Adaptive Neuro-Fuzzy Inference System Based Path Planning ...downloads.hindawi.com/journals/jr/2018/2571243.pdf · ResearchArticle Adaptive Neuro-Fuzzy Inference System Based Path

Research ArticleAdaptive Neuro-Fuzzy Inference System Based PathPlanning for Excavator Arm

Nga Thi-Thuy Vu Nam Phuong Tran and NamHoai Nguyen

Hanoi University of Science and Technology Vietnam

Correspondence should be addressed to NgaThi-Thuy Vu ngavuthithuyhusteduvn

Received 21 August 2018 Revised 8 November 2018 Accepted 19 November 2018 Published 2 December 2018

Academic Editor Huosheng Hu

Copyright copy 2018 Nga Thi-Thuy Vu et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper presents a scheme based on Adaptive Neuro-Fuzzy Inference Systems (ANFIS) to generate trajectory for excavator armFirstly the trajectory is predesigned with some specific points in the work space to meet the requirements about the shape Nextthe inverse kinematic is used and optimization problems are solved to generate the via-points in the joint space These via-pointsare used as training set for ANFIS to synthesis the smooth curve In this scheme the outcome trajectory satisfies the requirementsabout both shape and optimization problems Moreover the algorithm is simple in calculation as the numbers of via-points arelarge Finally the simulation is done for two cases to test the effect of ANFIS structure on the generated trajectory The simulationresults demonstrate that by using suitable structure of ANFIS the proposed scheme can build the smooth trajectory which has thegood matching with desired trajectory even that the desired trajectory has the complicated shape

1 Introduction

In the construction and mine fields the excavator which isused to dig and transport of soil or coal is one of the importantmachines The work environment of excavator is usuallydangerous and harsh Therefore developing the automaticexcavator system is the general trend In the unmanual oper-ation system ie excavator system the trajectory generationfor the excavator base and arm is the hot spot because itdetermines the efficiencies of overall system

In the real the excavator arm is a three-degree of freedom(3DOF) manipulator robot The trajectory planning can bedone in both working space and joint space In the workingspace the trajectory is built for end-effectors in three-dimension reference frame so it is quite visual However thetrajectory built in this space has to face with problems ofinverse kinematic and manipulator redundancy [1] There-fore in the most case the trajectory of the manipulator robotis planned in the joint space [2]

In the joint space the trajectory is planned to meetsome specific requirements such as time optimization energyoptimization jerk optimization obstacle avoidance etc Inorder to satisfy these conditions the trajectory is usually

predesigned with some via-points then the smooth curve isbuilt using several interpolation such as polynomial splineBezier etc In [3 4] polynomial functions are used to generatethe paths for robot arms Reference [3] proposed a series ofpolynomials to create desired trajectory for robotic motionvia a set of given point they also addressed a problemof acceleration and jerk optimization However the maindrawback of [3] is that numbers of parameter proportion tonumbers of via-point which leads to explosion of calculationwhen the numbers of given point are large The problems ofreducing vibration are solved in [4] however the generatedtrajectory is partial smooth The Bezier Curve and modifiergenetic algorithm are interested in [5] in order to create a pathin dynamic field with avoiding obstacle and minimum pathrsquoslength

In recent year neural networks and fuzzy systems whichhave ability to approximate functions and fit curves have beenwidely applied in the path planning field These algorithmsseem to be more flexible and potential than traditional onebecause the methods based on neural network and fuzzysystem can create a path through many via-points withoutexplosion of calculation In [6ndash10] the shunting modeltechnique is used to build neural network for path planning

HindawiJournal of RoboticsVolume 2018 Article ID 2571243 7 pageshttpsdoiorg10115520182571243

2 Journal of Robotics

Base

Bucket

Stick

Boom

+

+

Figure 1 Block diagram of the excavator arm

problems In this method the neural dynamics of each neu-ron is characterized by a shunting equation or simple additiveequation [9] The trajectories in [6]-[8] are generated forrobots to avoid the static obstacles while in [9 10] robots canwork in dynamic environments with moving obstacles Thepulse-couple neural network is used in many application [11]and it is also applied into trajectory generation [12 13] Thisscheme can work in both static and dynamic environmentsbut the complete information about working conditions isnecessary In the field of learning method fuzzy system alsois used to solve the path planning problems [14ndash17] In [14]the fuzzy logic based on fuzzy sets algorithm is approachedto plan the path for the robotic placement of fabrics on awork table This fuzzy logic system is developed based onexperimental data and it has ability to work with variousmaterials and sizes while optimal fuzzy scheme is introducedin [15] for path planning of manipulator robots This is rule-based method which needs specific rules to generate thetrajectory for robots and it can deal with moving obstaclesIn order to generate a real-time and obstacle avoiding pathfor cushion robot a fuzzy system which have capability totransform directly human knowledge in machine is utilizedin [16] Moreover in [17] the fuzzy logic path planningalgorithm is investigated to guarantee the safe motion withobstacle avoidance for mobile robot

For the excavator in order to meet the requirement ofautomatic trend there are also some researches focusing onpath planning topic In [18 19] the laser scanner cameraand sensors are used to build 3D trajectory for automatedexcavator This method gives the good result in the cleanenvironment but the reliability of laser scanner and camerawill reduce in the dusty environment In [20] the currentposition of excavator arm is feedback to control system to pre-dict the trajectory for next cycle The neural network is usedin [21] to determine the characteristic of the soil From thisresult in combination with the reaction force exerted on thebucket the optimal trajectory is generated for excavator armIn [22ndash24] the velocity and acceleration of bucket are used tobuild the path for excavator arm The generated trajectory isoptimal but velocity and acceleration are difficult to measure

In this paper an algorithm based on ANFIS is proposedto generate trajectory for excavator arm Firstly the trajectoryis predesigned with some specific points in the work spaceto meet the requirements about the shape Next the inversekinematic is used and optimization problems are solved togenerate the via-points in the joint space These via-pointsare used as training set for ANFIS to synthesis the smoothcurve In this scheme the outcome trajectory satisfies therequirements about both shape and optimization problemsMoreover the algorithm is simple in calculation as thenumbers of via-points are large Finally the simulation isdone for two cases to test the effect of ANFIS structure on thegenerated trajectoryThe simulation results demonstrate thatby using suitable structure of ANFIS the proposed schemecan build the smooth trajectory which has the goodmatchingwith desired trajectory even that the desired trajectory has thecomplicated shape

2 Path Planning for Excavator ArmBased on ANFIS

21 Problem Description Consider the excavator system asshown in Figure 1 It is assumed that the base is fixed and thearm of excavator operates in the x0O0z0 plane

To execute the digging task with satisfying technical con-straints the trajectory of excavator arm should go throughsome predesigned points These points are selected from thedesired shape optimization criteria constraints etc Fromgiven via-point it is necessary to build the smooth curve forexcavator to operate

In order to minimize the time and jerk the followingoptimization problem should be solvent [25]

119891119894119899119889 min 119869 = 119896119879119873119899minus1sum119894=1

ℎ119894 + 119896119869int1199051198910(119902 (119905))2 119889119905

119904119906119887119895119890119888119905 119905119900 10038161003816100381610038161003816 119902119895 (119905)10038161003816100381610038161003816 le 119881119862119895 119895 = 1 sdot sdot sdot 11987310038161003816100381610038161003816 119902119895 (119905)10038161003816100381610038161003816 le 119882119862119895 119895 = 1 sdot sdot sdot 11987310038161003816100381610038161003816119902119895 (119905)10038161003816100381610038161003816 le 119869119862119895 119895 = 1 sdot sdot sdot 119873

(1)

Journal of Robotics 3

input inputmf rule outputmf output

Figure 2 The ANFIS architecture

where kT and kJ are scalars N are the numbers of joint n arethe numbers of via-points of hi is time interval between twovia-points 119902(119905) 119902(119905) and 119902(119905) are velocity acceleration andjerk of the jth joint respectively and VCj WCj and JCj isthe bound of velocity acceleration and jerk for the jth jointrespectively

The objective function (1) can be expressed as follows[26]

119869 = 119896119879119873119899minus1sum119894=1

ℎ119894 + 119896119869 119873sum119895=1

119899minus1sum119894=1

[120572119894119895 minus 1205722119894119895ℎ119894 ] (2)

subject to the constraints

max 10038161003816100381610038161003816120572119895110038161003816100381610038161003816 1003816100381610038161003816100381612057211989511989910038161003816100381610038161003816 le 119881119862119895forall119895 = 1 119873 forall119894 = 1 119899 minus 1

max 10038161003816100381610038161003816120572119895110038161003816100381610038161003816 1003816100381610038161003816100381612057211989511989910038161003816100381610038161003816 le 119882119862119895 forall119895 = 1 11987310038161003816100381610038161003816100381610038161003816120572119895119894+1 minus 120572119895119894ℎ119894

10038161003816100381610038161003816100381610038161003816 le 119869119862119895forall119895 = 1 119873 forall119894 = 1 119899 minus 1

(3)

where 120572ij is the acceleration of the jth joint at the ith via-point

Solve the optimal problem (2) by using SequentialQuadratic Programing technique (Optimization Toolbox ofMatlab) to get the via-points

After getting suitable via-points the ANFIS is used tocreate the smooth trajectory for three joints

22 ANFIS System Design and Training In this researchANFIS is utilized like a tool for curve fitting The taskof designing reference trajectory is to create a smooth-continuous path which passes some given points ThreeANFIS systems which are based on the Sugeno model aredesigned to plan paths for three joints Each ANFIS systemuses the same membership function for fuzzy sets so weare going to analyze and represent one of the three ANFISsystems

The input and output of each ANFIS system is timevariable ldquotrdquo and joint variable ldquothetardquo respectively The ith if-then rule is as follows

Rule 119894 If 119905 is small then theta = 119891i (119905) (4)

The ANFIS architecture is shown as Figure 2 It consistsof five layers

(i) Layer 1 this layer performs a fuzzification processTheGauss function is used as membership function in this studyIt is defined as follows

1198741119894 = 120583119894 = 119890minus(119905minus119888119894)221205902119894 (5)

The parameters ci and 120590i of first layer are typically referredas to the premise parameters

(ii) Layer 2 this layer is fixed and nonadaptive Its nodehas a functionwhichmultiplies the incoming signals from theoutputs of the previous layer to obtain the firing strength ofconditional clauses If there exists only one input then

1198742119894 = 120572119894 = 120583119894 (6)

(iii) Layer 3 this layer also has not included trainableparameters The output of each node is the ratio of the ithrulersquos matching degree to the total of all rulesrsquo matchingdegree

1198743119894 = 120572119894 = 120572119894sum119894 120572119894 (7)

(iv) Layer 4 the parameters of this layer can be modifiedto adapt to training data The function in each node of thelayer is defined as

1198744119894 = 120572119894 times 119891119894 = 120572119894 times (p1198941199051 + 119903119894) (8)

where pi ri are referred as to consequent parameters(v) Layer 5 this layer has only one node Its output is the

sum of all outputs from the fourth layer

1198745 = sum119894

120572119894119891119894 (9)

For training the ANFIS it is able to apply the gradientmethod But thismethod has slow convergence rate and tendsto be trapped at local minima To deal with this problem [27]proposed amethod which is the combination of the gradientmethod and the least square estimator (LSE)method namelythe hybrid algorithm The training process is divided intotwo parts that is referred as forward-path and backward-pathIn forward-path premise parameters are kept unchanged sothe output of the ANFIS is a linear function of consequentparameters Then the least square error (LSE) method isapplied to adjust these parameters Next the consequentparameters are fixed and premise parameters are updatedbased on the gradient algorithmThis hybrid algorithm is ableto provide faster convergence and avoid the occurrence oflocal minima because of the reduction in dimension of thesearch space For these advantages of hybrid algorithm wewill use this method for the ANFIS training

23 Path Planning Procedure With the information in theprevious parts it is possible to generate the trajectory forexcavator arm which satisfies some requirements about opti-mization and smooth The sequence for this process has thefollowing steps

(i) Step 1 get the desired points based on shaped andoptimal issues then use inverse kinematics to obtain the via-points in the joint space as training sample

(ii) Step 2 design ANFIS architecture(iii) Step 3 train ANFIS


Table 1 Parameters of the ANFIS after training

ci 120590119894 pi ri

1st joint 24929 31575 -00260 0692328817 156040 00059 0345034474 207265 -00102 10390

2nd joint 12196 66245 -00359 -1494513634 81598 -00171 -1774109156 139925 00016 -20630

3rd joint 15545 49146 00681 0795440780 160198 00401 1131433035 204656 00327 02277

Table 2 Parameters of the ANFIS after training for the 1st joint (Case 2)ci 120590119894 pi ri11440 01237 -00235 0689414447 32746 -00236 0691016017 62853 00179 0686017003 74553 00518 -0146707788 96823 00055 0360104393 128548 00059 0397205287 158631 00434 -0126105801 188813 00434 -0125604406 223654 0 0785910550 250155 0 07855

Table 3 Parameters of the ANFIS after training for the 2nd joint (Case 2)ci 120590119894 pi ri26620 05242 -00485 -1511322012 46932 -00550 -1414606739 100057 -00124 -1813016379 152547 -00005 -2032322804 198801 00034 -2096520898 249830 00014 -20627

(iv) Step 4 use ANFIS to generate the trajectory for eachjoint

In this work the inverse dynamic calculation for excava-tor arm is based on the [28]

3 Simulation and Results

In order to verify the effectiveness of this scheme the simu-lation is setup based on Optimization and Fuzzy toolboxes ofMatlab The constraints for optimal problem are similar as in[25] The parameters for ANFIS are presented in detail in thefollowing

The simulation is done for two cases(i) Case 1 The numbers of rule are 3 for each joint(ii) Case 2 The numbers of rule are 6 9 and 10 for the

first the second and the third joint respectivelyFor Case 1 the parameters of the ANFIS for each joint

after training are shown in the Table 1

Simulation results for this case are shown in Figure 3In Figure 3 (a) (b) (c) and (d) are the matching errors of

the first the second and the third joint and trajectory in theworkspace respectively It can be seen fromFigures 3(a) 3(b)and 3(c) that the matching error of each joint is quite smallThe maximum absolute error is 0015 rad for the first and thethird joint while this is about 0006 rad for the second jointIn Figure 3(d) the desired trajectory and the approximatedtrajectory are presented From this figure it is seen that thegenerated trajectory is quite close to the desired trajectoryexcept the case of sudden change in the motion direction

For Case 2 the numbers of rule for the first the secondand the third joint are 10 6 and 9 respectively The parame-ters for each joint are given in Tables 2 3 and 4 The resultsfor this case are illustrated in Figure 4

In the Figure 4 it is shown that the matching errors forall cases are insignificant ie maximum absolute error forthe first joint is 3e-3 rad for the second joint is 5e-3 rad and


Table 4 Parameters of the ANFIS after training for the 3rd joint (Case 2)ci 120590119894 pi ri19499 08483 00684 0839623933 36964 00802 0733904202 78501 00859 0701608204 103098 00127 1382205266 125082 -00044 1621108842 162364 -00438 2171705693 189473 -00471 2230103972 223126 00001 1238310464 250587 0 12392

0 5 10 15 20 25Time (sec)

(a)

(c)

(b)

(d)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-fir

st jo

int (

rad)

0 5 10 15 20 25Time (sec)

minus0015

minus001

minus0005

0

0005

001

Erro

r-se

cond

join

t (ra

d)

0 5 10 15 20 25Time (sec)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-th

ird

join

t (ra

d)

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)

Desired trajectoryLearned trajectory

End point

Start point

Figure 3 Training result for Case 1

for the third joint is 4e-4 rad The learned trajectory exactlyfollows the designed trajectory even under the condition ofabrupt alteration of motion direction

From the above simulation results it is feasible to buildthe trajectory for excavator arm using an ANFIS By choosing

suitable structure and parameters of neural network as wellas the numbers of fuzzy rule the ANFIS can create thesmooth trajectory which has the good matching with desiredone despite the condition that the desired trajectory has acomplicated shape


0 5 10 15 20 25Time (sec)

minus2

minus15

minus1

minus05

0

05

1

15

2Er

ror-

first

join

t (ra

d)times-

0 5 10 15 20 25Time (sec)

minus2

minus1

0

1

2

3

Erro

r-se

cond

join

t (ra

d)

times-

0 5 10 15 20 25Time (sec)

minus3

minus2

minus1

0

1

2

3

Erro

r-th

ird

join

t (ra

d)

times-

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point

(a)

(c)

(b)

(d)


4 Conclusion

In order to generate the reference trajectory for excavatorarm a method has been shown in this paper The proposedscheme is based on the optimal requirements combining withANFIS technique In comparison with methods using B-spline technique the presented algorithm is simpler as thenumber of via-points is large so the quality of the generatedtrajectory can be improved by increasing the number of via-points Also this characteristic helps the proposedmethod todeal with complicated shape trajectories Finally the simula-tion was shown for two cases to test the effect of the ANFISstructure on the generated trajectory The simulation resultsdemonstrated that by using a suitable structure of theANFISthe proposed scheme can build the smooth trajectory whichhas the good matching with desired trajectory regardlessof the fact that the desired trajectory has the complicatedshape

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is funded by Ministry of Education and Training(MOET) under Grant no B2018-BKA-70

References

[1] J Huang P Hu K Wu and M Zeng ldquoOptimal time-jerk tra-jectory planning for industrial robotsrdquoMechanism andMachineeory vol 121 pp 530ndash544 2018


[2] A Gasparetto P Boscariol A Lanzutti and R VidonildquoPath planning and trajectory planning algorithms a generaloverviewrdquo Mechanisms and Machine Science vol 29 pp 3ndash272015

[3] Y Guan K Yokoi O Stasse and A Kheddar ldquoOn robotictrajectory planning using polynomial interpolationsrdquo in Pro-ceedings of the 2005 IEEE International Conference on Roboticsand Biomimetics pp 111ndash116 Shatin China July 2005

[4] M Dupac and P Sewell ldquoQuick 3D trajectory planning forrotating extensible manipulators using piecewise polynomialinterpolationrdquo in Proceedings of the Congress on NumericalMethods in Engineering Spain 2017

[5] M Elhoseny A Tharwat and A E Hassanien ldquoBezier CurveBased Path Planning in a Dynamic Field using ModifiedGenetic Algorithmrdquo Journal of Computational Science vol 25pp 339ndash350 2018

[6] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of mobile robots using neural dynamics basedapproachesrdquo IEEE Trans Neural Netw vol 14 no 6 pp 1541ndash1552 2003

[7] A R Willms and S X Yang ldquoReal-time robot path planningvia a distance-propagating dynamic system with obstacle clear-ancerdquo IEEE Transaction on Systems Man and Cybernetics PartB Cybernetics vol 38 no 3 pp 884ndash893 2008

[8] X Yuan and S X Yang ldquoMulti-robot-based nanoassembly plan-ning with automated path generationrdquo IEEEASME Transactionon Mechatronics vol 12 no 3 pp 352ndash356 2007

[9] H Li S X Yang and M L Seto ldquoNeural network basedpath planning for a multirobot system with moving obstaclesrdquoIEEE Transaction on System Man and Cybernetics Part CApplications and Reviews vol 39 no 4 pp 410ndash419 2009

[10] S X Yang and M Meng ldquoNeural network approaches todynamic collision-free trajectory generationrdquo IEEE Transactionon Systems Man and Cybernetics Part B Cybernetics vol 31no 3 pp 302ndash318 2001

[11] D Wang and D Terman ldquoImage segmentation based onoscillatory correlationrdquo Neural Computation vol 9 no 4 pp805ndash836 1997

[12] H Qu S X Yang A R Willms and Z Yi ldquoReal-time robotpath planning based on modified pulse-couple neural networkmodelrdquo IEEE Trans Neural Netw vol 20 no 11 pp 1724ndash17392009

[13] W Xueli G Yapei and Z Jianhua ldquoA novel algorithm forshortest path problem based on pulse couple neural networkrdquoin Proceedings of the Chinese Control and Decision Conferencepp 2468ndash2473 2015

[14] G T Zoumponos and N A Aspragathos ldquoFuzzy logic pathplanning for the robotic placement of fabrics on a work tablerdquoRobotics and Computer-Integrated Manufacturing vol 24 no 2pp 174ndash186 2008

[15] C Son ldquoIntelligent rule-based sequence planning algorithmwith fuzzy optimization for robot manipulation tasks in par-tially dynamic environmentsrdquo Information Sciences vol 342 pp209ndash221 2016

[16] P Sun and Z Yu ldquoTracking control for a cushion robot basedon fuzzy path planning with safe angular velocityrdquo Journal ofAutomatica Sinica vol 4 no 4 pp 610ndash619 2017

[17] G Zhou N Wang X Lu and J Ma ldquoResearch on the fuzzyalgorithm of path planning of mobile robotrdquo in Proceedings ofthe International Conference on Computer System Electronicsand Control China 2017

[18] H Shao H Yamamoto Y Sakaida T Yamaguchi Y Yanag-isawa and A Nozue ldquoAutomatic excavation planning ofhydraulic excavatorrdquo in Proceedings of the International Confer-ence on Intelligent Robotics and Applications 2008

[19] A Stentz J Bares S Singh and P Rowe ldquoA robotic excavatorfor autonomous truck loadingrdquo in Proceedings of the IEEERJSConf on Intelligent Robots and Systems pp 1885ndash1893 VictoriaCanada 1998

[20] Y H Zweiri L D Seneviratne and K Althoefer ldquoModel-basedautomation for heavy duty mobile excavatorrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems vol 3 pp 2967ndash2972 October 2002

[21] S Lee D Hong and H Park ldquoOptimal path generationfor excavator with neural networks based soil modelsrdquo inProceedings of the IEEE International Conference onMultisensorFusion and integration for intelligent Systems pp 632ndash637 SeoulKorea 2008

[22] F Y Wang and P J A Lever ldquoOn-Line trajectory planning forautonomous robotic excavation based on forcetorque sensormeasurementsrdquo in Proceedings of the IEEE International Confer-ence onMultisensor Fusion and Integration for Intelligent Systempp 371ndash378 Las Vegas NV USA 1994

[23] Z Li X Li S Liu and L Jin ldquoA study on trajectory planningof hydraulic robotic excavator based on movement stabilityrdquo inProceedings of the 13th International Conference on UbiquitousRobots and Ambient Intelligence URAI pp 582ndash586 August2016

[24] Y B Kim J Ha H Kang P Y Kim J Park and F C ParkldquoDynamically optimal trajectories for earthmoving excavatorsrdquoAutomation in Construction vol 35 pp 568ndash578 2013

[25] A Gasparetto and V Zanotto ldquoA new method for smoothtrajectory planning of robot manipulatorsrdquo Mechanism andMachine eory vol 42 no 4 pp 455ndash471 2007

[26] A Gasparetto and V Zanotto ldquoA technique for time-jerkoptimal planning of robot trajectoriesrdquo Robotics and Computer-Integrated Manufacturing vol 24 no 3 pp 415ndash426 2008

[27] J S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[28] A J Koivo M Thoma E Kocaoglan and J Andrade-CettoldquoModeling and control of excavator dynamics during diggingoperationrdquo Journal of Aerospace Engineering vol 9 no 1 pp10ndash18 1996

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Submit your manuscripts atwwwhindawicom


Base

Bucket

Stick

Boom

+

+

Figure 1 Block diagram of the excavator arm

problems In this method the neural dynamics of each neu-ron is characterized by a shunting equation or simple additiveequation [9] The trajectories in [6]-[8] are generated forrobots to avoid the static obstacles while in [9 10] robots canwork in dynamic environments with moving obstacles Thepulse-couple neural network is used in many application [11]and it is also applied into trajectory generation [12 13] Thisscheme can work in both static and dynamic environmentsbut the complete information about working conditions isnecessary In the field of learning method fuzzy system alsois used to solve the path planning problems [14ndash17] In [14]the fuzzy logic based on fuzzy sets algorithm is approachedto plan the path for the robotic placement of fabrics on awork table This fuzzy logic system is developed based onexperimental data and it has ability to work with variousmaterials and sizes while optimal fuzzy scheme is introducedin [15] for path planning of manipulator robots This is rule-based method which needs specific rules to generate thetrajectory for robots and it can deal with moving obstaclesIn order to generate a real-time and obstacle avoiding pathfor cushion robot a fuzzy system which have capability totransform directly human knowledge in machine is utilizedin [16] Moreover in [17] the fuzzy logic path planningalgorithm is investigated to guarantee the safe motion withobstacle avoidance for mobile robot

For the excavator in order to meet the requirement ofautomatic trend there are also some researches focusing onpath planning topic In [18 19] the laser scanner cameraand sensors are used to build 3D trajectory for automatedexcavator This method gives the good result in the cleanenvironment but the reliability of laser scanner and camerawill reduce in the dusty environment In [20] the currentposition of excavator arm is feedback to control system to pre-dict the trajectory for next cycle The neural network is usedin [21] to determine the characteristic of the soil From thisresult in combination with the reaction force exerted on thebucket the optimal trajectory is generated for excavator armIn [22ndash24] the velocity and acceleration of bucket are used tobuild the path for excavator arm The generated trajectory isoptimal but velocity and acceleration are difficult to measure

In this paper an algorithm based on ANFIS is proposedto generate trajectory for excavator arm Firstly the trajectoryis predesigned with some specific points in the work spaceto meet the requirements about the shape Next the inversekinematic is used and optimization problems are solved togenerate the via-points in the joint space These via-pointsare used as training set for ANFIS to synthesis the smoothcurve In this scheme the outcome trajectory satisfies therequirements about both shape and optimization problemsMoreover the algorithm is simple in calculation as thenumbers of via-points are large Finally the simulation isdone for two cases to test the effect of ANFIS structure on thegenerated trajectoryThe simulation results demonstrate thatby using suitable structure of ANFIS the proposed schemecan build the smooth trajectory which has the goodmatchingwith desired trajectory even that the desired trajectory has thecomplicated shape

2 Path Planning for Excavator ArmBased on ANFIS

21 Problem Description Consider the excavator system asshown in Figure 1 It is assumed that the base is fixed and thearm of excavator operates in the x0O0z0 plane

To execute the digging task with satisfying technical con-straints the trajectory of excavator arm should go throughsome predesigned points These points are selected from thedesired shape optimization criteria constraints etc Fromgiven via-point it is necessary to build the smooth curve forexcavator to operate

In order to minimize the time and jerk the followingoptimization problem should be solvent [25]

119891119894119899119889 min 119869 = 119896119879119873119899minus1sum119894=1

ℎ119894 + 119896119869int1199051198910(119902 (119905))2 119889119905

119904119906119887119895119890119888119905 119905119900 10038161003816100381610038161003816 119902119895 (119905)10038161003816100381610038161003816 le 119881119862119895 119895 = 1 sdot sdot sdot 11987310038161003816100381610038161003816 119902119895 (119905)10038161003816100381610038161003816 le 119882119862119895 119895 = 1 sdot sdot sdot 11987310038161003816100381610038161003816119902119895 (119905)10038161003816100381610038161003816 le 119869119862119895 119895 = 1 sdot sdot sdot 119873

(1)






119869 = 119896119879119873119899minus1sum119894=1

ℎ119894 + 119896119869 119873sum119895=1

119899minus1sum119894=1

[120572119894119895 minus 1205722119894119895ℎ119894 ] (2)





(3)









1198741119894 = 120583119894 = 119890minus(119905minus119888119894)221205902119894 (5)



1198742119894 = 120572119894 = 120583119894 (6)


1198743119894 = 120572119894 = 120572119894sum119894 120572119894 (7)


1198744119894 = 120572119894 times 119891119894 = 120572119894 times (p1198941199051 + 119903119894) (8)



1198745 = sum119894

120572119894119891119894 (9)







ci 120590119894 pi ri

1st joint 24929 31575 -00260 0692328817 156040 00059 0345034474 207265 -00102 10390

2nd joint 12196 66245 -00359 -1494513634 81598 -00171 -1774109156 139925 00016 -20630

3rd joint 15545 49146 00681 0795440780 160198 00401 1131433035 204656 00327 02277
















0 5 10 15 20 25Time (sec)

(a)

(c)

(b)

(d)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-fir

st jo

int (

rad)

0 5 10 15 20 25Time (sec)

minus0015

minus001

minus0005

0

0005

001

Erro

r-se

cond

join

t (ra

d)

0 5 10 15 20 25Time (sec)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-th

ird

join

t (ra

d)

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point






0 5 10 15 20 25Time (sec)

minus2

minus15

minus1

minus05

0

05

1

15

2Er

ror-

first

join

t (ra

d)times-

0 5 10 15 20 25Time (sec)

minus2

minus1

0

1

2

3

Erro

r-se

cond

join

t (ra

d)

times-

0 5 10 15 20 25Time (sec)

minus3

minus2

minus1

0

1

2

3

Erro

r-th

ird

join

t (ra

d)

times-

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point

(a)

(c)

(b)

(d)


4 Conclusion


Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







119869 = 119896119879119873119899minus1sum119894=1

ℎ119894 + 119896119869 119873sum119895=1

119899minus1sum119894=1

[120572119894119895 minus 1205722119894119895ℎ119894 ] (2)





(3)









1198741119894 = 120583119894 = 119890minus(119905minus119888119894)221205902119894 (5)



1198742119894 = 120572119894 = 120583119894 (6)


1198743119894 = 120572119894 = 120572119894sum119894 120572119894 (7)


1198744119894 = 120572119894 times 119891119894 = 120572119894 times (p1198941199051 + 119903119894) (8)



1198745 = sum119894

120572119894119891119894 (9)







ci 120590119894 pi ri

1st joint 24929 31575 -00260 0692328817 156040 00059 0345034474 207265 -00102 10390

2nd joint 12196 66245 -00359 -1494513634 81598 -00171 -1774109156 139925 00016 -20630

3rd joint 15545 49146 00681 0795440780 160198 00401 1131433035 204656 00327 02277
















0 5 10 15 20 25Time (sec)

(a)

(c)

(b)

(d)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-fir

st jo

int (

rad)

0 5 10 15 20 25Time (sec)

minus0015

minus001

minus0005

0

0005

001

Erro

r-se

cond

join

t (ra

d)

0 5 10 15 20 25Time (sec)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-th

ird

join

t (ra

d)

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point






0 5 10 15 20 25Time (sec)

minus2

minus15

minus1

minus05

0

05

1

15

2Er

ror-

first

join

t (ra

d)times-

0 5 10 15 20 25Time (sec)

minus2

minus1

0

1

2

3

Erro

r-se

cond

join

t (ra

d)

times-

0 5 10 15 20 25Time (sec)

minus3

minus2

minus1

0

1

2

3

Erro

r-th

ird

join

t (ra

d)

times-

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point

(a)

(c)

(b)

(d)


4 Conclusion


Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




ci 120590119894 pi ri

1st joint 24929 31575 -00260 0692328817 156040 00059 0345034474 207265 -00102 10390

2nd joint 12196 66245 -00359 -1494513634 81598 -00171 -1774109156 139925 00016 -20630

3rd joint 15545 49146 00681 0795440780 160198 00401 1131433035 204656 00327 02277
















0 5 10 15 20 25Time (sec)

(a)

(c)

(b)

(d)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-fir

st jo

int (

rad)

0 5 10 15 20 25Time (sec)

minus0015

minus001

minus0005

0

0005

001

Erro

r-se

cond

join

t (ra

d)

0 5 10 15 20 25Time (sec)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-th

ird

join

t (ra

d)

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point






0 5 10 15 20 25Time (sec)

minus2

minus15

minus1

minus05

0

05

1

15

2Er

ror-

first

join

t (ra

d)times-

0 5 10 15 20 25Time (sec)

minus2

minus1

0

1

2

3

Erro

r-se

cond

join

t (ra

d)

times-

0 5 10 15 20 25Time (sec)

minus3

minus2

minus1

0

1

2

3

Erro

r-th

ird

join

t (ra

d)

times-

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point

(a)

(c)

(b)

(d)


4 Conclusion


Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0 5 10 15 20 25Time (sec)

(a)

(c)

(b)

(d)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-fir

st jo

int (

rad)

0 5 10 15 20 25Time (sec)

minus0015

minus001

minus0005

0

0005

001

Erro

r-se

cond

join

t (ra

d)

0 5 10 15 20 25Time (sec)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

Erro

r-th

ird

join

t (ra

d)

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point






0 5 10 15 20 25Time (sec)

minus2

minus15

minus1

minus05

0

05

1

15

2Er

ror-

first

join

t (ra

d)times-

0 5 10 15 20 25Time (sec)

minus2

minus1

0

1

2

3

Erro

r-se

cond

join

t (ra

d)

times-

0 5 10 15 20 25Time (sec)

minus3

minus2

minus1

0

1

2

3

Erro

r-th

ird

join

t (ra

d)

times-

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point

(a)

(c)

(b)

(d)


4 Conclusion


Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 5 10 15 20 25Time (sec)

minus2

minus15

minus1

minus05

0

05

1

15

2Er

ror-

first

join

t (ra

d)times-

0 5 10 15 20 25Time (sec)

minus2

minus1

0

1

2

3

Erro

r-se

cond

join

t (ra

d)

times-

0 5 10 15 20 25Time (sec)

minus3

minus2

minus1

0

1

2

3

Erro

r-th

ird

join

t (ra

d)

times-

58 6 62 64 66 68 7 72X (m)

minus05

0

05

1

15

Z (m

)


End point

Start point

(a)

(c)

(b)

(d)


4 Conclusion


Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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