Research Article A Novel Path Control Algorithm for Networked Underwater Robot Minghong She 1,2 and Liyu Tian 2 1 School of Automation, Chongqing University, Chongqing, China 2 Computer College, Chongqing College of Electronic Engineering, Chongqing, China Correspondence should be addressed to Minghong She; mh [email protected] Received 13 December 2017; Accepted 20 May 2018; Published 2 July 2018 Academic Editor: Keigo Watanabe Copyright © 2018 Minghong She and Liyu Tian. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Under the network environment, the traditional control method of underwater Robot path has the disadvantages of low control accuracy, large error, and inefficiency. is paper proposes a novel path control method for underwater Robots based on the NURBS (nonuniform rational B-spline, NURBS) curve fitting method, which utilizes a sensor or camera to detect the static and dynamic obstacles, establishes the kinematics model of underwater Robots, gets the target function of rob shortest path, and analyzes underwater Robot constraints. According to the basic fluid mechanics, the resistance of the underwater Robot is determined. e filter function is used to smooth the process, and the NURBS curve fitting method is applied to control the path of the underwater Robot. Experimental results show that the improved method that proved to be practical is superior to the traditional one in the aspect of control time and accuracy. 1. Introduction With the depletion of land resources, money, time, and manpower are invested to develop underwater resources [1]. erefore, underwater Robots are a concern for people of many countries [2]. In order to complete an under- water task for one time, a variety of underwater Robots complex operation and safe navigation are to be carried out in accordance with the corresponding navigation path [3, 4]. To achieve the best navigation plan and keep the under- water Robot running on the scheduled course [5], it is necessary to ensure the maneuverability of the underwater Robot [6, 7]. When the underwater Robot has good handling performance, it cannot only maintain stable driving course, depth, and speed but also quickly change the heading, depth, and speed and correctly perform all kinds of oper- ations [8]. e path control of underwater Robot affects the performance of underwater Robot [9]. e method of networking can effectively control the running path of underwater Robots and shorten the control time [10, 11]. erefore, the underwater Robot path control under the networked environment has become the focus of research in this field and has attracted the attention of many schol- ars. Mahmoodabadi, Mohammad Javad et al. [12] mainly aims at controlling the path of underwater Robot when the underwater Robot is avoiding the obstacle and the direction of movement is not corrected. Based on the establishment of integrated navigation model and the detection based dynamic obstacle avoidance strategy, the discrete time multithread concurrent simulation framework and model are used to design the effective control of underwater Robot path. How- ever, the method wastes much time. Zanoli, Silvia M., and Giuseppe Conte [13] aim at resolving the problem of low con- trol speed or zero speed state in traditional control method, and the frame control moment gyroscope is introduced as the path control executive mechanism to realize the path control of the underwater Robot. is method can effectively shorten the control time of the path, but with a problem of low control accuracy [14]. To solve the above problems, a path control method of underwater Robot based on NURBS curve fitting method is proposed. e experimental results show that the control accuracy and efficiency are improved by adopting the pre- sented control method. Hindawi Journal of Robotics Volume 2018, Article ID 1520981, 7 pages https://doi.org/10.1155/2018/1520981
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Research ArticleA Novel Path Control Algorithm forNetworked Underwater Robot
Minghong She 12 and Liyu Tian2
1School of Automation Chongqing University Chongqing China2Computer College Chongqing College of Electronic Engineering Chongqing China
Correspondence should be addressed to Minghong She mh she126com
Received 13 December 2017 Accepted 20 May 2018 Published 2 July 2018
Academic Editor Keigo Watanabe
Copyright copy 2018 Minghong She and Liyu TianThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited
Under the network environment the traditional control method of underwater Robot path has the disadvantages of low controlaccuracy large error and inefficiencyThis paper proposes a novel path controlmethod for underwater Robots based on theNURBS(nonuniform rational B-spline NURBS) curve fitting method which utilizes a sensor or camera to detect the static and dynamicobstacles establishes the kinematics model of underwater Robots gets the target function of rob shortest path and analyzesunderwater Robot constraints According to the basic fluid mechanics the resistance of the underwater Robot is determined Thefilter function is used to smooth the process and the NURBS curve fitting method is applied to control the path of the underwaterRobot Experimental results show that the improved method that proved to be practical is superior to the traditional one in theaspect of control time and accuracy
1 Introduction
With the depletion of land resources money time andmanpower are invested to develop underwater resources[1] Therefore underwater Robots are a concern for peopleof many countries [2] In order to complete an under-water task for one time a variety of underwater Robotscomplex operation and safe navigation are to be carriedout in accordance with the corresponding navigation path[3 4]
To achieve the best navigation plan and keep the under-water Robot running on the scheduled course [5] it isnecessary to ensure the maneuverability of the underwaterRobot [6 7] When the underwater Robot has good handlingperformance it cannot only maintain stable driving coursedepth and speed but also quickly change the headingdepth and speed and correctly perform all kinds of oper-ations [8] The path control of underwater Robot affectsthe performance of underwater Robot [9] The methodof networking can effectively control the running path ofunderwater Robots and shorten the control time [10 11]Therefore the underwater Robot path control under thenetworked environment has become the focus of research
in this field and has attracted the attention of many schol-ars
Mahmoodabadi Mohammad Javad et al [12] mainlyaims at controlling the path of underwater Robot when theunderwater Robot is avoiding the obstacle and the directionof movement is not corrected Based on the establishment ofintegrated navigationmodel and the detection based dynamicobstacle avoidance strategy the discrete time multithreadconcurrent simulation framework and model are used todesign the effective control of underwater Robot path How-ever the method wastes much time Zanoli Silvia M andGiuseppe Conte [13] aim at resolving the problem of low con-trol speed or zero speed state in traditional control methodand the frame controlmoment gyroscope is introduced as thepath control executive mechanism to realize the path controlof the underwater RobotThismethod can effectively shortenthe control time of the path but with a problem of low controlaccuracy [14]
To solve the above problems a path control method ofunderwater Robot based on NURBS curve fitting methodis proposed The experimental results show that the controlaccuracy and efficiency are improved by adopting the pre-sented control method
HindawiJournal of RoboticsVolume 2018 Article ID 1520981 7 pageshttpsdoiorg10115520181520981
2 Journal of Robotics
2 Construction of Kinematics Model ofUnderwater Robot
When the underwater Robot is effectively controlled underthe condition of network it is necessary to have a goodunderstanding of the underwater Robot The use of sensorsor cameras to detect static and dynamic obstacles and theestablishment of underwater Robot kinematics model canimprove the path control method to provide the basis
When the kinematic model of the underwater Robot isestablished the head adjustment of the target underwaterRobot can be obtained by adjusting the amount of integrationprocessing [15] The kinematic model is given by
1198671198921 = sum1198701199032119862119903 (1)
where 119862119903 is output value and1198701199032 is weighted coefficientFor the existence of the interference of underwater
Robots the use of arithmetic mean filtering method forfiltering to eliminate the Gaussian noise has a positive effect[16] When using the most single arithmetic mean filter thedata received at each time is replaced by the average of thereceived data in the neighborhood of the length of time Theexpression is
119910 (119899) = 1119898119898sum119894=1
119909 (119899 minus 119894) (2)
where119898 is constant 119894 is the number of filters and 119909(119899 minus 119894) isthe wavelength of 119899 minus 119894 filter
In the filter the high frequency of interference removaleffect will not achieve the best results In this case it isnecessary to suppress a higher frequency of interferenceby adding a virtual damping force [17 18] This makes theresponse of the underwater Robot relatively slow increasingits stability The expression is
119906119894 = Δ119905119890119894 + 119879119906119894minus1Δ119905 + 119879 (3)
where Δ119905 is the sampling period 119879 is the inertia constant 119890119894is the time deviation of 119894 and 119906119894minus1 is the response time of time119894
In the case of satisfying the absolute stability of theunderwater Robot the positive moment is used as thestability storage device [18] and then the balance coefficientcan be changed as follows
119862V = 1 minus 119872119908 (1198981015840 + 1198851015840119902)11987210158401199021198851015840119908 (4)
During the operation of the underwater Robot theobstacle in the underwater environment will form a certainpotential field and the repulsion force of 119865119903119890119901 is generatedfor the underwater Robot The closer the distance is thelarger 119865119903119890119901 will that is to say the closer the underwaterRobot and the obstacle the greater the potential energy of
the underwater Robot and vice versa [19] This potential fieldis similar to the potential field inversely proportional to thedistance so the repulsive potential function can be expressedas
119870119903120588 (119883119883119900119887119904) 120588 le 1205881198980 120588 ≺ 120588119898
(5)
where 119870119903 is the repulsive potential field constant 119883 is theposition vector of the underwater Robot 119883119900119887119904 is the obstacleposition vector in thewater 120588 is the shortest distance betweenthe underwater Robot and the obstacle and 120588119898 is the rangeof the repulsive potential field When the distance betweenthe underwater Robot and the obstacle is greater than 120588119898 therepulsive potential field does not interfere with the operationof the underwater Robot
To avoid the collision between the underwater Robot andthe obstacle it is required to set a minimum safe distance1205880 when 120588 rarr 1205880 and 119865119903119890119901 rarr infin and to ensure that 119865119903119890119901 iscontinuous the expression of 119865119903119890119901 is119865119903119890119901=
119870119903( 1(120588 (119883119883119900119887119904) minus 1205880)2 minus
1(120588119898 minus 1205880)2) 120588 le 120588119898
0 120588 ≻ 120588119898(6)
Based on the above sensors or cameras are used tomonitor static and dynamic underwater obstacles and toobtain the position speed and acceleration information ofobstacles in real time These messages can fuse into movingobstacles A number of navigation paths represented by time 119905can be used in the obstacle motion constraints of underwaterRobots Suppose that 119900119887119904119896 is a rigid body with a center of120572119896(119905) = (1205721119896(119905) 1205722119896(119905)) 119896 = 1 2 119902 119905 isin [0 119905119896] and 120572119896() =1 2 119902 is a continuous real vector valued function also thepath of motion obstacles Suppose that the underwater Robotand obstacle 119896 can be represented by119879119903119900119887 and119879119896 respectively119896 = 1 2 119902 When the constraint of the underwater Robotis 1 sin 120579 minus 2 cos 120579 = 0 without lateral collision and thegeneral coordinate system is 119902(119905) = [1199091(119905)1199092(119905)120579(119905)]119879 thekinematic model of the underwater Robot is expressed as fol-lows
119902 = [[[cos 120579119905 0sin 120579119905 00 0
]]][V (119905)119908 (119905)] (7)
where 120592(119905) and 120596(119905) are respectively tangential velocity andangular velocity In the navigation process the speed ofunderwater Robot should be regulated within the maximumallowable speed to prevent the underwater Robot fromcolliding meanwhile the underwater Robot must follow therules of acceleration
Journal of Robotics 3
3 Improvement of Path Control Method forUnderwater Robot
31 Constraint Analysis According to the kinematicmodel ofthe underwater Robot the objective function of minimizingthe path length is obtained
119891 (ℎ) = minsum ℎ(2sum119865119891=1 119864 (119891ℎ) minus 119864 (0) minus 119864 (119905119891))2 (8)
On this basis various constraints are introduced into theobjective function as the penalty term and the expression ofthe self-adaptation function is obtained
min119865119901119888119899119886 = sum ℎ (2sum119865119891=1 119864 (119891ℎ) minus 119864 (0) minus 119864 (119905119891))2+ 119888119899 119865sum119891=0
max (0 119883119897 minus 119864 (1199051015840))(9)
where 1199051015840 = 119891ℎ 119888119899 is a larger value that is penalized forbreaking the constraint 119899 = 1 9 119883119897 is the boundary areaof its 119903119900119887 activity Their constraint types are as follows
(i) Boundary Constraint Assuming that 119883 is the boundaryof the selected area the underwater Robot should be subjectto the following motion boundary constraints during themoving process
119901 (0) = (1199090 1205790)119901 (119905119891) = (119909119891 120579119891)1198830 119883119891 isin 119883
(10)
(ii) Movement Restriction In the process of underwaterRobot navigation there is a certain motion constraint Whenthe ship is sailing along the planning path its acceleration andspeed are prevented from colliding in the prescribed area Inliterature [20] its motion constraint is expressed as follows
120592 (119905) ge 120592min
120592 (119905) le 120592max
120596 (119905) ge 120596min
120596 (119905) le 120596max
119905 isin [0 119905119891]
(11)
(iii) Obstacle Avoidance Constraint To ensure that underwa-ter Robots maintain a minimum safe distance from otherstatic or moving underwater obstacles during navigation119889119900119903119887 119896 and 119889119900119896 are setting as the given safety distance andactual distance of 119903119900119887 and 120572119896 respectively therefore 119889119900119903119887 119896is expressed as
119889119900119903119887 119896 = 1003817100381710038171003817119909 (119905) minus 120572119896 (119905)10038171003817100381710038172 minus (119903 + 119903119896) (12)
where 1 le 119896 le 119902 Thus in119883 119903119900119887 should satisfy the followingbarrier constraints
119889119900119887119904 119896 minus 119889119900119896 (119905) le 0forall119896 = 1 119902 119905 isin [0max (119905119891 119905119896)] (13)
32 Implementation of the Proposed Method Based on theanalysis of constraints for underwater Robot and the basicfluid mechanics the resistance of underwater Robot is deter-mined the filter functions are smoothed and underwaterRobot path is controlled by using NURBS curve fittingmethod
In view of the basic fluid dynamics the total resistance 119877119905of the underwater Robot can be divided into frictional resis-tance 119877119891 and residual resistance 119877119903 When the underwaterRobot is inwater for a long period of time thewave resistanceis negligible and the resistance is as follows
119877119898 = 051205881198812119904 119878 (119862119891 + Δ119862119891 + 119862119901V) (14)
where 120588 is the density of water 119881119904 is the speed of underwaterRobot 119878 is wet surface area 119862119891 is friction resistance coeffi-cient Δ119862119891 is friction resistance subsidy coefficient and 119862119901Vis viscosity resistance coefficient
Supposing that the running path of an underwater Robotcan be represented by a weighted directed graph 119866(119881 119864)in which the set 119881 is a set of fixed points 119899 is the fixed-point number of the fixed-point set 119864 is the arc set of the119898 arc ⟨V119894 V119895⟩ is the arc from V119894 to V119895 in 119864 and 119889⟨V119894 V119895⟩ is thenonnegative weight of the arc ⟨V119894 V119895⟩ Assuming that V119894 andV119895 are the paths from vertex V119894 to V119895 in 119881 the expression is asfollows
119875 = V0 = V119894 V119899 = V119895 (15)
For a path sequence consisting of 119899 path points the lengthof the [1199010 1199011 119901119899minus1 119901119899] path is
119871119899 = 119899sum119896=1
119889119901119896minus1 119901119896 (16)
where 119889119901119896minus1119901119896 is the straight-line distance of the 119901119896minus1 and 119901119896path segments The evaluation function is 119891119871 = 119871119899119889minincluding the fact that 119889min is the linear length of 1199010 and119901119899 When 119891119871 = 1 the path length is the shortest thatis the underwater Robot can sail straight from 1199010 to 119901119899Considering the operating state of underwater Robot as adiscrete process the position of some obstacles will changecausing it to be controlled in the wrong direction So thefiltering function is used to smooth the filtering function
ℎ119896 = ℎ119896minus119897 + 2ℎ119896minus119897+1 + sdot sdot sdot + 2ℎ119896+119897minus12119897 + 1 (17)
where ℎ119896 is the density of obstacles after smoothing and 119897 isthe filter length
It is assumed that the entire underwater Robot path usingthe 119863119875119878119878 algorithm is 119863 = 1198891 1198892 119889119899 including the fact
4 Journal of Robotics
Figure 1 The structure of the cable detection underwater Robot
that 119889119899 is the 119899 obstacle node on the path and the Euclideandistance between all two adjacent obstacles is defined as
119871 = 119897sum119899=1
radic(119909119899+1 minus 119909119899)2 + (119910119899+1 minus 119910119899)2 (18)
where (119909119899 119910119899) is the coordinates of the grid node 119889119899The minimum turning radius 119877min is the limit condition
which cannot be ignored in underwater Robot path planningPath control adopts the NURBS curve fitting method todetermine the minimum turning radius of the underwaterRobot so as to realize the rapid and safe navigation of theunderwater Robot in water Expression is as follows
119891119877 =
119899sum119896=1
1(119903119896 minus 119877min) 119903119896 ge 119877min
infin 119903119896 ≺ 119877min
(19)
In (19) 119903119896 is the turning radius of the path 119896 pointWhen 119903119896 ≺119877min the path control caused by the turning is infinite notworth the candle
In order to satisfy the minimum turning radius of anunderwater Robot the maximum curvature 119896max of theoptimal path generatedmust satisfy the following constraints
119896max ≺ 1119877min(20)
For the underwater Robots with different running pathsit is possible to satisfy the minimum turning radius require-ment of the underwater Robot by selecting the appropriateparameter 119877 to set up the upper model The path controlmethod obtained from the previous analysis is in accord withthe control characteristics and motion characteristics of theunderwater Robot
4 Simulation Results
In order to verify the effectiveness and feasibility of theimproved control method it is necessary to make a com-parative analysis of the improved methods The experiment
e shortest path of the Backstepping method
e real pathe Backstepping method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
Figure 2 The shortest path of the Backstepping method
is simulated by MATLAB and the result is compared byNURBS curve fitting method The simulated cable detectionunderwater Robot is shown in Figure 1 The hardware testplatform is under the condition of single-phase inverter unitand controlled rectifier of model PM201CL1A061 Platformidentification algorithm is DSP27334 main control chip Theproduction company is TI
41 Navigation Path Comparison In order to verify the effec-tiveness of the improved method the experimental rangeis set at a certain number of underwater faults in 100lowast40Backstepping method immune fuzzy PID method andimproved method are adopted to control the shortest pathrespectively The results are shown in Figures 2 3 4 and 5
In Figure 2 the black dotted line represents the controlpoint of the underwater Robot Backstepping method in thecase of underwater obstacles
In Figure 3 the blue cross line represents the control pointof the underwater Robot immune fuzzy PID method in thecase of underwater obstacles
Journal of Robotics 5
e shortest path of immune fuzzy PID method
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe immune fuzzy PID method
Figure 3 The shortest path of immune fuzzy PID method
e shortest path of the improved control method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
e real pathe improved control method
Figure 4 The shortest path of the improved control method
e shortest path of the three methods
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe Backstepping methode immune fuzzy PID methode improved control method
Figure 5 The comparison of the shortest paths of the three-controlmethods
5101520253035404550
time (
min
)
10 20 30 40 50 60 70 80 90 1000path length (m)
e immune fuzzy PID methode Backstepping methode improved method of this paper
Figure 6 Time comparison analysis
The light green dotted line in Figure 4 shows the controlpoint of the underwater Robot of the improved controlmethod in the case of underwater obstacles
In Figure 5 shows the result of the comparison of theshortest paths of the three-control methods
As can be seen from Figures 2ndash5 the results of threemethods are different under the condition of underwaterRobot that has a certain range of motion The Backsteppingmethodwas controlled 62 times of which only 29were on thebest path for the underwater Robot When the obstacles inthe water increase the trajectory of the Robot deviates fromthe optimal path and the control is not effective enough Theimmune fuzzy PID method increases the number of controlaccordingly and the control increases to 85 times with theincrease of the obstacles in water The path of navigationdeviates from the optimumpath only 4 times returning to thebest path but rapidly deviatingThis shows that the stability ispoor the improved method can make the number of control100 times the whole path of the underwater Robot deviateslittle from the optimal path and it coincides with the optimalpathmany times It shows good stability From this we can seethat the presented method has certain advantages
42 Complexity Analysis In the optimal path controlmethodof underwater Robot the degree of underwater Robot pathcontrol is described by the running time of underwater Robotunder the same path of the same length This quantitativedescription of underwater Robot navigation path controlmethod is highly operational and can be used to determinethe trajectory control of underwater Robot directly As aresult the time of the voyage can be calculated directly by thelength of the section and the speed of sailing The expressionfor travel time is
119877119905119894119898119890 = 119877119889119894119904119905119877119904119901119886119888119890 (21)
119877119889119894119904119905 is the length of the current section and 119877119904119901119886119888119890 is theaverage speed of the underwater RobotThe time required forthe Robot to run in three ways is shown in Figure 6
6 Journal of Robotics
As you can see from Figure 6 when the path lengthis constant the three methods vary in time By using theBackstepping method the running time is about 2189 minand the time spent in 0-20M is rapidly increasing while thetime spent in 20-30 does not increase After 30m it had beenon the rise and hadno tendency to declineThe immune fuzzyPIDmethod takes about 325 min time and takes a long timeAs the path of the ship increases the time of sailing increasesaccordingly Only when the region is stable at 40-60 m doesthe rest of the road become on the rise The time taken bythe improved method is about 498 min and the runningtime increases with the increase of path length but the risingtrend is not significant This method has good stability andhas some advantages
5 Concluding Remarks
The traditional control methods always have the problemsof poor effect nonfixed path selection and long timeconsuming Hence a path control method for underwaterRobots based on NURBS curve fitting method is proposedExperimental comparison results are illustrated
(i) Although the number of control is greater than theBackstepping method and the immune fuzzy PID methodwhen navigating in the same path length area the overallcontrol is better than the Backstepping and the immune fuzzyPID method
(ii) Compared with the Backstepping and the immunefuzzy PID method the navigation time of the improvedmethod is shortened by 1691 min and 2752 min respectivelywith good stability and advantages
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work is supported by the Science and TechnologyResearch Program of ChongqingMunicipal Education Com-mission (Grant no KJ1729403) the National Natural ScienceFoundation of China (no 61403055) Chongqing EducationScience and Planning Issues project name the CurrentSituation Analysis and Countermeasure Research of ModernApprenticeship Practice in Vocational Colleges (no 2017-GX-422) the Fundamental Research Funds for the CentralUniversities (Grant no CDJXS12 17 11 01) Intelligent RobotTechnology Research Center of Chongqing College of Elec-tronic Engineering (no XJPT201705)
References
[1] F A AzisM SM ArasM Z A RashidM N Othman and SS Abdullah ldquoProblem identification for Underwater RemotelyOperated Vehicle (ROV) A case studyrdquo in Proceedings of the2nd International Symposium on Robotics and Intelligent Sensors2012 IRIS 2012 pp 554ndash560 mys September 2012
[2] W Zheng Q Zou andWNi ldquoDesign and application of under-water unmanned vehicle simulation system for navigation and
obstacle avoidancerdquoXitong Fangzhen Xuebao Journal of SystemSimulation vol 28 no 1 pp 91ndash98 2016
[3] L Li X Yibo L Li and et al ldquoPath control of submarine swingarm tracked mobile platform based on Backstepping methodrdquoMining and Metallurgy Engineering vol 35 no 6 pp 1ndash5 2015
[4] Z Chaohua T Guoyuan H Daomin and et al ldquoDesign ofDSP control system for attitude control moment gyros groupof autonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[5] O Cerman and P Husek ldquoAdaptive fuzzy sliding mode controlfor electro-hydraulic servo mechanismrdquo Expert Systems withApplications vol 39 no 11 pp 10269ndash10277 2012
[6] M J Mahmoodabadi M Taherkhorsandi and A BagherildquoOptimal robust sliding mode tracking control of a biped robotbased on ingenious multi-objective PSOrdquo Neurocomputing vol124 pp 194ndash209 2014
[7] A Bagheri T Karimi and N Amanifard ldquoTracking perfor-mance control of a cable communicated underwater vehicleusing adaptive neural network controllersrdquo Applied Soft Com-puting vol 10 no 3 pp 908ndash918 2010
[8] S-Y Li C-H Yang C-T Lin L-W Ko and T-T ChiuldquoAdaptive synchronization of chaotic systems with unknownparameters via new backstepping strategyrdquo Nonlinear Dynam-ics vol 70 no 3 pp 2129ndash2143 2012
[9] J Javadi Moghaddam M H Farahani and N Amanifard ldquoAneural network-based sliding-mode control for rotating stalland surge in axial compressorsrdquo Applied Soft Computing vol11 no 1 pp 1036ndash1043 2011
[10] M J Mahmoodabadi S Momennejad and A Bagheri ldquoOnlineoptimal decoupled sliding mode control based on moving leastsquares and particle swarm optimizationrdquo Information Sciencesvol 268 pp 342ndash356 2014
[11] M J Mahmoodabadi S Arabani Mostaghim A Bagheri andN Nariman-zadeh ldquoPareto optimal design of the decoupledsliding mode controller for an inverted pendulum system andits stability simulation via Java programmingrdquo Mathematicaland Computer Modelling vol 57 no 5-6 pp 1070ndash1082 2013
[12] J J Valera Garcıa V Gomez Garay E Irigoyen Gordo FArtaza Fano and M Larrea Sukia ldquoIntelligent Multi-ObjectiveNonlinear Model Predictive Control (iMO-NMPC) Towardsthe rsquoon-linersquo optimization of highly complex control problemsrdquoExpert Systems with Applications vol 39 no 7 pp 6527ndash65402012
[13] S M Zanoli and G Conte ldquoRemotely operated vehicle depthcontrolrdquoControl Engineering Practice vol 11 no 4 pp 453ndash4592003
[14] J Javadi-Moghaddam and A Bagheri ldquoAn adaptive neuro-fuzzy sliding mode based genetic algorithm control system forunder water remotely operated vehiclerdquo Expert Systems withApplications vol 37 no 1 pp 647ndash660 2010
[15] B W Hobson A D Sherman and P R McGill ldquoImagingand sampling beneath free-drifting icebergs with a remotelyoperated vehiclerdquo Deep-Sea Research Part II Topical Studies inOceanography vol 58 no 11-12 pp 1311ndash1317 2011
[16] Z Chaohua T Guoyuan T Daomin et al ldquoDesign of DSPcontrol system for attitude control moment gyros group ofautonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[17] Z Yang F Liu and Y Wang ldquoPath following of underactuatedsurface vessels based on neural sliding moderdquo Ship Building ofChina vol 56 no 2 pp 45ndash55 2015
Journal of Robotics 7
[18] W Yanqiong and C Shiping ldquoDual path routing admissioncontrol protocol for smart road wireless networksrdquo ComputerEngineering vol 41 no 11 pp 24ndash29 2015
[19] SWei H Yulong and L Baoshan ldquoNon symmetric unmannedamphibious platform path tracking controlrdquo Acta Armamen-tarii vol 37 no 7 pp 1161ndash1169 2016
[20] ZChuD Zhu and S X Yang ldquoObserver-based adaptive neuralnetwork trajectory tracking control for remotely operatedvehiclerdquo IEEE Transactions on Neural Networks and LearningSystems vol 28 no 7 pp 1633ndash1645 2017
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Submit your manuscripts atwwwhindawicom
2 Journal of Robotics
2 Construction of Kinematics Model ofUnderwater Robot
When the underwater Robot is effectively controlled underthe condition of network it is necessary to have a goodunderstanding of the underwater Robot The use of sensorsor cameras to detect static and dynamic obstacles and theestablishment of underwater Robot kinematics model canimprove the path control method to provide the basis
When the kinematic model of the underwater Robot isestablished the head adjustment of the target underwaterRobot can be obtained by adjusting the amount of integrationprocessing [15] The kinematic model is given by
1198671198921 = sum1198701199032119862119903 (1)
where 119862119903 is output value and1198701199032 is weighted coefficientFor the existence of the interference of underwater
Robots the use of arithmetic mean filtering method forfiltering to eliminate the Gaussian noise has a positive effect[16] When using the most single arithmetic mean filter thedata received at each time is replaced by the average of thereceived data in the neighborhood of the length of time Theexpression is
119910 (119899) = 1119898119898sum119894=1
119909 (119899 minus 119894) (2)
where119898 is constant 119894 is the number of filters and 119909(119899 minus 119894) isthe wavelength of 119899 minus 119894 filter
In the filter the high frequency of interference removaleffect will not achieve the best results In this case it isnecessary to suppress a higher frequency of interferenceby adding a virtual damping force [17 18] This makes theresponse of the underwater Robot relatively slow increasingits stability The expression is
119906119894 = Δ119905119890119894 + 119879119906119894minus1Δ119905 + 119879 (3)
where Δ119905 is the sampling period 119879 is the inertia constant 119890119894is the time deviation of 119894 and 119906119894minus1 is the response time of time119894
In the case of satisfying the absolute stability of theunderwater Robot the positive moment is used as thestability storage device [18] and then the balance coefficientcan be changed as follows
119862V = 1 minus 119872119908 (1198981015840 + 1198851015840119902)11987210158401199021198851015840119908 (4)
During the operation of the underwater Robot theobstacle in the underwater environment will form a certainpotential field and the repulsion force of 119865119903119890119901 is generatedfor the underwater Robot The closer the distance is thelarger 119865119903119890119901 will that is to say the closer the underwaterRobot and the obstacle the greater the potential energy of
the underwater Robot and vice versa [19] This potential fieldis similar to the potential field inversely proportional to thedistance so the repulsive potential function can be expressedas
119870119903120588 (119883119883119900119887119904) 120588 le 1205881198980 120588 ≺ 120588119898
(5)
where 119870119903 is the repulsive potential field constant 119883 is theposition vector of the underwater Robot 119883119900119887119904 is the obstacleposition vector in thewater 120588 is the shortest distance betweenthe underwater Robot and the obstacle and 120588119898 is the rangeof the repulsive potential field When the distance betweenthe underwater Robot and the obstacle is greater than 120588119898 therepulsive potential field does not interfere with the operationof the underwater Robot
To avoid the collision between the underwater Robot andthe obstacle it is required to set a minimum safe distance1205880 when 120588 rarr 1205880 and 119865119903119890119901 rarr infin and to ensure that 119865119903119890119901 iscontinuous the expression of 119865119903119890119901 is119865119903119890119901=
119870119903( 1(120588 (119883119883119900119887119904) minus 1205880)2 minus
1(120588119898 minus 1205880)2) 120588 le 120588119898
0 120588 ≻ 120588119898(6)
Based on the above sensors or cameras are used tomonitor static and dynamic underwater obstacles and toobtain the position speed and acceleration information ofobstacles in real time These messages can fuse into movingobstacles A number of navigation paths represented by time 119905can be used in the obstacle motion constraints of underwaterRobots Suppose that 119900119887119904119896 is a rigid body with a center of120572119896(119905) = (1205721119896(119905) 1205722119896(119905)) 119896 = 1 2 119902 119905 isin [0 119905119896] and 120572119896() =1 2 119902 is a continuous real vector valued function also thepath of motion obstacles Suppose that the underwater Robotand obstacle 119896 can be represented by119879119903119900119887 and119879119896 respectively119896 = 1 2 119902 When the constraint of the underwater Robotis 1 sin 120579 minus 2 cos 120579 = 0 without lateral collision and thegeneral coordinate system is 119902(119905) = [1199091(119905)1199092(119905)120579(119905)]119879 thekinematic model of the underwater Robot is expressed as fol-lows
119902 = [[[cos 120579119905 0sin 120579119905 00 0
]]][V (119905)119908 (119905)] (7)
where 120592(119905) and 120596(119905) are respectively tangential velocity andangular velocity In the navigation process the speed ofunderwater Robot should be regulated within the maximumallowable speed to prevent the underwater Robot fromcolliding meanwhile the underwater Robot must follow therules of acceleration
Journal of Robotics 3
3 Improvement of Path Control Method forUnderwater Robot
31 Constraint Analysis According to the kinematicmodel ofthe underwater Robot the objective function of minimizingthe path length is obtained
119891 (ℎ) = minsum ℎ(2sum119865119891=1 119864 (119891ℎ) minus 119864 (0) minus 119864 (119905119891))2 (8)
On this basis various constraints are introduced into theobjective function as the penalty term and the expression ofthe self-adaptation function is obtained
min119865119901119888119899119886 = sum ℎ (2sum119865119891=1 119864 (119891ℎ) minus 119864 (0) minus 119864 (119905119891))2+ 119888119899 119865sum119891=0
max (0 119883119897 minus 119864 (1199051015840))(9)
where 1199051015840 = 119891ℎ 119888119899 is a larger value that is penalized forbreaking the constraint 119899 = 1 9 119883119897 is the boundary areaof its 119903119900119887 activity Their constraint types are as follows
(i) Boundary Constraint Assuming that 119883 is the boundaryof the selected area the underwater Robot should be subjectto the following motion boundary constraints during themoving process
119901 (0) = (1199090 1205790)119901 (119905119891) = (119909119891 120579119891)1198830 119883119891 isin 119883
(10)
(ii) Movement Restriction In the process of underwaterRobot navigation there is a certain motion constraint Whenthe ship is sailing along the planning path its acceleration andspeed are prevented from colliding in the prescribed area Inliterature [20] its motion constraint is expressed as follows
120592 (119905) ge 120592min
120592 (119905) le 120592max
120596 (119905) ge 120596min
120596 (119905) le 120596max
119905 isin [0 119905119891]
(11)
(iii) Obstacle Avoidance Constraint To ensure that underwa-ter Robots maintain a minimum safe distance from otherstatic or moving underwater obstacles during navigation119889119900119903119887 119896 and 119889119900119896 are setting as the given safety distance andactual distance of 119903119900119887 and 120572119896 respectively therefore 119889119900119903119887 119896is expressed as
119889119900119903119887 119896 = 1003817100381710038171003817119909 (119905) minus 120572119896 (119905)10038171003817100381710038172 minus (119903 + 119903119896) (12)
where 1 le 119896 le 119902 Thus in119883 119903119900119887 should satisfy the followingbarrier constraints
119889119900119887119904 119896 minus 119889119900119896 (119905) le 0forall119896 = 1 119902 119905 isin [0max (119905119891 119905119896)] (13)
32 Implementation of the Proposed Method Based on theanalysis of constraints for underwater Robot and the basicfluid mechanics the resistance of underwater Robot is deter-mined the filter functions are smoothed and underwaterRobot path is controlled by using NURBS curve fittingmethod
In view of the basic fluid dynamics the total resistance 119877119905of the underwater Robot can be divided into frictional resis-tance 119877119891 and residual resistance 119877119903 When the underwaterRobot is inwater for a long period of time thewave resistanceis negligible and the resistance is as follows
119877119898 = 051205881198812119904 119878 (119862119891 + Δ119862119891 + 119862119901V) (14)
where 120588 is the density of water 119881119904 is the speed of underwaterRobot 119878 is wet surface area 119862119891 is friction resistance coeffi-cient Δ119862119891 is friction resistance subsidy coefficient and 119862119901Vis viscosity resistance coefficient
Supposing that the running path of an underwater Robotcan be represented by a weighted directed graph 119866(119881 119864)in which the set 119881 is a set of fixed points 119899 is the fixed-point number of the fixed-point set 119864 is the arc set of the119898 arc ⟨V119894 V119895⟩ is the arc from V119894 to V119895 in 119864 and 119889⟨V119894 V119895⟩ is thenonnegative weight of the arc ⟨V119894 V119895⟩ Assuming that V119894 andV119895 are the paths from vertex V119894 to V119895 in 119881 the expression is asfollows
119875 = V0 = V119894 V119899 = V119895 (15)
For a path sequence consisting of 119899 path points the lengthof the [1199010 1199011 119901119899minus1 119901119899] path is
119871119899 = 119899sum119896=1
119889119901119896minus1 119901119896 (16)
where 119889119901119896minus1119901119896 is the straight-line distance of the 119901119896minus1 and 119901119896path segments The evaluation function is 119891119871 = 119871119899119889minincluding the fact that 119889min is the linear length of 1199010 and119901119899 When 119891119871 = 1 the path length is the shortest thatis the underwater Robot can sail straight from 1199010 to 119901119899Considering the operating state of underwater Robot as adiscrete process the position of some obstacles will changecausing it to be controlled in the wrong direction So thefiltering function is used to smooth the filtering function
ℎ119896 = ℎ119896minus119897 + 2ℎ119896minus119897+1 + sdot sdot sdot + 2ℎ119896+119897minus12119897 + 1 (17)
where ℎ119896 is the density of obstacles after smoothing and 119897 isthe filter length
It is assumed that the entire underwater Robot path usingthe 119863119875119878119878 algorithm is 119863 = 1198891 1198892 119889119899 including the fact
4 Journal of Robotics
Figure 1 The structure of the cable detection underwater Robot
that 119889119899 is the 119899 obstacle node on the path and the Euclideandistance between all two adjacent obstacles is defined as
119871 = 119897sum119899=1
radic(119909119899+1 minus 119909119899)2 + (119910119899+1 minus 119910119899)2 (18)
where (119909119899 119910119899) is the coordinates of the grid node 119889119899The minimum turning radius 119877min is the limit condition
which cannot be ignored in underwater Robot path planningPath control adopts the NURBS curve fitting method todetermine the minimum turning radius of the underwaterRobot so as to realize the rapid and safe navigation of theunderwater Robot in water Expression is as follows
119891119877 =
119899sum119896=1
1(119903119896 minus 119877min) 119903119896 ge 119877min
infin 119903119896 ≺ 119877min
(19)
In (19) 119903119896 is the turning radius of the path 119896 pointWhen 119903119896 ≺119877min the path control caused by the turning is infinite notworth the candle
In order to satisfy the minimum turning radius of anunderwater Robot the maximum curvature 119896max of theoptimal path generatedmust satisfy the following constraints
119896max ≺ 1119877min(20)
For the underwater Robots with different running pathsit is possible to satisfy the minimum turning radius require-ment of the underwater Robot by selecting the appropriateparameter 119877 to set up the upper model The path controlmethod obtained from the previous analysis is in accord withthe control characteristics and motion characteristics of theunderwater Robot
4 Simulation Results
In order to verify the effectiveness and feasibility of theimproved control method it is necessary to make a com-parative analysis of the improved methods The experiment
e shortest path of the Backstepping method
e real pathe Backstepping method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
Figure 2 The shortest path of the Backstepping method
is simulated by MATLAB and the result is compared byNURBS curve fitting method The simulated cable detectionunderwater Robot is shown in Figure 1 The hardware testplatform is under the condition of single-phase inverter unitand controlled rectifier of model PM201CL1A061 Platformidentification algorithm is DSP27334 main control chip Theproduction company is TI
41 Navigation Path Comparison In order to verify the effec-tiveness of the improved method the experimental rangeis set at a certain number of underwater faults in 100lowast40Backstepping method immune fuzzy PID method andimproved method are adopted to control the shortest pathrespectively The results are shown in Figures 2 3 4 and 5
In Figure 2 the black dotted line represents the controlpoint of the underwater Robot Backstepping method in thecase of underwater obstacles
In Figure 3 the blue cross line represents the control pointof the underwater Robot immune fuzzy PID method in thecase of underwater obstacles
Journal of Robotics 5
e shortest path of immune fuzzy PID method
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe immune fuzzy PID method
Figure 3 The shortest path of immune fuzzy PID method
e shortest path of the improved control method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
e real pathe improved control method
Figure 4 The shortest path of the improved control method
e shortest path of the three methods
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe Backstepping methode immune fuzzy PID methode improved control method
Figure 5 The comparison of the shortest paths of the three-controlmethods
5101520253035404550
time (
min
)
10 20 30 40 50 60 70 80 90 1000path length (m)
e immune fuzzy PID methode Backstepping methode improved method of this paper
Figure 6 Time comparison analysis
The light green dotted line in Figure 4 shows the controlpoint of the underwater Robot of the improved controlmethod in the case of underwater obstacles
In Figure 5 shows the result of the comparison of theshortest paths of the three-control methods
As can be seen from Figures 2ndash5 the results of threemethods are different under the condition of underwaterRobot that has a certain range of motion The Backsteppingmethodwas controlled 62 times of which only 29were on thebest path for the underwater Robot When the obstacles inthe water increase the trajectory of the Robot deviates fromthe optimal path and the control is not effective enough Theimmune fuzzy PID method increases the number of controlaccordingly and the control increases to 85 times with theincrease of the obstacles in water The path of navigationdeviates from the optimumpath only 4 times returning to thebest path but rapidly deviatingThis shows that the stability ispoor the improved method can make the number of control100 times the whole path of the underwater Robot deviateslittle from the optimal path and it coincides with the optimalpathmany times It shows good stability From this we can seethat the presented method has certain advantages
42 Complexity Analysis In the optimal path controlmethodof underwater Robot the degree of underwater Robot pathcontrol is described by the running time of underwater Robotunder the same path of the same length This quantitativedescription of underwater Robot navigation path controlmethod is highly operational and can be used to determinethe trajectory control of underwater Robot directly As aresult the time of the voyage can be calculated directly by thelength of the section and the speed of sailing The expressionfor travel time is
119877119905119894119898119890 = 119877119889119894119904119905119877119904119901119886119888119890 (21)
119877119889119894119904119905 is the length of the current section and 119877119904119901119886119888119890 is theaverage speed of the underwater RobotThe time required forthe Robot to run in three ways is shown in Figure 6
6 Journal of Robotics
As you can see from Figure 6 when the path lengthis constant the three methods vary in time By using theBackstepping method the running time is about 2189 minand the time spent in 0-20M is rapidly increasing while thetime spent in 20-30 does not increase After 30m it had beenon the rise and hadno tendency to declineThe immune fuzzyPIDmethod takes about 325 min time and takes a long timeAs the path of the ship increases the time of sailing increasesaccordingly Only when the region is stable at 40-60 m doesthe rest of the road become on the rise The time taken bythe improved method is about 498 min and the runningtime increases with the increase of path length but the risingtrend is not significant This method has good stability andhas some advantages
5 Concluding Remarks
The traditional control methods always have the problemsof poor effect nonfixed path selection and long timeconsuming Hence a path control method for underwaterRobots based on NURBS curve fitting method is proposedExperimental comparison results are illustrated
(i) Although the number of control is greater than theBackstepping method and the immune fuzzy PID methodwhen navigating in the same path length area the overallcontrol is better than the Backstepping and the immune fuzzyPID method
(ii) Compared with the Backstepping and the immunefuzzy PID method the navigation time of the improvedmethod is shortened by 1691 min and 2752 min respectivelywith good stability and advantages
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work is supported by the Science and TechnologyResearch Program of ChongqingMunicipal Education Com-mission (Grant no KJ1729403) the National Natural ScienceFoundation of China (no 61403055) Chongqing EducationScience and Planning Issues project name the CurrentSituation Analysis and Countermeasure Research of ModernApprenticeship Practice in Vocational Colleges (no 2017-GX-422) the Fundamental Research Funds for the CentralUniversities (Grant no CDJXS12 17 11 01) Intelligent RobotTechnology Research Center of Chongqing College of Elec-tronic Engineering (no XJPT201705)
References
[1] F A AzisM SM ArasM Z A RashidM N Othman and SS Abdullah ldquoProblem identification for Underwater RemotelyOperated Vehicle (ROV) A case studyrdquo in Proceedings of the2nd International Symposium on Robotics and Intelligent Sensors2012 IRIS 2012 pp 554ndash560 mys September 2012
[2] W Zheng Q Zou andWNi ldquoDesign and application of under-water unmanned vehicle simulation system for navigation and
obstacle avoidancerdquoXitong Fangzhen Xuebao Journal of SystemSimulation vol 28 no 1 pp 91ndash98 2016
[3] L Li X Yibo L Li and et al ldquoPath control of submarine swingarm tracked mobile platform based on Backstepping methodrdquoMining and Metallurgy Engineering vol 35 no 6 pp 1ndash5 2015
[4] Z Chaohua T Guoyuan H Daomin and et al ldquoDesign ofDSP control system for attitude control moment gyros groupof autonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[5] O Cerman and P Husek ldquoAdaptive fuzzy sliding mode controlfor electro-hydraulic servo mechanismrdquo Expert Systems withApplications vol 39 no 11 pp 10269ndash10277 2012
[6] M J Mahmoodabadi M Taherkhorsandi and A BagherildquoOptimal robust sliding mode tracking control of a biped robotbased on ingenious multi-objective PSOrdquo Neurocomputing vol124 pp 194ndash209 2014
[7] A Bagheri T Karimi and N Amanifard ldquoTracking perfor-mance control of a cable communicated underwater vehicleusing adaptive neural network controllersrdquo Applied Soft Com-puting vol 10 no 3 pp 908ndash918 2010
[8] S-Y Li C-H Yang C-T Lin L-W Ko and T-T ChiuldquoAdaptive synchronization of chaotic systems with unknownparameters via new backstepping strategyrdquo Nonlinear Dynam-ics vol 70 no 3 pp 2129ndash2143 2012
[9] J Javadi Moghaddam M H Farahani and N Amanifard ldquoAneural network-based sliding-mode control for rotating stalland surge in axial compressorsrdquo Applied Soft Computing vol11 no 1 pp 1036ndash1043 2011
[10] M J Mahmoodabadi S Momennejad and A Bagheri ldquoOnlineoptimal decoupled sliding mode control based on moving leastsquares and particle swarm optimizationrdquo Information Sciencesvol 268 pp 342ndash356 2014
[11] M J Mahmoodabadi S Arabani Mostaghim A Bagheri andN Nariman-zadeh ldquoPareto optimal design of the decoupledsliding mode controller for an inverted pendulum system andits stability simulation via Java programmingrdquo Mathematicaland Computer Modelling vol 57 no 5-6 pp 1070ndash1082 2013
[12] J J Valera Garcıa V Gomez Garay E Irigoyen Gordo FArtaza Fano and M Larrea Sukia ldquoIntelligent Multi-ObjectiveNonlinear Model Predictive Control (iMO-NMPC) Towardsthe rsquoon-linersquo optimization of highly complex control problemsrdquoExpert Systems with Applications vol 39 no 7 pp 6527ndash65402012
[13] S M Zanoli and G Conte ldquoRemotely operated vehicle depthcontrolrdquoControl Engineering Practice vol 11 no 4 pp 453ndash4592003
[14] J Javadi-Moghaddam and A Bagheri ldquoAn adaptive neuro-fuzzy sliding mode based genetic algorithm control system forunder water remotely operated vehiclerdquo Expert Systems withApplications vol 37 no 1 pp 647ndash660 2010
[15] B W Hobson A D Sherman and P R McGill ldquoImagingand sampling beneath free-drifting icebergs with a remotelyoperated vehiclerdquo Deep-Sea Research Part II Topical Studies inOceanography vol 58 no 11-12 pp 1311ndash1317 2011
[16] Z Chaohua T Guoyuan T Daomin et al ldquoDesign of DSPcontrol system for attitude control moment gyros group ofautonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[17] Z Yang F Liu and Y Wang ldquoPath following of underactuatedsurface vessels based on neural sliding moderdquo Ship Building ofChina vol 56 no 2 pp 45ndash55 2015
Journal of Robotics 7
[18] W Yanqiong and C Shiping ldquoDual path routing admissioncontrol protocol for smart road wireless networksrdquo ComputerEngineering vol 41 no 11 pp 24ndash29 2015
[19] SWei H Yulong and L Baoshan ldquoNon symmetric unmannedamphibious platform path tracking controlrdquo Acta Armamen-tarii vol 37 no 7 pp 1161ndash1169 2016
[20] ZChuD Zhu and S X Yang ldquoObserver-based adaptive neuralnetwork trajectory tracking control for remotely operatedvehiclerdquo IEEE Transactions on Neural Networks and LearningSystems vol 28 no 7 pp 1633ndash1645 2017
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Journal of Robotics 3
3 Improvement of Path Control Method forUnderwater Robot
31 Constraint Analysis According to the kinematicmodel ofthe underwater Robot the objective function of minimizingthe path length is obtained
119891 (ℎ) = minsum ℎ(2sum119865119891=1 119864 (119891ℎ) minus 119864 (0) minus 119864 (119905119891))2 (8)
On this basis various constraints are introduced into theobjective function as the penalty term and the expression ofthe self-adaptation function is obtained
min119865119901119888119899119886 = sum ℎ (2sum119865119891=1 119864 (119891ℎ) minus 119864 (0) minus 119864 (119905119891))2+ 119888119899 119865sum119891=0
max (0 119883119897 minus 119864 (1199051015840))(9)
where 1199051015840 = 119891ℎ 119888119899 is a larger value that is penalized forbreaking the constraint 119899 = 1 9 119883119897 is the boundary areaof its 119903119900119887 activity Their constraint types are as follows
(i) Boundary Constraint Assuming that 119883 is the boundaryof the selected area the underwater Robot should be subjectto the following motion boundary constraints during themoving process
119901 (0) = (1199090 1205790)119901 (119905119891) = (119909119891 120579119891)1198830 119883119891 isin 119883
(10)
(ii) Movement Restriction In the process of underwaterRobot navigation there is a certain motion constraint Whenthe ship is sailing along the planning path its acceleration andspeed are prevented from colliding in the prescribed area Inliterature [20] its motion constraint is expressed as follows
120592 (119905) ge 120592min
120592 (119905) le 120592max
120596 (119905) ge 120596min
120596 (119905) le 120596max
119905 isin [0 119905119891]
(11)
(iii) Obstacle Avoidance Constraint To ensure that underwa-ter Robots maintain a minimum safe distance from otherstatic or moving underwater obstacles during navigation119889119900119903119887 119896 and 119889119900119896 are setting as the given safety distance andactual distance of 119903119900119887 and 120572119896 respectively therefore 119889119900119903119887 119896is expressed as
119889119900119903119887 119896 = 1003817100381710038171003817119909 (119905) minus 120572119896 (119905)10038171003817100381710038172 minus (119903 + 119903119896) (12)
where 1 le 119896 le 119902 Thus in119883 119903119900119887 should satisfy the followingbarrier constraints
119889119900119887119904 119896 minus 119889119900119896 (119905) le 0forall119896 = 1 119902 119905 isin [0max (119905119891 119905119896)] (13)
32 Implementation of the Proposed Method Based on theanalysis of constraints for underwater Robot and the basicfluid mechanics the resistance of underwater Robot is deter-mined the filter functions are smoothed and underwaterRobot path is controlled by using NURBS curve fittingmethod
In view of the basic fluid dynamics the total resistance 119877119905of the underwater Robot can be divided into frictional resis-tance 119877119891 and residual resistance 119877119903 When the underwaterRobot is inwater for a long period of time thewave resistanceis negligible and the resistance is as follows
119877119898 = 051205881198812119904 119878 (119862119891 + Δ119862119891 + 119862119901V) (14)
where 120588 is the density of water 119881119904 is the speed of underwaterRobot 119878 is wet surface area 119862119891 is friction resistance coeffi-cient Δ119862119891 is friction resistance subsidy coefficient and 119862119901Vis viscosity resistance coefficient
Supposing that the running path of an underwater Robotcan be represented by a weighted directed graph 119866(119881 119864)in which the set 119881 is a set of fixed points 119899 is the fixed-point number of the fixed-point set 119864 is the arc set of the119898 arc ⟨V119894 V119895⟩ is the arc from V119894 to V119895 in 119864 and 119889⟨V119894 V119895⟩ is thenonnegative weight of the arc ⟨V119894 V119895⟩ Assuming that V119894 andV119895 are the paths from vertex V119894 to V119895 in 119881 the expression is asfollows
119875 = V0 = V119894 V119899 = V119895 (15)
For a path sequence consisting of 119899 path points the lengthof the [1199010 1199011 119901119899minus1 119901119899] path is
119871119899 = 119899sum119896=1
119889119901119896minus1 119901119896 (16)
where 119889119901119896minus1119901119896 is the straight-line distance of the 119901119896minus1 and 119901119896path segments The evaluation function is 119891119871 = 119871119899119889minincluding the fact that 119889min is the linear length of 1199010 and119901119899 When 119891119871 = 1 the path length is the shortest thatis the underwater Robot can sail straight from 1199010 to 119901119899Considering the operating state of underwater Robot as adiscrete process the position of some obstacles will changecausing it to be controlled in the wrong direction So thefiltering function is used to smooth the filtering function
ℎ119896 = ℎ119896minus119897 + 2ℎ119896minus119897+1 + sdot sdot sdot + 2ℎ119896+119897minus12119897 + 1 (17)
where ℎ119896 is the density of obstacles after smoothing and 119897 isthe filter length
It is assumed that the entire underwater Robot path usingthe 119863119875119878119878 algorithm is 119863 = 1198891 1198892 119889119899 including the fact
4 Journal of Robotics
Figure 1 The structure of the cable detection underwater Robot
that 119889119899 is the 119899 obstacle node on the path and the Euclideandistance between all two adjacent obstacles is defined as
119871 = 119897sum119899=1
radic(119909119899+1 minus 119909119899)2 + (119910119899+1 minus 119910119899)2 (18)
where (119909119899 119910119899) is the coordinates of the grid node 119889119899The minimum turning radius 119877min is the limit condition
which cannot be ignored in underwater Robot path planningPath control adopts the NURBS curve fitting method todetermine the minimum turning radius of the underwaterRobot so as to realize the rapid and safe navigation of theunderwater Robot in water Expression is as follows
119891119877 =
119899sum119896=1
1(119903119896 minus 119877min) 119903119896 ge 119877min
infin 119903119896 ≺ 119877min
(19)
In (19) 119903119896 is the turning radius of the path 119896 pointWhen 119903119896 ≺119877min the path control caused by the turning is infinite notworth the candle
In order to satisfy the minimum turning radius of anunderwater Robot the maximum curvature 119896max of theoptimal path generatedmust satisfy the following constraints
119896max ≺ 1119877min(20)
For the underwater Robots with different running pathsit is possible to satisfy the minimum turning radius require-ment of the underwater Robot by selecting the appropriateparameter 119877 to set up the upper model The path controlmethod obtained from the previous analysis is in accord withthe control characteristics and motion characteristics of theunderwater Robot
4 Simulation Results
In order to verify the effectiveness and feasibility of theimproved control method it is necessary to make a com-parative analysis of the improved methods The experiment
e shortest path of the Backstepping method
e real pathe Backstepping method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
Figure 2 The shortest path of the Backstepping method
is simulated by MATLAB and the result is compared byNURBS curve fitting method The simulated cable detectionunderwater Robot is shown in Figure 1 The hardware testplatform is under the condition of single-phase inverter unitand controlled rectifier of model PM201CL1A061 Platformidentification algorithm is DSP27334 main control chip Theproduction company is TI
41 Navigation Path Comparison In order to verify the effec-tiveness of the improved method the experimental rangeis set at a certain number of underwater faults in 100lowast40Backstepping method immune fuzzy PID method andimproved method are adopted to control the shortest pathrespectively The results are shown in Figures 2 3 4 and 5
In Figure 2 the black dotted line represents the controlpoint of the underwater Robot Backstepping method in thecase of underwater obstacles
In Figure 3 the blue cross line represents the control pointof the underwater Robot immune fuzzy PID method in thecase of underwater obstacles
Journal of Robotics 5
e shortest path of immune fuzzy PID method
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe immune fuzzy PID method
Figure 3 The shortest path of immune fuzzy PID method
e shortest path of the improved control method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
e real pathe improved control method
Figure 4 The shortest path of the improved control method
e shortest path of the three methods
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe Backstepping methode immune fuzzy PID methode improved control method
Figure 5 The comparison of the shortest paths of the three-controlmethods
5101520253035404550
time (
min
)
10 20 30 40 50 60 70 80 90 1000path length (m)
e immune fuzzy PID methode Backstepping methode improved method of this paper
Figure 6 Time comparison analysis
The light green dotted line in Figure 4 shows the controlpoint of the underwater Robot of the improved controlmethod in the case of underwater obstacles
In Figure 5 shows the result of the comparison of theshortest paths of the three-control methods
As can be seen from Figures 2ndash5 the results of threemethods are different under the condition of underwaterRobot that has a certain range of motion The Backsteppingmethodwas controlled 62 times of which only 29were on thebest path for the underwater Robot When the obstacles inthe water increase the trajectory of the Robot deviates fromthe optimal path and the control is not effective enough Theimmune fuzzy PID method increases the number of controlaccordingly and the control increases to 85 times with theincrease of the obstacles in water The path of navigationdeviates from the optimumpath only 4 times returning to thebest path but rapidly deviatingThis shows that the stability ispoor the improved method can make the number of control100 times the whole path of the underwater Robot deviateslittle from the optimal path and it coincides with the optimalpathmany times It shows good stability From this we can seethat the presented method has certain advantages
42 Complexity Analysis In the optimal path controlmethodof underwater Robot the degree of underwater Robot pathcontrol is described by the running time of underwater Robotunder the same path of the same length This quantitativedescription of underwater Robot navigation path controlmethod is highly operational and can be used to determinethe trajectory control of underwater Robot directly As aresult the time of the voyage can be calculated directly by thelength of the section and the speed of sailing The expressionfor travel time is
119877119905119894119898119890 = 119877119889119894119904119905119877119904119901119886119888119890 (21)
119877119889119894119904119905 is the length of the current section and 119877119904119901119886119888119890 is theaverage speed of the underwater RobotThe time required forthe Robot to run in three ways is shown in Figure 6
6 Journal of Robotics
As you can see from Figure 6 when the path lengthis constant the three methods vary in time By using theBackstepping method the running time is about 2189 minand the time spent in 0-20M is rapidly increasing while thetime spent in 20-30 does not increase After 30m it had beenon the rise and hadno tendency to declineThe immune fuzzyPIDmethod takes about 325 min time and takes a long timeAs the path of the ship increases the time of sailing increasesaccordingly Only when the region is stable at 40-60 m doesthe rest of the road become on the rise The time taken bythe improved method is about 498 min and the runningtime increases with the increase of path length but the risingtrend is not significant This method has good stability andhas some advantages
5 Concluding Remarks
The traditional control methods always have the problemsof poor effect nonfixed path selection and long timeconsuming Hence a path control method for underwaterRobots based on NURBS curve fitting method is proposedExperimental comparison results are illustrated
(i) Although the number of control is greater than theBackstepping method and the immune fuzzy PID methodwhen navigating in the same path length area the overallcontrol is better than the Backstepping and the immune fuzzyPID method
(ii) Compared with the Backstepping and the immunefuzzy PID method the navigation time of the improvedmethod is shortened by 1691 min and 2752 min respectivelywith good stability and advantages
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work is supported by the Science and TechnologyResearch Program of ChongqingMunicipal Education Com-mission (Grant no KJ1729403) the National Natural ScienceFoundation of China (no 61403055) Chongqing EducationScience and Planning Issues project name the CurrentSituation Analysis and Countermeasure Research of ModernApprenticeship Practice in Vocational Colleges (no 2017-GX-422) the Fundamental Research Funds for the CentralUniversities (Grant no CDJXS12 17 11 01) Intelligent RobotTechnology Research Center of Chongqing College of Elec-tronic Engineering (no XJPT201705)
References
[1] F A AzisM SM ArasM Z A RashidM N Othman and SS Abdullah ldquoProblem identification for Underwater RemotelyOperated Vehicle (ROV) A case studyrdquo in Proceedings of the2nd International Symposium on Robotics and Intelligent Sensors2012 IRIS 2012 pp 554ndash560 mys September 2012
[2] W Zheng Q Zou andWNi ldquoDesign and application of under-water unmanned vehicle simulation system for navigation and
obstacle avoidancerdquoXitong Fangzhen Xuebao Journal of SystemSimulation vol 28 no 1 pp 91ndash98 2016
[3] L Li X Yibo L Li and et al ldquoPath control of submarine swingarm tracked mobile platform based on Backstepping methodrdquoMining and Metallurgy Engineering vol 35 no 6 pp 1ndash5 2015
[4] Z Chaohua T Guoyuan H Daomin and et al ldquoDesign ofDSP control system for attitude control moment gyros groupof autonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[5] O Cerman and P Husek ldquoAdaptive fuzzy sliding mode controlfor electro-hydraulic servo mechanismrdquo Expert Systems withApplications vol 39 no 11 pp 10269ndash10277 2012
[6] M J Mahmoodabadi M Taherkhorsandi and A BagherildquoOptimal robust sliding mode tracking control of a biped robotbased on ingenious multi-objective PSOrdquo Neurocomputing vol124 pp 194ndash209 2014
[7] A Bagheri T Karimi and N Amanifard ldquoTracking perfor-mance control of a cable communicated underwater vehicleusing adaptive neural network controllersrdquo Applied Soft Com-puting vol 10 no 3 pp 908ndash918 2010
[8] S-Y Li C-H Yang C-T Lin L-W Ko and T-T ChiuldquoAdaptive synchronization of chaotic systems with unknownparameters via new backstepping strategyrdquo Nonlinear Dynam-ics vol 70 no 3 pp 2129ndash2143 2012
[9] J Javadi Moghaddam M H Farahani and N Amanifard ldquoAneural network-based sliding-mode control for rotating stalland surge in axial compressorsrdquo Applied Soft Computing vol11 no 1 pp 1036ndash1043 2011
[10] M J Mahmoodabadi S Momennejad and A Bagheri ldquoOnlineoptimal decoupled sliding mode control based on moving leastsquares and particle swarm optimizationrdquo Information Sciencesvol 268 pp 342ndash356 2014
[11] M J Mahmoodabadi S Arabani Mostaghim A Bagheri andN Nariman-zadeh ldquoPareto optimal design of the decoupledsliding mode controller for an inverted pendulum system andits stability simulation via Java programmingrdquo Mathematicaland Computer Modelling vol 57 no 5-6 pp 1070ndash1082 2013
[12] J J Valera Garcıa V Gomez Garay E Irigoyen Gordo FArtaza Fano and M Larrea Sukia ldquoIntelligent Multi-ObjectiveNonlinear Model Predictive Control (iMO-NMPC) Towardsthe rsquoon-linersquo optimization of highly complex control problemsrdquoExpert Systems with Applications vol 39 no 7 pp 6527ndash65402012
[13] S M Zanoli and G Conte ldquoRemotely operated vehicle depthcontrolrdquoControl Engineering Practice vol 11 no 4 pp 453ndash4592003
[14] J Javadi-Moghaddam and A Bagheri ldquoAn adaptive neuro-fuzzy sliding mode based genetic algorithm control system forunder water remotely operated vehiclerdquo Expert Systems withApplications vol 37 no 1 pp 647ndash660 2010
[15] B W Hobson A D Sherman and P R McGill ldquoImagingand sampling beneath free-drifting icebergs with a remotelyoperated vehiclerdquo Deep-Sea Research Part II Topical Studies inOceanography vol 58 no 11-12 pp 1311ndash1317 2011
[16] Z Chaohua T Guoyuan T Daomin et al ldquoDesign of DSPcontrol system for attitude control moment gyros group ofautonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[17] Z Yang F Liu and Y Wang ldquoPath following of underactuatedsurface vessels based on neural sliding moderdquo Ship Building ofChina vol 56 no 2 pp 45ndash55 2015
Journal of Robotics 7
[18] W Yanqiong and C Shiping ldquoDual path routing admissioncontrol protocol for smart road wireless networksrdquo ComputerEngineering vol 41 no 11 pp 24ndash29 2015
[19] SWei H Yulong and L Baoshan ldquoNon symmetric unmannedamphibious platform path tracking controlrdquo Acta Armamen-tarii vol 37 no 7 pp 1161ndash1169 2016
[20] ZChuD Zhu and S X Yang ldquoObserver-based adaptive neuralnetwork trajectory tracking control for remotely operatedvehiclerdquo IEEE Transactions on Neural Networks and LearningSystems vol 28 no 7 pp 1633ndash1645 2017
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
4 Journal of Robotics
Figure 1 The structure of the cable detection underwater Robot
that 119889119899 is the 119899 obstacle node on the path and the Euclideandistance between all two adjacent obstacles is defined as
119871 = 119897sum119899=1
radic(119909119899+1 minus 119909119899)2 + (119910119899+1 minus 119910119899)2 (18)
where (119909119899 119910119899) is the coordinates of the grid node 119889119899The minimum turning radius 119877min is the limit condition
which cannot be ignored in underwater Robot path planningPath control adopts the NURBS curve fitting method todetermine the minimum turning radius of the underwaterRobot so as to realize the rapid and safe navigation of theunderwater Robot in water Expression is as follows
119891119877 =
119899sum119896=1
1(119903119896 minus 119877min) 119903119896 ge 119877min
infin 119903119896 ≺ 119877min
(19)
In (19) 119903119896 is the turning radius of the path 119896 pointWhen 119903119896 ≺119877min the path control caused by the turning is infinite notworth the candle
In order to satisfy the minimum turning radius of anunderwater Robot the maximum curvature 119896max of theoptimal path generatedmust satisfy the following constraints
119896max ≺ 1119877min(20)
For the underwater Robots with different running pathsit is possible to satisfy the minimum turning radius require-ment of the underwater Robot by selecting the appropriateparameter 119877 to set up the upper model The path controlmethod obtained from the previous analysis is in accord withthe control characteristics and motion characteristics of theunderwater Robot
4 Simulation Results
In order to verify the effectiveness and feasibility of theimproved control method it is necessary to make a com-parative analysis of the improved methods The experiment
e shortest path of the Backstepping method
e real pathe Backstepping method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
Figure 2 The shortest path of the Backstepping method
is simulated by MATLAB and the result is compared byNURBS curve fitting method The simulated cable detectionunderwater Robot is shown in Figure 1 The hardware testplatform is under the condition of single-phase inverter unitand controlled rectifier of model PM201CL1A061 Platformidentification algorithm is DSP27334 main control chip Theproduction company is TI
41 Navigation Path Comparison In order to verify the effec-tiveness of the improved method the experimental rangeis set at a certain number of underwater faults in 100lowast40Backstepping method immune fuzzy PID method andimproved method are adopted to control the shortest pathrespectively The results are shown in Figures 2 3 4 and 5
In Figure 2 the black dotted line represents the controlpoint of the underwater Robot Backstepping method in thecase of underwater obstacles
In Figure 3 the blue cross line represents the control pointof the underwater Robot immune fuzzy PID method in thecase of underwater obstacles
Journal of Robotics 5
e shortest path of immune fuzzy PID method
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe immune fuzzy PID method
Figure 3 The shortest path of immune fuzzy PID method
e shortest path of the improved control method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
e real pathe improved control method
Figure 4 The shortest path of the improved control method
e shortest path of the three methods
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe Backstepping methode immune fuzzy PID methode improved control method
Figure 5 The comparison of the shortest paths of the three-controlmethods
5101520253035404550
time (
min
)
10 20 30 40 50 60 70 80 90 1000path length (m)
e immune fuzzy PID methode Backstepping methode improved method of this paper
Figure 6 Time comparison analysis
The light green dotted line in Figure 4 shows the controlpoint of the underwater Robot of the improved controlmethod in the case of underwater obstacles
In Figure 5 shows the result of the comparison of theshortest paths of the three-control methods
As can be seen from Figures 2ndash5 the results of threemethods are different under the condition of underwaterRobot that has a certain range of motion The Backsteppingmethodwas controlled 62 times of which only 29were on thebest path for the underwater Robot When the obstacles inthe water increase the trajectory of the Robot deviates fromthe optimal path and the control is not effective enough Theimmune fuzzy PID method increases the number of controlaccordingly and the control increases to 85 times with theincrease of the obstacles in water The path of navigationdeviates from the optimumpath only 4 times returning to thebest path but rapidly deviatingThis shows that the stability ispoor the improved method can make the number of control100 times the whole path of the underwater Robot deviateslittle from the optimal path and it coincides with the optimalpathmany times It shows good stability From this we can seethat the presented method has certain advantages
42 Complexity Analysis In the optimal path controlmethodof underwater Robot the degree of underwater Robot pathcontrol is described by the running time of underwater Robotunder the same path of the same length This quantitativedescription of underwater Robot navigation path controlmethod is highly operational and can be used to determinethe trajectory control of underwater Robot directly As aresult the time of the voyage can be calculated directly by thelength of the section and the speed of sailing The expressionfor travel time is
119877119905119894119898119890 = 119877119889119894119904119905119877119904119901119886119888119890 (21)
119877119889119894119904119905 is the length of the current section and 119877119904119901119886119888119890 is theaverage speed of the underwater RobotThe time required forthe Robot to run in three ways is shown in Figure 6
6 Journal of Robotics
As you can see from Figure 6 when the path lengthis constant the three methods vary in time By using theBackstepping method the running time is about 2189 minand the time spent in 0-20M is rapidly increasing while thetime spent in 20-30 does not increase After 30m it had beenon the rise and hadno tendency to declineThe immune fuzzyPIDmethod takes about 325 min time and takes a long timeAs the path of the ship increases the time of sailing increasesaccordingly Only when the region is stable at 40-60 m doesthe rest of the road become on the rise The time taken bythe improved method is about 498 min and the runningtime increases with the increase of path length but the risingtrend is not significant This method has good stability andhas some advantages
5 Concluding Remarks
The traditional control methods always have the problemsof poor effect nonfixed path selection and long timeconsuming Hence a path control method for underwaterRobots based on NURBS curve fitting method is proposedExperimental comparison results are illustrated
(i) Although the number of control is greater than theBackstepping method and the immune fuzzy PID methodwhen navigating in the same path length area the overallcontrol is better than the Backstepping and the immune fuzzyPID method
(ii) Compared with the Backstepping and the immunefuzzy PID method the navigation time of the improvedmethod is shortened by 1691 min and 2752 min respectivelywith good stability and advantages
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work is supported by the Science and TechnologyResearch Program of ChongqingMunicipal Education Com-mission (Grant no KJ1729403) the National Natural ScienceFoundation of China (no 61403055) Chongqing EducationScience and Planning Issues project name the CurrentSituation Analysis and Countermeasure Research of ModernApprenticeship Practice in Vocational Colleges (no 2017-GX-422) the Fundamental Research Funds for the CentralUniversities (Grant no CDJXS12 17 11 01) Intelligent RobotTechnology Research Center of Chongqing College of Elec-tronic Engineering (no XJPT201705)
References
[1] F A AzisM SM ArasM Z A RashidM N Othman and SS Abdullah ldquoProblem identification for Underwater RemotelyOperated Vehicle (ROV) A case studyrdquo in Proceedings of the2nd International Symposium on Robotics and Intelligent Sensors2012 IRIS 2012 pp 554ndash560 mys September 2012
[2] W Zheng Q Zou andWNi ldquoDesign and application of under-water unmanned vehicle simulation system for navigation and
obstacle avoidancerdquoXitong Fangzhen Xuebao Journal of SystemSimulation vol 28 no 1 pp 91ndash98 2016
[3] L Li X Yibo L Li and et al ldquoPath control of submarine swingarm tracked mobile platform based on Backstepping methodrdquoMining and Metallurgy Engineering vol 35 no 6 pp 1ndash5 2015
[4] Z Chaohua T Guoyuan H Daomin and et al ldquoDesign ofDSP control system for attitude control moment gyros groupof autonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[5] O Cerman and P Husek ldquoAdaptive fuzzy sliding mode controlfor electro-hydraulic servo mechanismrdquo Expert Systems withApplications vol 39 no 11 pp 10269ndash10277 2012
[6] M J Mahmoodabadi M Taherkhorsandi and A BagherildquoOptimal robust sliding mode tracking control of a biped robotbased on ingenious multi-objective PSOrdquo Neurocomputing vol124 pp 194ndash209 2014
[7] A Bagheri T Karimi and N Amanifard ldquoTracking perfor-mance control of a cable communicated underwater vehicleusing adaptive neural network controllersrdquo Applied Soft Com-puting vol 10 no 3 pp 908ndash918 2010
[8] S-Y Li C-H Yang C-T Lin L-W Ko and T-T ChiuldquoAdaptive synchronization of chaotic systems with unknownparameters via new backstepping strategyrdquo Nonlinear Dynam-ics vol 70 no 3 pp 2129ndash2143 2012
[9] J Javadi Moghaddam M H Farahani and N Amanifard ldquoAneural network-based sliding-mode control for rotating stalland surge in axial compressorsrdquo Applied Soft Computing vol11 no 1 pp 1036ndash1043 2011
[10] M J Mahmoodabadi S Momennejad and A Bagheri ldquoOnlineoptimal decoupled sliding mode control based on moving leastsquares and particle swarm optimizationrdquo Information Sciencesvol 268 pp 342ndash356 2014
[11] M J Mahmoodabadi S Arabani Mostaghim A Bagheri andN Nariman-zadeh ldquoPareto optimal design of the decoupledsliding mode controller for an inverted pendulum system andits stability simulation via Java programmingrdquo Mathematicaland Computer Modelling vol 57 no 5-6 pp 1070ndash1082 2013
[12] J J Valera Garcıa V Gomez Garay E Irigoyen Gordo FArtaza Fano and M Larrea Sukia ldquoIntelligent Multi-ObjectiveNonlinear Model Predictive Control (iMO-NMPC) Towardsthe rsquoon-linersquo optimization of highly complex control problemsrdquoExpert Systems with Applications vol 39 no 7 pp 6527ndash65402012
[13] S M Zanoli and G Conte ldquoRemotely operated vehicle depthcontrolrdquoControl Engineering Practice vol 11 no 4 pp 453ndash4592003
[14] J Javadi-Moghaddam and A Bagheri ldquoAn adaptive neuro-fuzzy sliding mode based genetic algorithm control system forunder water remotely operated vehiclerdquo Expert Systems withApplications vol 37 no 1 pp 647ndash660 2010
[15] B W Hobson A D Sherman and P R McGill ldquoImagingand sampling beneath free-drifting icebergs with a remotelyoperated vehiclerdquo Deep-Sea Research Part II Topical Studies inOceanography vol 58 no 11-12 pp 1311ndash1317 2011
[16] Z Chaohua T Guoyuan T Daomin et al ldquoDesign of DSPcontrol system for attitude control moment gyros group ofautonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[17] Z Yang F Liu and Y Wang ldquoPath following of underactuatedsurface vessels based on neural sliding moderdquo Ship Building ofChina vol 56 no 2 pp 45ndash55 2015
Journal of Robotics 7
[18] W Yanqiong and C Shiping ldquoDual path routing admissioncontrol protocol for smart road wireless networksrdquo ComputerEngineering vol 41 no 11 pp 24ndash29 2015
[19] SWei H Yulong and L Baoshan ldquoNon symmetric unmannedamphibious platform path tracking controlrdquo Acta Armamen-tarii vol 37 no 7 pp 1161ndash1169 2016
[20] ZChuD Zhu and S X Yang ldquoObserver-based adaptive neuralnetwork trajectory tracking control for remotely operatedvehiclerdquo IEEE Transactions on Neural Networks and LearningSystems vol 28 no 7 pp 1633ndash1645 2017
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Journal of Robotics 5
e shortest path of immune fuzzy PID method
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe immune fuzzy PID method
Figure 3 The shortest path of immune fuzzy PID method
e shortest path of the improved control method
5
10
15
20
25
30
35
40
Wid
th (m
)
20 40 60 80 100 1200Length (m)
e real pathe improved control method
Figure 4 The shortest path of the improved control method
e shortest path of the three methods
20 40 60 80 100 1200Length (m)
5
10
15
20
25
30
35
40
Wid
th (m
)
e real pathe Backstepping methode immune fuzzy PID methode improved control method
Figure 5 The comparison of the shortest paths of the three-controlmethods
5101520253035404550
time (
min
)
10 20 30 40 50 60 70 80 90 1000path length (m)
e immune fuzzy PID methode Backstepping methode improved method of this paper
Figure 6 Time comparison analysis
The light green dotted line in Figure 4 shows the controlpoint of the underwater Robot of the improved controlmethod in the case of underwater obstacles
In Figure 5 shows the result of the comparison of theshortest paths of the three-control methods
As can be seen from Figures 2ndash5 the results of threemethods are different under the condition of underwaterRobot that has a certain range of motion The Backsteppingmethodwas controlled 62 times of which only 29were on thebest path for the underwater Robot When the obstacles inthe water increase the trajectory of the Robot deviates fromthe optimal path and the control is not effective enough Theimmune fuzzy PID method increases the number of controlaccordingly and the control increases to 85 times with theincrease of the obstacles in water The path of navigationdeviates from the optimumpath only 4 times returning to thebest path but rapidly deviatingThis shows that the stability ispoor the improved method can make the number of control100 times the whole path of the underwater Robot deviateslittle from the optimal path and it coincides with the optimalpathmany times It shows good stability From this we can seethat the presented method has certain advantages
42 Complexity Analysis In the optimal path controlmethodof underwater Robot the degree of underwater Robot pathcontrol is described by the running time of underwater Robotunder the same path of the same length This quantitativedescription of underwater Robot navigation path controlmethod is highly operational and can be used to determinethe trajectory control of underwater Robot directly As aresult the time of the voyage can be calculated directly by thelength of the section and the speed of sailing The expressionfor travel time is
119877119905119894119898119890 = 119877119889119894119904119905119877119904119901119886119888119890 (21)
119877119889119894119904119905 is the length of the current section and 119877119904119901119886119888119890 is theaverage speed of the underwater RobotThe time required forthe Robot to run in three ways is shown in Figure 6
6 Journal of Robotics
As you can see from Figure 6 when the path lengthis constant the three methods vary in time By using theBackstepping method the running time is about 2189 minand the time spent in 0-20M is rapidly increasing while thetime spent in 20-30 does not increase After 30m it had beenon the rise and hadno tendency to declineThe immune fuzzyPIDmethod takes about 325 min time and takes a long timeAs the path of the ship increases the time of sailing increasesaccordingly Only when the region is stable at 40-60 m doesthe rest of the road become on the rise The time taken bythe improved method is about 498 min and the runningtime increases with the increase of path length but the risingtrend is not significant This method has good stability andhas some advantages
5 Concluding Remarks
The traditional control methods always have the problemsof poor effect nonfixed path selection and long timeconsuming Hence a path control method for underwaterRobots based on NURBS curve fitting method is proposedExperimental comparison results are illustrated
(i) Although the number of control is greater than theBackstepping method and the immune fuzzy PID methodwhen navigating in the same path length area the overallcontrol is better than the Backstepping and the immune fuzzyPID method
(ii) Compared with the Backstepping and the immunefuzzy PID method the navigation time of the improvedmethod is shortened by 1691 min and 2752 min respectivelywith good stability and advantages
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work is supported by the Science and TechnologyResearch Program of ChongqingMunicipal Education Com-mission (Grant no KJ1729403) the National Natural ScienceFoundation of China (no 61403055) Chongqing EducationScience and Planning Issues project name the CurrentSituation Analysis and Countermeasure Research of ModernApprenticeship Practice in Vocational Colleges (no 2017-GX-422) the Fundamental Research Funds for the CentralUniversities (Grant no CDJXS12 17 11 01) Intelligent RobotTechnology Research Center of Chongqing College of Elec-tronic Engineering (no XJPT201705)
References
[1] F A AzisM SM ArasM Z A RashidM N Othman and SS Abdullah ldquoProblem identification for Underwater RemotelyOperated Vehicle (ROV) A case studyrdquo in Proceedings of the2nd International Symposium on Robotics and Intelligent Sensors2012 IRIS 2012 pp 554ndash560 mys September 2012
[2] W Zheng Q Zou andWNi ldquoDesign and application of under-water unmanned vehicle simulation system for navigation and
obstacle avoidancerdquoXitong Fangzhen Xuebao Journal of SystemSimulation vol 28 no 1 pp 91ndash98 2016
[3] L Li X Yibo L Li and et al ldquoPath control of submarine swingarm tracked mobile platform based on Backstepping methodrdquoMining and Metallurgy Engineering vol 35 no 6 pp 1ndash5 2015
[4] Z Chaohua T Guoyuan H Daomin and et al ldquoDesign ofDSP control system for attitude control moment gyros groupof autonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[5] O Cerman and P Husek ldquoAdaptive fuzzy sliding mode controlfor electro-hydraulic servo mechanismrdquo Expert Systems withApplications vol 39 no 11 pp 10269ndash10277 2012
[6] M J Mahmoodabadi M Taherkhorsandi and A BagherildquoOptimal robust sliding mode tracking control of a biped robotbased on ingenious multi-objective PSOrdquo Neurocomputing vol124 pp 194ndash209 2014
[7] A Bagheri T Karimi and N Amanifard ldquoTracking perfor-mance control of a cable communicated underwater vehicleusing adaptive neural network controllersrdquo Applied Soft Com-puting vol 10 no 3 pp 908ndash918 2010
[8] S-Y Li C-H Yang C-T Lin L-W Ko and T-T ChiuldquoAdaptive synchronization of chaotic systems with unknownparameters via new backstepping strategyrdquo Nonlinear Dynam-ics vol 70 no 3 pp 2129ndash2143 2012
[9] J Javadi Moghaddam M H Farahani and N Amanifard ldquoAneural network-based sliding-mode control for rotating stalland surge in axial compressorsrdquo Applied Soft Computing vol11 no 1 pp 1036ndash1043 2011
[10] M J Mahmoodabadi S Momennejad and A Bagheri ldquoOnlineoptimal decoupled sliding mode control based on moving leastsquares and particle swarm optimizationrdquo Information Sciencesvol 268 pp 342ndash356 2014
[11] M J Mahmoodabadi S Arabani Mostaghim A Bagheri andN Nariman-zadeh ldquoPareto optimal design of the decoupledsliding mode controller for an inverted pendulum system andits stability simulation via Java programmingrdquo Mathematicaland Computer Modelling vol 57 no 5-6 pp 1070ndash1082 2013
[12] J J Valera Garcıa V Gomez Garay E Irigoyen Gordo FArtaza Fano and M Larrea Sukia ldquoIntelligent Multi-ObjectiveNonlinear Model Predictive Control (iMO-NMPC) Towardsthe rsquoon-linersquo optimization of highly complex control problemsrdquoExpert Systems with Applications vol 39 no 7 pp 6527ndash65402012
[13] S M Zanoli and G Conte ldquoRemotely operated vehicle depthcontrolrdquoControl Engineering Practice vol 11 no 4 pp 453ndash4592003
[14] J Javadi-Moghaddam and A Bagheri ldquoAn adaptive neuro-fuzzy sliding mode based genetic algorithm control system forunder water remotely operated vehiclerdquo Expert Systems withApplications vol 37 no 1 pp 647ndash660 2010
[15] B W Hobson A D Sherman and P R McGill ldquoImagingand sampling beneath free-drifting icebergs with a remotelyoperated vehiclerdquo Deep-Sea Research Part II Topical Studies inOceanography vol 58 no 11-12 pp 1311ndash1317 2011
[16] Z Chaohua T Guoyuan T Daomin et al ldquoDesign of DSPcontrol system for attitude control moment gyros group ofautonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[17] Z Yang F Liu and Y Wang ldquoPath following of underactuatedsurface vessels based on neural sliding moderdquo Ship Building ofChina vol 56 no 2 pp 45ndash55 2015
Journal of Robotics 7
[18] W Yanqiong and C Shiping ldquoDual path routing admissioncontrol protocol for smart road wireless networksrdquo ComputerEngineering vol 41 no 11 pp 24ndash29 2015
[19] SWei H Yulong and L Baoshan ldquoNon symmetric unmannedamphibious platform path tracking controlrdquo Acta Armamen-tarii vol 37 no 7 pp 1161ndash1169 2016
[20] ZChuD Zhu and S X Yang ldquoObserver-based adaptive neuralnetwork trajectory tracking control for remotely operatedvehiclerdquo IEEE Transactions on Neural Networks and LearningSystems vol 28 no 7 pp 1633ndash1645 2017
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
6 Journal of Robotics
As you can see from Figure 6 when the path lengthis constant the three methods vary in time By using theBackstepping method the running time is about 2189 minand the time spent in 0-20M is rapidly increasing while thetime spent in 20-30 does not increase After 30m it had beenon the rise and hadno tendency to declineThe immune fuzzyPIDmethod takes about 325 min time and takes a long timeAs the path of the ship increases the time of sailing increasesaccordingly Only when the region is stable at 40-60 m doesthe rest of the road become on the rise The time taken bythe improved method is about 498 min and the runningtime increases with the increase of path length but the risingtrend is not significant This method has good stability andhas some advantages
5 Concluding Remarks
The traditional control methods always have the problemsof poor effect nonfixed path selection and long timeconsuming Hence a path control method for underwaterRobots based on NURBS curve fitting method is proposedExperimental comparison results are illustrated
(i) Although the number of control is greater than theBackstepping method and the immune fuzzy PID methodwhen navigating in the same path length area the overallcontrol is better than the Backstepping and the immune fuzzyPID method
(ii) Compared with the Backstepping and the immunefuzzy PID method the navigation time of the improvedmethod is shortened by 1691 min and 2752 min respectivelywith good stability and advantages
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This work is supported by the Science and TechnologyResearch Program of ChongqingMunicipal Education Com-mission (Grant no KJ1729403) the National Natural ScienceFoundation of China (no 61403055) Chongqing EducationScience and Planning Issues project name the CurrentSituation Analysis and Countermeasure Research of ModernApprenticeship Practice in Vocational Colleges (no 2017-GX-422) the Fundamental Research Funds for the CentralUniversities (Grant no CDJXS12 17 11 01) Intelligent RobotTechnology Research Center of Chongqing College of Elec-tronic Engineering (no XJPT201705)
References
[1] F A AzisM SM ArasM Z A RashidM N Othman and SS Abdullah ldquoProblem identification for Underwater RemotelyOperated Vehicle (ROV) A case studyrdquo in Proceedings of the2nd International Symposium on Robotics and Intelligent Sensors2012 IRIS 2012 pp 554ndash560 mys September 2012
[2] W Zheng Q Zou andWNi ldquoDesign and application of under-water unmanned vehicle simulation system for navigation and
obstacle avoidancerdquoXitong Fangzhen Xuebao Journal of SystemSimulation vol 28 no 1 pp 91ndash98 2016
[3] L Li X Yibo L Li and et al ldquoPath control of submarine swingarm tracked mobile platform based on Backstepping methodrdquoMining and Metallurgy Engineering vol 35 no 6 pp 1ndash5 2015
[4] Z Chaohua T Guoyuan H Daomin and et al ldquoDesign ofDSP control system for attitude control moment gyros groupof autonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[5] O Cerman and P Husek ldquoAdaptive fuzzy sliding mode controlfor electro-hydraulic servo mechanismrdquo Expert Systems withApplications vol 39 no 11 pp 10269ndash10277 2012
[6] M J Mahmoodabadi M Taherkhorsandi and A BagherildquoOptimal robust sliding mode tracking control of a biped robotbased on ingenious multi-objective PSOrdquo Neurocomputing vol124 pp 194ndash209 2014
[7] A Bagheri T Karimi and N Amanifard ldquoTracking perfor-mance control of a cable communicated underwater vehicleusing adaptive neural network controllersrdquo Applied Soft Com-puting vol 10 no 3 pp 908ndash918 2010
[8] S-Y Li C-H Yang C-T Lin L-W Ko and T-T ChiuldquoAdaptive synchronization of chaotic systems with unknownparameters via new backstepping strategyrdquo Nonlinear Dynam-ics vol 70 no 3 pp 2129ndash2143 2012
[9] J Javadi Moghaddam M H Farahani and N Amanifard ldquoAneural network-based sliding-mode control for rotating stalland surge in axial compressorsrdquo Applied Soft Computing vol11 no 1 pp 1036ndash1043 2011
[10] M J Mahmoodabadi S Momennejad and A Bagheri ldquoOnlineoptimal decoupled sliding mode control based on moving leastsquares and particle swarm optimizationrdquo Information Sciencesvol 268 pp 342ndash356 2014
[11] M J Mahmoodabadi S Arabani Mostaghim A Bagheri andN Nariman-zadeh ldquoPareto optimal design of the decoupledsliding mode controller for an inverted pendulum system andits stability simulation via Java programmingrdquo Mathematicaland Computer Modelling vol 57 no 5-6 pp 1070ndash1082 2013
[12] J J Valera Garcıa V Gomez Garay E Irigoyen Gordo FArtaza Fano and M Larrea Sukia ldquoIntelligent Multi-ObjectiveNonlinear Model Predictive Control (iMO-NMPC) Towardsthe rsquoon-linersquo optimization of highly complex control problemsrdquoExpert Systems with Applications vol 39 no 7 pp 6527ndash65402012
[13] S M Zanoli and G Conte ldquoRemotely operated vehicle depthcontrolrdquoControl Engineering Practice vol 11 no 4 pp 453ndash4592003
[14] J Javadi-Moghaddam and A Bagheri ldquoAn adaptive neuro-fuzzy sliding mode based genetic algorithm control system forunder water remotely operated vehiclerdquo Expert Systems withApplications vol 37 no 1 pp 647ndash660 2010
[15] B W Hobson A D Sherman and P R McGill ldquoImagingand sampling beneath free-drifting icebergs with a remotelyoperated vehiclerdquo Deep-Sea Research Part II Topical Studies inOceanography vol 58 no 11-12 pp 1311ndash1317 2011
[16] Z Chaohua T Guoyuan T Daomin et al ldquoDesign of DSPcontrol system for attitude control moment gyros group ofautonomous underwater Robotrdquo China Ship Research vol 11no 5 pp 107ndash112 2016
[17] Z Yang F Liu and Y Wang ldquoPath following of underactuatedsurface vessels based on neural sliding moderdquo Ship Building ofChina vol 56 no 2 pp 45ndash55 2015
Journal of Robotics 7
[18] W Yanqiong and C Shiping ldquoDual path routing admissioncontrol protocol for smart road wireless networksrdquo ComputerEngineering vol 41 no 11 pp 24ndash29 2015
[19] SWei H Yulong and L Baoshan ldquoNon symmetric unmannedamphibious platform path tracking controlrdquo Acta Armamen-tarii vol 37 no 7 pp 1161ndash1169 2016
[20] ZChuD Zhu and S X Yang ldquoObserver-based adaptive neuralnetwork trajectory tracking control for remotely operatedvehiclerdquo IEEE Transactions on Neural Networks and LearningSystems vol 28 no 7 pp 1633ndash1645 2017
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Journal of Robotics 7
[18] W Yanqiong and C Shiping ldquoDual path routing admissioncontrol protocol for smart road wireless networksrdquo ComputerEngineering vol 41 no 11 pp 24ndash29 2015
[19] SWei H Yulong and L Baoshan ldquoNon symmetric unmannedamphibious platform path tracking controlrdquo Acta Armamen-tarii vol 37 no 7 pp 1161ndash1169 2016
[20] ZChuD Zhu and S X Yang ldquoObserver-based adaptive neuralnetwork trajectory tracking control for remotely operatedvehiclerdquo IEEE Transactions on Neural Networks and LearningSystems vol 28 no 7 pp 1633ndash1645 2017
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Related Documents
