Path following of unmanned surface vessel under effect of positionmeasurement noise

Use your smartphone to scan this QR code and download this article ABSTRACT A manipulation system for unmanned surface vessels (USVs) as well as other unmanned vehicles and autonomous vehicles are commonly built up by three vital components which are guidance system, navigation system and control system, regardless of the mechanical aspects. In which, the navigation system will first use sensors to measure and estimate parameters, then feedback to the guidance system and the control system as input data. Based on those data and assignments from user, the guidance system calculates and outputs reference data for the control system. The control system will drive the vessel according to the reference data from guidance system to achieve those assignments. However, the process of measuring and estimating, in fact, is always affected by disturbances which cause input error for guidance system. Consequently, the reference data provided by the guidance system will be skewed and confused the control system, thereby reducing the quality of control and may cause instability for the whole system. This paper examines the problem of controlling an unmanned surface vessel following straight paths created by the waypoints which given by user. To solve the path-following for straight line problem, the paper will build a guidance system using the Line of Sight (LOS) method with lookahead distance and design a controller using Backstepping algorithm. In addition, this paper will also study, analyze and propose amethod to reduce the influence of positionmeasurement noise to the process of calculating the reference data of guidance system. Thereby, the quality of the built system will be guaranteed when operating under the influence of measurement noise. The results of the proposed method will be shown through simulation on MATLAB/SIMULINK software. These simulation results will demonstrate the effectiveness and feasibility of the proposed method.


INTRODUCTION
In the age of technological explosion, automatic, un-2 manned and other intelligent devices are more and 3 more widely researched and developed at a fast pace 4 and easily applied to practice. This has created a lot of 5 premises for people to explore the world and find new 6 resources, especially the water environment which 7 covers more than 70% of the earth's surface. Hence, 8 we have to use robots in those situations where hu-9 mans cannot discover by themselves. As a result, au- there were also many USVs that had been studied 21 for military purposes such as USV KATANA of Is-22 rael, USV Protector Rafael of the United States. In the 23 field of civil purposes, there was the autonomous sur-24 face vessel (ASV) C-Worker 12P used for transport or 25 ASV Waste Shark used to clean up the trash on rivers, 26 lakes, etc. Such applications of those types of un-27 manned surface vessel are described in 1,2 , and 3 . At 28 the same time, underwater vehicles have also grown 29 at a dramatic rate. People nowadays tend to incor-30 porate USV, autonomous underwater vehicle (AUV), 31 remotely operated vehicle (ROV) into a more com-32 plete system for various purposes. Some applications, 33 as well as underwater vehicles, are described in 4-7 .

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In this paper, we will consider the problem of con-35 structing a system for an unmanned surface vessel so 36 that it can follow a straight path formed by the given 37 waypoints. In addition, we will also consider the ef-38 fect of position measurement noise on the system. A 39 USV as well as any other unmanned vehicles, in or-40 der to follow a trajectory, cannot lack the guidance 41 and control system as described in 8 . Hence, this pa-42 per will present how to build a guidance system us-43 method to reduce the effect of position measurement 48 noise on the quality control of the mentioned system.
where is the distance from the center of gravity of 85 vessel to the origin of the body-fixed frame {b}. The 86 } are hydrodynamic pa-87 rameters according to the notation in 10 and τ = 88 [τ 1 , τ 2 , τ 3 ] τ is the control input. Equation (1) can be 89 expressed as: The thruster configuration of USV is shown in Fig-92 ure 2 and the force and torque are related to the con-93 trol input τ through the equation:

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This paper considers the path following problem for 99 unmanned vehicles, in which the path is formed 100 by connecting the given waypoints. To solve this 101 problem there are many different methods, however, 102 for marine craft Line of Sight (LOS) is the popular 103 method and LOS has proved very effective because of 104 the way it works similar to the helmsman, which will 105 typically steer the vessel towards a point lying a con-106 stant distance, called the look-ahead distance, ahead 107 of the vessel, along the desired path 11 . Furthermore 108 LOS guidance algorithms allow the vehicle at any ini-109 tial position outside the desired path to converge and 110 stay on the path. So this paper choose LOS method to 111 design guidance.

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Suppose that USV needs to be converged on the 114 path that are connected by two way-points wp(k) and 115 wp(k+1) as inFigure 3, when the angle α p can be de-116 termined by formula: For the USV located at (x, y), the along-track (x e ) and 119 cross-track (y e ) are defined by:

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where (x k , y k ) is the coordinates of wp(k) in an earth-122 fixed inertial frame (k = 1 … N). Expanding (10) we get: The goal is making the vessel converge and stay on the  With the LOS vector defined above, the desired head-143 ing can be determined by formula: The target is find the function ∆ (y e ) to minimize   Heading controller 223 We will use Backstepping Sliding mode for design 224 heading controller. From (6): Step 1: Define the second CLF r+b .
Choose the control law when the result of Step 2 is V 2 < 0∀e ψ so s ψ → 0 and e ψ → 0.

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This section presents simulation results of the com-  Because the guidance with Delta noise converges on 281 the path faster, it makes the trajectory longer and 282 needs more time to finish. However, we can see the 283 heading response from Figure 5 and Figure 9 where 284 the heading response of Delta noise has the best qual-285 ity.

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In case 1, the moment control input shown in Fig-287 ure 7 is possible in practice for all Delta. However, in 288 Figure 11 of case 2, only the moment control input of 289 Delta 2 and Delta noise can apply in experiment and 290 Delta noise has the best quality.

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When the vessel reaches wp(k), the desired heading 292 ψ d and cross-track error y e will be recalculated ac-293 cording to the new waypoint wp(k+1). Hence, to eval-294 uate the results of the selected Delta noise, we need 295 consider the process from start to reach at the first 296 waypoint or from t = 0 to t = 42. Through the result in 297 Figure 12, the selected Delta noise has helped the sys-298 tem works very well and the maximum value of □ ψ d is 299 less than 0.6 degrees and obviously satisfies the maxi-300 mum allowed angular error P. Summary the proposed 301 method to reduce the effect of position measurement 302 noise on the quality control has been verified.

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In this paper, a guidance and control system for un-305 manned surface vessels is developed to solve the con-306 trol objective of making the vessel follow a desired 307 path in the presence of measurement noise which ef-308 fect to guidance and quality of heading controller.

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Simulation results have demonstrated the effective-310 ness and feasibility of the proposed method. The com-311 bined system helps the vessel converge on the path 312 and stay on it, besides that it still guarantee the speed 313 assignment in case of measurement noise.

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Further works focus on applying this method even for 315 curve path and studying new control algorithm. Be-316 side that it is possible to consider the effect of external 317 disturbances on the system so that simulation results 318 still ensure the quality when applied in practice.  325 The author declares that this paper has no conflict of 326 interests.