17 i5 ijaet0511556 intelligent inverse kinematic copyright ijaet

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In this paper, an Adaptive Neuro-Fuzzy Inference System (ANFIS) method based on the Artificial Neural Network (ANN) is applied to design an Inverse Kinematic based controller forthe inverse kinematical control of SCORBOT-ER V Plus. The proposed ANFIS controller combines the advantages of a fuzzy controller as well as the quick response and adaptability nature of an Artificial Neural Network (ANN). The ANFIS structures were trained using the generated database by the fuzzy controller of the SCORBOT-ER V Plus.The performance of the proposed system has been compared with the experimental setup prepared with SCORBOT-ER V Plus robot manipulator. Computer Simulation is conducted to demonstrate accuracyof the proposed controller to generate an appropriate joint angle for reaching desired Cartesian state, without any error. The entire system has been modeled using MATLAB 2011.

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17 i5 ijaet0511556 intelligent inverse kinematic copyright ijaet

  1. 1. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963 INTELLIGENT INVERSE KINEMATIC CONTROL OF SCORBOT-ER V PLUS ROBOT MANIPULATOR Himanshu Chaudhary and Rajendra Prasad Department of Electrical Engineering, IIT Roorkee, IndiaABSTRACTIn this paper, an Adaptive Neuro-Fuzzy Inference System (ANFIS) method based on the Artificial NeuralNetwork (ANN) is applied to design an Inverse Kinematic based controller forthe inverse kinematical control ofSCORBOT-ER V Plus. The proposed ANFIS controller combines the advantages of a fuzzy controller as well asthe quick response and adaptability nature of an Artificial Neural Network (ANN). The ANFIS structures weretrained using the generated database by the fuzzy controller of the SCORBOT-ER V Plus.The performance ofthe proposed system has been compared with the experimental setup prepared with SCORBOT-ER V Plus robotmanipulator. Computer Simulation is conducted to demonstrate accuracyof the proposed controller to generatean appropriate joint angle for reaching desired Cartesian state, without any error. The entire system has beenmodeled using MATLAB 2011.KEYWORDS: DOF, BPN, ANFIS, ANN, RBF, BP I. INTRODUCTIONInverse kinematic solution plays an important role in modelling of robotic arm. As DOF (Degree of Freedom) ofrobot is increased it becomes a difficult task to find the solution through inverse kinematics.Three traditionalmethod used for calculating inverse kinematics of any robot manipulator are:geometric[1][2] ,algebraic[3][4][5] and iterative [6] methods. While algebraic methods cannot guarantee closed formsolutions. Geometric methods must have closed form solutions for the first three joints of themanipulator geometrically. The iterative methods converge only to a single solution and this solutiondepends on the starting point.The architecture and learning procedure underlying ANFIS, which is a fuzzy inference systemimplemented in the framework of adaptive networks was presented in [7]. By using a hybrid learningprocedure, the proposed ANFIS was ableto construct an input-output mapping based on both humanknowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs.Neuro-Genetic approach for the inverse kinematics problem solution of robotic manipulators wasproposed in [8]. A multilayer feed-forward networks was applied to inverse kinematic problem of a 3-degrees-of freedom (DOF) spatial manipulator robot in [9]to get algorithmic solution.To solve the inverse kinematics problem for three different cases of a 3-degrees-of freedom (DOF)manipulator in 3D space,a solution was proposed in [10]usingfeed-forward neural networks.Thisintroduces the fault-tolerant and high-speed advantages of neural networks to the inverse kinematicsproblem.A three-layer partially recurrent neural network was proposed by [11]for trajectory planning and tosolve the inverse kinematics as well as the inverse dynamics problems in a single processing stage forthe PUMA 560 manipulator.Hierarchical control technique was proposed in[12]for controlling a robotic manipulator.It was basedon the establishment of a non-linear mapping between Cartesian and joint coordinates using fuzzylogic in order to direct each individual joint. Commercial Microbot with three degrees of freedom wasutilized to evaluate this methodology.Structured neural networks based solution was suggested in[13] that could be trained quickly. Theproposed method yields multiple and precise solutions and it was suitable for real-time applications. 158 Vol. 1, Issue 5, pp. 158-169
  2. 2. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963To overcome the discontinuity of the inverse kinematics function,a novel modular neural networksystem that consists of a number of expert neural networks was proposed in[14].Neural network based inverse kinematics solution of a robotic manipulator was suggested in[15]. Inthis study, three-joint robotic manipulator simulation software was developed and then a designedneural network was used to solve the inverse kinematics problem.An Artificial Neural Network (ANN) using backpropagation algorithm was applied in [16]to solveinverse kinematics problems of industrial robot manipulator.The inverse kinematic solution of the MOTOMAN manipulator using Artificial Neural Network wasimplemented in [17]. The radial basis function (RBF) networks was used to show the nonlinearmapping between the joint space and the operation space of the robot manipulator which in turnsillustrated the better computation precision and faster convergence than back propagation (BP)networks.Bees Algorithm was used to train multi-layer perceptron neural networks in [18]to model the inversekinematics of an articulated robot manipulator arm.This paper is organized into four sections. In the next section, the kinematicsanalysis (Forward as wellas inverse kinematics) of SCORBOT-ER V Plus has been derived with the help of DH algorithm aswell as conventional techniques such as geometric[1][2], algebraic[3][4][5] and iterative [6] methods.Basics of ANFIS are introduced in section3. It also explains the wayfor input selection for ANFISmodeling. Simulation results are discussed in section 4. Section 5 gives concluding remarks.II. KINEMATICS OF SCORBOT-ER V PLUSSCORBOT-ER V Plus [19] is a vertical articulated robot, with five revolute joints. It has a Stationarybase, shoulder, elbow, tool pitch and tool roll. Figure 1.1 identifies the joints and links of themechanical arm.2.1. SCORBOT–ER V PLUS STRUCTUREAll joints are revolute, and with an attached gripper it has six degree of freedom. Each joint isrestricted by the mechanical rotation its limits are shown below.Joint Limits:Axis 1: Base Rotation: 310°Axis 2: Shoulder Rotation: + 130° / – 35°Axis 3: Elbow Rotation: ± 130°Axis 4: Wrist Pitch: ± 130°Axis 5: Wrist Roll Unlimited (electrically 570°)Maximum Gripper Opening: 75 mm (3") without rubber pads 65 mm (2.6") with rubber padsThe length of the links and the degree of rotation of the joints determine the robot’s work envelope.Figure 1.2 and 1.3 show the dimensions and reach of the SCORBOT-ER V Plus. The base of the robotis normally fixed to a stationary work surface. It may, however, be attached to a slide base, resultingin an extended working range. 159 Vol. 1, Issue 5, pp. 158-169
  3. 3. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-19632.2. FRAME ASSIGNMENT TO SCORBOT–ER V PLUSFor the kinematic model of SCORBOT first we have to assign frame to each link starting from base(frame {0}) to end-effector (frame {5}). The frame assignment is shown in figure 1.4.Here in model the frame {3} and frame {4} coincide at same joint, and the frame {5} is end– effectorposition in space. Joint i ( ) ( ) Operating range 1 − /2 16 349 1 −155° + 155° 2 0 221 0 2 −35° + 130° 3 0 221 0 3 −130° + 130° 4 /2 0 0 /2 + 4 −130° + 130° 5 0 0 145 5 −570° 570°2.3. FORWARD KINEMATIC OF SCORBOT–ER V PLUSOnce the DH coordinate system has been established for each link, a homogeneous transformationmatrix can easily be developed considering frame {i-1} and frame {i}. This transformation consists offour basic transformations. 0 T5 = 0T1 * 1T2 * 2T3 * 3T4 * 4T5 (1) C1 0 − S1 a1 * C1    0T =  S1 0 C1 a1 * S1  (2) 1  0 −1 0 d1    0 0 0 1    160 Vol. 1, Issue 5, pp. 158-169
  4. 4. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963 C2 − S2 0 a2 * C2  S C2 0 a2 * S 2  1 T2 =  2  (3) 0 0 1 0    0 0 0 1  C3 − S3 0 a3 * C3  S C3 0 a3 * S3  2 T3 =  3  (4) 0 0 1 0    0 0 0 1  − S 4 0 C 4 0  S 4 0 3T =  C 4 0  (5) 4  0 1 0 0    0 0 0 1 C 5 − S 5 0 0  0 0 4T =  S 5 C 5  (6) 5 0 0 1 d 5   0 0 0 1Finally, the transformation matrix is as follow: - −S S − C C S 1 5 −C S + C S S 1 5 CC234 C (a + a C + a C + d C ) 5 1 1 5 234 1 234 1 1 2 2 3 23 5 234 CS −SCS CC +SS S SC S (a + a C + a C + d C )  T = T =  0 1 5 1 5 234 1 5 1 5 234 1 234 1 1 2 2 3 23 5 234 (7)  −C C (d − a S − a S − d S )  5 5 SC 234 −S 5 234 234 1 2 2 3 23 5 234    0 0 0 1 Where, = ( ), = ( ) = ( + + ), = ( + + ).The T is all over transformation matrix of kinematic model of SCORBOT-ER V Plus, from this wehave to extract position and orientation of end –effector with respect to base is done in the followingsection.2.4. OBTAINING POSITION IN CARTESIAN SPACEThe value of , , is found from last column of transformation matrix as: - (8) X = C1 (a1 + a2 C2 + a3C23 + d5C234 ) Y = S1 (a1 + a2 C2 + a3C23 − d5C234 ) (9) Z = ( d1 − a2 S 2 − a3 S23 − d5 S 234 ) (10)For Orientation of end-effector frame {5} and frame {1} should be coincide with same axis but in ourmodel it is not coincide so we have to take rotation of −90° of frame {5} over y5 axis, so the overallrotation matrix is multiplied with −90° as follow: -  cos( −90o ) 0 sin(−90o )    Ry =  0 1 0     − sin(−90o ) 0 cos(−90o )   0 0 −1 Ry = 0 1 0    (11) 1 0 0   The Rotation matrix is: - 0 0 −1  − S1S5 − C1C5 S234 −C5 S1 + C1 S5 S234 C1C234  R = 0 1 0  ×  C1 S5 − S1C5 S 234    C1C5 + S1S5 S234 S5C234   1 0 0      −C5C234 S5C234 − S234   161 Vol. 1, Issue 5, pp. 158-169
  5. 5. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963  C5C234 − S5C234 S 234  R =  C1S5 − S1C5 S 234  C1C5 + S1S5 S234 S5C234    − S1S5 − C1C5 S 234  −C5 S1 + C1 S5 S 234 C1C234   (12)Pitch: Pitch is the angle of rotation about y5 axis of end-effector pitchβ = θ 2 + θ 3 + θ 4 = θ 234 (13) 2 2 θ 234 = a tan 2( r13, ± r 23 + r 33 ) (14)Here we use atan2 because its range is [− , ], where the range of atan is [− /2, /2].Roll: The = 5 is derived as follow: - θ5 = a tan 2(r12 / C234 , r11 / C234 ) (15)Yaw: Here for SCORBOT yaw is not free and bounded by 1.2.5. HOME POSITION IN MODELINGAt home position all angle are zero so in equation (1.7) put 1 = 0, 2 = 0, 3 = 0, 4 = 0, 5 =0So the transformation matrix reduced to:- 0 0 1 a1 + a2 + a3 + d5   0 0 1 603 0 1 0 0  0 1 0 0  THome = =  (16)  −1 0 0 d1   −1 0 0 349      0 0 0 1  0 0 0 1 The home position transformation matrix gives the orientation and position of end-effector frame.From the 3×3 matrix orientation is describe as follow, the frame {5} is rotated relative to frame {0}such that 5 axis is parallel and in same direction to 0 axis of base frame; 5is parallel and in samedirection to 0 axis of base frame; and 5axis is parallel to 0but in opposite direction. The position is Tgiven by the 3 × 1 displacement matrix a1 + a2 + a3 + d5 0 d1  .  2.6. INVERSE KINEMATICS OF SCORBOT-ER V PLUSFor SCORBOT we have five parameter in Cartesian space is x, y, z, roll ( ), pitch ( ).For jointparameter evaluation we have to construct transformation matrix from five parameters in Cartesiancoordinate space. For that rotation matrix is generated which is depends on only roll, pitch and yaw ofrobotic arm. For SCORBOT there is no yaw but it is the rotation of first joint 1.So the calculation of yaw is as follow: - α = θ1 = a tan 2( x, y ) (17)Now for rotation matrix rotate frame {5} at an angle – about its x axis then rotate the new frame {5′} by an angle with its own principal axes ′ , finally rotate the new frame {5′′} by an angle withits own principal axes . = (− )∗ ( )∗ ( ) 1 0 0   Cγ 0 Sγ  Cα − Sα 0     =  0 Cβ Sβ  ×  0 1 0  ×  Sα  Cα 0  0 − Sβ Cβ   − Sγ 0 Cγ   0 0 1       162 Vol. 1, Issue 5, pp. 158-169
  6. 6. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963  Cα Cγ −Cγ Sα Sγ    =  Cβ Sα − Cα S β Sγ Cβ Cα + S β Sγ Sα Cγ S β   − S β Sα − Cα Cβ Sγ − S β Cα + Sα Cβ Sγ Cβ Cγ    (18)Now rotate matrix by 90° about y axis: -  COS (90o ) 0 SIN (90o )    Ry ( −90o ) =  0 1 0   o o   − SIN (90 ) 0 COS (90 )   0 0 1 R y (−90o ) =  0 1 0    (19)  −1 0 0   After pre multiplying the equation 19 with equation 18, one will get following rotation matrix: -  − S β Sα − Cα Cβ Sγ − S β Cα + Sα Cβ Sγ Cβ Cγ    =  Cβ Sα − Cα S β Sγ Cβ Cα + S β Sγ Sα Cγ S β   −Cα Cγ Cγ Sα − Sγ    (20)So, the total transformation matrix is as follows: -  − S β Sα − Cα Cβ Sγ − S β Cα + Sα Cβ Sγ Cβ Cγ X  C S −C S S Cβ Cα + S β Sγ Sα Cγ S β Y T = β α α β γ   −Cα Cγ Cγ Sα − Sγ Z    0 0 0 1 (21)After comparing the transformation matrix in equation (7) with matrix in equation (21), one candeduce: - 1 = , 234 = , 5= ,Now, we have 1 and 5 directly but 2, 3 4 are merged in 234 so we have separate them, toseparate them we have used geometric solution method as shown in Figure 1.6Here for finding 2, 3, 4, we have X, Y, Z in Cartesian coordinate space from that we can take:- X 1 = ( X 2 + Y 2 ) andY1 = Z (22)We have pitch of end-effector 234 = , from that we can find point 2, 2 is calculated as follows: - X 2 = X 1 − d5 cos θ 234 (23) Y2 = Y1 + d5 sin θ 234 163 Vol. 1, Issue 5, pp. 158-169
  7. 7. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963Now the distance 3and 3can be found: - X 3 = X 2 − a1 Y3 = Y2From the low of cosines applied to triangle ABC, we have: - ( X 3 + Y32 − a2 − a3 ) 2 2 2 cos θ 3 = 2 a2 a3 θ3 = a tan 2(± 1 − cos 2 θ3 , cos θ3 ) (24)From figure 1.6 2 = −∅ − or θ 2 = −a tan 2(Y3 , X 3 ) − a tan 2(a3 sin θ3 , a2 + cos θ3 ) (25)Finally we will get: - θ 4 = θ 234 − θ 2 − θ3 (26)III. INVERSE KINEMATICS OF SCORBOT-ER V PLUS USING ADAPTIVE NEURO FUZZY INFERENCE SYSTEM (ANFIS)The proposed ANFIS[7][20][21] controller is based on Sugeno-type Fuzzy Inference System (FIS)controller.The parameters of the FIS are governed by the neural-network back propagation method.The ANFIS controller is designed by taking the Cartesian coordinates plus pitch as the inputs, and thejoint angles of the manipulator to reach a particular coordinate in 3 dimensional spaces as the output.The output stabilizing signals, i.e., joint angles are computed using the fuzzy membership functionsdepending on the input variables. The effectiveness of the proposed approach to the modeling isimplemented with the help of a program specially written for this in MATLAB. The informationrelated to data used to train is given inTable 1.2. Sr. Manipulator No. of No. of Parameters Total No. of No. of No. of No. of No. Angles Nodes Parameters Training Checking Fuzzy Linear Nonlinear Data Pairs Data Pairs Rules 01. Theta1 193 405 36 441 4500 4500 81 02. Theta2 193 405 36 441 4500 4500 81 03. Theta3 193 405 36 441 4500 4500 81 04. Theta4 193 405 36 441 4500 4500 81The procedure executed to train ANFIS is as follows:(1) Data generation: To design the ANFIS controller, the training data have been generated by usingan experimental setup with the help of SCORBOT-ER V Plus. A MATLAB program is written togovern the manipulator to get the input –output data set. 9000 samples were recorded through theexecution of the program for the input variables i.e., Cartesian coordinates as well as Pitch. Cartesiancoordinates combination for all thetas are given in Fig.1.7 164 Vol. 1, Issue 5, pp. 158-169
  8. 8. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963(2) Rule extraction and membership functions: After generating the data, the next step is to estimatethe initial rules. A hybrid learning algorithm is used for training to modify the above parameters afterobtaining the Fuzzy inference system from subtracting clustering. This algorithm iteratively learns theparameter of the premise membership functions and optimizes them with the help of back propagationand least-squares estimation. The training is continued until the error minimization..The input as wellas output member function used was triangular shaped member function.The final fuzzy inferencesystem chosen was the one associated with the minimum checking error, as shown in figure 1.8.itshown the final membership function for the thetas after training. D e g r e e o f m e m b e r s h ip D e g r e e o f m e m b e r s h ip D e g r e e o f m e m b e r s h ip D e g r e e o f m e m b e r s h ip D e g re e o f m e m b e rs h ip D e g re e o f m e m b e rs h ip D e g re e o f m e m b e rs h ip D e g re e o f m e m b e rs h ip in11 m f1 i n 1 m f2 i n 1 m f3 in12 m f1 i n 2 m f2 i n 2 m f3 in1 m f1 1 in 1 m f2 in 1 m f3 in12 m f1 in 2 m f2 in 2 m f3 0.5 0.5 0.5 0.5 0 0 0 0 -0 . 5 0 0 .5 -0 . 4 -0 . 2 0 0 .2 0 .4 -0 . 5 0 0 .5 -0 . 4 -0 . 2 0 0.2 0.4 in p u t 1 in p u t 2 in p u t 1 in p u t 2 in13 m f1 in 3 m f2 i n 3 m f3 i n1 m f1 4 in 4 m f2 in 4 m f3 i n1 m f1 3 i n 3 m f2 i n 3 m f3 in1 m f1 4 i n 4 m f2 i n 4 m f3 0.5 0.5 0.5 0.5 0 0 0 0 -0 . 2 0 0 .2 0.4 in p u t 3 0.6 0.8 -4 -2 0 in p u t 4 2 4 θ2 o f m e m b e rs h ip o f m e m b e rs h ip θ1 o f m e m b e rs h ip o f m e m b e rs h ip -0 .2 0 0.2 0 .4 0.6 0 .8 -4 -2 0 2 4 in p u t 3 in p u t 4 in1 m f1 1 i n 1 m f2 i n 1 m f3 i n 1 m f1 2 i n 2 m f2 in 2 m f3 i n1 m f 1 1 in 1 m f2 in 1 m f3 i n12 m f 1 in 2 m f2 i n 2 m f3 0 .5 0 .5 0 .5 0 .5 o f m e m b e r sDh ei pg r e e o f m e m b e r sDh e pg r e e o f m e m b e r s Dh e pg r e e o f m e m b e r s Dh e pg r e e i i i 0 0 0 0 -0 .5 0 0 .5 -0 .4 -0 . 2 0 0 .2 0 .4 -0 .5 0 0 .5 -0 . 4 -0 .2 0 0 .2 0 .4 in p u t1 in p u t 2 in p u t 1 in p u t 2 i n13 m f1 i n 3 m f2 i n 3 m f3 i n 1 m f1 4 i n 4 m f2 in 4 m f3 i n13 m f1 i n 3 m f2 in 3 m f3 i n 1 m f1 4 in 4 m f2 i n 4 m f3 0 .5 0 .5 0 .5 0 .5 D e g re e D e g re e D e g re e D e g re e 0 0 θ3 0 0 θ4 -0 .2 0 0 .2 0 .4 0 .6 0 .8 -4 -2 0 2 4 -0 . 2 0 0 .2 0 .4 0 .6 0 .8 -4 -2 0 2 4 in p u t3 in p u t 4 in p u t 3 in p u t 4(3) Results: The ANFIS learning was tested on a variety of linear and nonlinear processes. TheANFIS was trained initially for 2 membership functions for 9000 data samples for each input as wellas output. Later on, it was increased to 3 membership functions for each input. To demonstrate theeffectiveness of the proposed combination, the results are reported for a system with81 rules and asystem with an optimized rule base. After reducingthe rules the computation becomes fast and it alsoconsumes less memory. The ANFIS architecture for θ1 is shownin Fig. 1.9. 165 Vol. 1, Issue 5, pp. 158-169
  9. 9. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963 Five angles have considered for the representation of robotic arm. But as the 5 is independentof other angles so only remaining four angles was considered to calculate forward kinematics. Now,for every combination of 1, θ2, θ3 andθ4 values the x and y as well as z coordinates are deduced usingforward kinematics formulas.IV. SIMULATION RESULTS AND DISCUSSIONThe plots displaying the root-mean-square error are shown in figure 1.10. The plot in blue representserror1, the error for training data. The plot in green represents error2, the error for checking data.From the figure one can easily predict thatthere is almost null difference between the training error aswell as checking error after the completion of training of ANFIS. E r r o r C u rve s E r r o r C u rve s 0 .9 0.34 R M S E (R oo t M ea n S q u a r e d E rro r ) R M S E (R oo t M ea n S q u a r e d E rro r ) 0.85 0.32 0 .8 0 .3 0.75 0.28 0 .7 0.26 0.65 0.24 0 .6 0.55 0 2 4 6 8 10 12 14 16 18 20 θ1 0.22 0 2 4 6 8 10 12 14 16 18 20 θ2 E poc hs E poc hs R M S E (R o o t M e a n S q u a r e d E r r o r ) E r r o r C u rve s E r r o r C u rve s R M S E (R o o t M e a n S q u a r e d E rro r) 0 .7 0 .44 0 .42 0 .65 0 .4 0 .6 0 .38 0 .55 0 .36 0 .5 0 .34 0 .45 θ3 0 .32 0 2 4 6 8 10 12 14 16 18 20 θ4 0 2 4 6 8 10 12 14 16 18 20 E pochs E poc hsIn addition to above error plots, the plot showing the ANFIS Thetas versus the actual Thetasare givenin figures1.11,1.12,1.13 and 1.14 respectively. The difference between the original thetas values andthe values estimated using ANFIS is very small. Theta1 and ANFIS Prediction theta13210-1-2-3 Experimental Theta1 ANFIS Predicted Theta1-4 0 50 100 150 200 250 300 350 Time (sec) Theta2 and ANFIS Prediction theta2 2 Experimental Theta2 ANFIS Predicted Theta2 1.5 1 0.5 0-0.5 -1 0 50 100 150 200 250 300 350 Time (sec) 166 Vol. 1, Issue 5, pp. 158-169
  10. 10. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963 Theta3 and ANFIS Prediction Theta33210-1-2 Experimental Theta3 ANFIS Predicted Theta3-3 0 50 100 150 200 250 300 350 Time (sec) Theta4 and ANFIS Prediction Theta4 2 1 0-1-2 Experimental Theta4 ANFIS Predicted Theta4-3 0 50 100 150 200 250 300 350 Time (sec)The prediction errors for all thetas appear in the figures 1.15, 1.16, 1.17, 1.18 respectively with a much finerscale. The ANFIS was trained initially for only 10 epochs. After that the no. of epochs were increased to 20 forapplying more extensive training to get better performance. Prediction Errors for THETA 13 Prediction Error Theta1210-1-2-3 0 50 100 150 200 250 300 350 Time (sec) Prediction Errors for THETA2 1 Prediction Error Theta20.5 0-0.5 -1-1.5 0 50 100 150 200 250 300 350 Time (sec) Prediction Errors for THETA3 2 Prediction Error Theta3 1 0-1-2-3 0 50 100 150 200 250 300 350 Time (sec) 167 Vol. 1, Issue 5, pp. 158-169
  11. 11. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963 Prediction Errors for THETA41.5 10.5 0-0.5 -1-1.5 Prediction Error Theta4 -2 0 50 100 150 200 250 300 350 Time (sec) V. CONCLUSIONFrom the experimental work one can see that the accuracy of the output of the ANFIS based inversekinematic model is nearly equal to the actual mathematical model output, hence this model can beused as an internal model for solving trajectory tracking problems of higher degree of freedom (DOF)robot manipulator. Asingle camera for the reverse mapping from camera coordinates to real worldcoordinateshas been used in the present work, if two cameras are used stereo vision can be achievedandproviding the height of an object as an input parameter would not be required. The methodologypresented herecan be extended to be used for trajectory planning and quite a few tracking applicationswith real world disturbances. Thepresent work did not make use of color image processing; makinguse of color image processing can helpdifferentiate objects according to their colors along with theirshapes.ACKNOWLEDGEMENTSAs it is the case in almost all parts of human endeavour so also the development in the field of robotics has beencarried on by engineers and scientists all over the world.It can be regarded as a duty to express the appreciationfor such relevant, interesting and outstanding work to which ample reference is made in this paper.REFERENCES[1] F. R, "Position and velocity transformation between robot end-effector coordinate and joint angle," International Journal of Robotics, vol. 2, no. 2, pp. 35-45, 1983.[2] L. G. C. S., "Robot arm kinematics, dynamics and control," IEEE, vol. 15, no. 12, pp. 62-79, 1982.[3] D. J., Analysis of Mechanism and Robot Manipulators. New York, USA: Wiley, 1980.[4] D. Manocha and J. Canny, "Efficient inverse kinematics for general 6r manipulators," IEEE Transaction on Robotics Automation, IEEE, vol. 10, no. 5, pp. 648-657, 1994.[5] R. Paul, B. Shimano, and G. Mayer, "Kinematic control equations for simple manipulators," IEEE Transaction on System, Man and Cybernetics, IEEE, vol. SMC-11, no. 6, pp. 66-72, 1982.[6] J. Korein and N. Balder, "Techniques for generating the goal-directed motion of articulated structures," IEEE Computer Graphics and Application, IEEE, vol. 2, no. 9, pp. 71-81, 1982.[7] J.-S. R. Jang, "ANFIS : Adap tive-Ne twork-Based Fuzzy," IEEE Transactions on Systems, Man and Cybernatics, IEEE, vol. 23, no. 3, pp. 665-685, Jun. 1993.[8] K. Rasit, "A neuro-genetic approach to the inverse kinematics solution of robotic manipulators," Scientific Research and Essays, The Academic Journals, vol. 6, no. 13, pp. 2784-2794, Jul. 2011.[9] B. B. Choi and C. Lawrence, "Inverse Kinematics Problem In Robotics Using Neural Networks," NASA Technical Memorandum 105869, pp. 1-23, 1992.[10] D. M. A. L. R. O. B. W. H. E. H. Jack, "Neural Networks and The Inverse Kinematics Problem," Journal of Intelligent Manufacturing, vol. 4, pp. 43-66, 1993.[11] A. F. R. Arahjo and H. D. Jr., "A Partially Recurrent Neural Network To Perform Trajectory Planning, Inverse Kinematics and Inverse Dynamics," Systems, Man and Cybernetics, IEEE, vol. 2, pp. 1784-1789, 1998.[12] D. W. Howard and A. Zilouchian, "Application of Fuzzy Logic for The Solution Of Inverse Kinematics And Hierarchical Controls Of Robotic Manipulators," Journal of Intelligent and Robotic Systems, Kluwer 168 Vol. 1, Issue 5, pp. 158-169
  12. 12. International Journal of Advances in Engineering & Technology, Nov 2011.©IJAET ISSN: 2231-1963 Academic Publishers, vol. 23, p. 217–247, 1998.[13] S. Tejomurtula and S. Kak, "Inverse Kinematics In Robotics Using Neural Networks," Elsevier Information Sciences, Elsevier, vol. 116, pp. 147-164, 1999.[14] E. Oyama, N. Y. Chong, A. Agah, T. Maeda, and S. Tachi, "Inverse Kinematics Learning By Modular Architecture Neural Networks With Performance Prediction Networks," International Conference On Robotics & Automation, IEEE, pp. 1006-1012, 2001.[15] R. Koker, C. Oz, T. Cakar, and H. Ekiz, "A Study Of Neural Network Based Inverse Kinematics Solution For A Three-Joint Robot," Robotics and Autonomous Systems, Elsvier, vol. 49, p. 227–234, 2004.[16] Z. Bingul, H. M. Ertunc, and C. Oysu, "Comparison Of Inverse Kinematics Solutions Using Neural Network For 6r Robot Manipulator With Offset," Computational Intelligence Methods And Applications, IEEE, pp. 1-5, 2005.[17] P.-Y. Zhang, T.-S. Lu, and Li-Bosong, "RBF Networks-Based Inverse Kinematics Of 6R Manipulator," International Journal Advance Manufacturing Technology, Springer-Verlag, vol. 26, p. 144–147, 2005.[18] D. T. Pham, M. Castellani, and A. A. Fahmy, "Learning The Inverse Kinematics Of A Robot Manipulator Using The Bees Algorithm," International Conference On Industrial Informatics, IEEE, pp. 493-498, 2008.[19] I. Inc. (2003) http://www.intelitekdownloads.com/Manuals/Robots/ER_V_plus_manual_100016.pdf.[20] S. R. Khuntia and S. Panda, "ANFIS approach for SSSC controller design for the improvement oftransient stability performance," Mathematical and Computer Modelling, Elsevier, pp. 1-12, Jun. 2011.[21] B. A. A. Omar, A. Y. M. Haikal, and F. F. G. Areed, "Design adaptive neuro-fuzzy speed controller for an electro-mechanical system," Ain Shams Engineering Journal, Elsevier, pp. 1-9, Jul. 2011.AuthorsHimanshu Chaudhary received his B.E. in Electronics and Telecommunication fromAmravati University, Amravati, India in 1996, M.E. in Automatic Controls and Roboticsfrom M.S. University, Baroda, Gujarat, India in 2000.Presently he is a research scholar inElectrical Engineering Department, IIT Roorkee, India. His area of interest includesindustrial robotics, computer networks and embedded systems.Rajendra Prasad received B.Sc. (Hons.) degree from Meerut University, India in 1973. Hereceived B.E.,M.E. and Ph.D. degree in Electrical Engineering from the University ofRoorkee, India in 1977, 1979 and 1990 respectively. . He also served as an AssistantEngineer in Madhya Pradesh Electricity Board (MPEB) from 1979- 1983. Currently, he is aProfessor in the Department of Electrical Engineering, Indian Institute of TechnologyRoorkee, Roorkee (India).He has more than 32 years of experience of teaching as well asindustry. He has published 176 papers in various Journals/conferences and received eightawards on his publications in various National/International Journals/Conferences Proceeding papers. He hasguided Seven PhD’s, and presently six PhD’s are under progress. His research interests include Control,Optimization, System Engineering and Model Order Reduction of Large Scale Systems and industrial robotics.

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