designated position.the ship would sail along the line AB to B and the along the line BC to the C and there is no obstacles on the line. From the figure 9,it shows that the controller seems to do well. The course is smooth and it coincides with the reality that the max deviation with the designated line is about 50 m. The second situation is that there is some obstacles on the designated course of the ship. The vehicle must avoid collision with the obstacle intelligently. n figure10, there are two obstacles one of which is on the designated course. t shows that the deviation is about 100m, a little bigger. But there is the wind effect, the performance is not so bad. n figure 11, there are four obstacles. t is obviously that the
track of ship changes frequently because of the wind. The figure 1 shows that there is no wind and the result is very good. So the fuzzy controller is available in the autonomous navigation. Figure 1. ship track control with 3 obstacles with no wind and current Figure 9. Ship track control with no obstacle V. CONCLUSONS This paper studied the architecture of a real-time DOF mathematical motion model for USV and a simulation project is established in Matlab/Simulink software to carry out a series of model tests on the ship maneuverability including turning test and zig-zag test. The results of these tests show that the proposed model can preferably reflect and simulate the maneuverability of the USV and is able to provide a simulation platform for the research and development of the USV. Then the fuzzy controller for navigation of an unmanned surface vehicle has been presented. t can take into consideration the occurrence of obstacles along the path of travel and avoid collision with the obstacles to achieve autonomous navigation, giving other relate researchers some reference. Figure 10. ship track control with obstacles REFERENCES [1] Serge Toxopeus: Mathematical Model of the Behaviour of Planing Ships (Delft University of Technology Publications, Netherlands 199. [] Odd M. Faltinsen: Hydrodynamics of High-Speed Marine Vehicles (Cambridge University Press Publications, the United States of America 005 [3] Serge Toxopeus: Model Experiments on Dynamic Stability of Planing Ships (Delft University of Technology Publications, Netherlands 199. [] Hussein, A S., Numerical Simulation of Neural Network-Controlled Unmanned Undersea Vehicle. WSEAS Transactions on Circuits and Systems. Vol., no. 3, pp. 08-15. July 003. [5] Meystel, A., Planning in a Hierarchical Nested Autonomous Control System, SPE Conference on Mobile Robots, Eds. W. J. Wolfe and N. Marquina, Cambridge, MA, pp. -7, 1987. [] Leonard, N.E., Periodic Forcing, Dynamics and Control of Underactuated Spacecraft and Underwater Vehicles, Proc. 3th EEE Conference on Decision and Control, pp. 3980-3985, December 1995. [7] Petterson, K.Y. and O. Egeland, Exponential Stabilization of an Underactuated Surface Vessel, Proc. 35th EEE Conf. on Decision and Control, pp. 97-970, December 199. [8] Pettersen, K.Y. and T.. Fossen, Underactuated Dynamic Positioning of Ship-Experimental Results, EEE Transactions on Control Systems Technology, pp. 85-83, September 000. Figure 11. ship track control with obstacles