Tomatoes have different water requirements in each growing period. Excessive water use or insufficient water 

supply will affect the growth and yield of tomato plants. Therefore, precise irrigation control is necessary during cultivation

to increase crop productivity. Traditionally, the soil moisture content or leaf water potential has been used as an indicator 

of plant water status. These methods, however, have limited accuracy and are time-consuming, making it difficult to be put 

into practice in tomato production. This study developed an online hyperspectral imaging system to measure the leaf water 

potential of tomato nondestructively. Linear Discriminant Analysis was utilized to automatically and quickly extract the leaf 

images, with the recognition accuracy of 94.68% was achieved. The mathematical processing of Standard Normal Variate 

scattering correction was used to remove the spectral variations caused by the defocused leave images. The developed leaf 

water potential prediction model based on the spectral image information attained using the developed system achieved the 

standard error of calibration of 0.201, coefficient of determination in calibration set of 0.814 and standard error of cross�validation of 0.230, and one minus the variance ratio of 0.755. The obtained performance indicated the feasibility of apply�ing the developed online hyperspectral imaging system as a real-time non-destructive measurement technique for the leaf 

water potential of tomato plants

Chao-Yin Tsai1,, Yin Tsai

Chen, Suming

h Tung, Chih Tung

Jer-Wei Lin1, Wei Lin

Pauline Ong, Pauline

Ping, Lang Yen

Yung, Huei Chang

UTHM Institutional Repository

VOL. X, NO. X, XXXXXXXX ARPN Journal of Engineering and Applied Sciences  ©2006-2013 Asian Research Publishing Network (ARPN). All rights reserved. ISSN 1819-6608 1    www.arpnjournals.com  INVERSE KINEMATICS ANALYSIS OF A 5-AXIS RV-2AJ ROBOT MANIPULATOR   Mohammad Afif Ayob1a, Wan Nurshazwani Wan Zakaria1b, Jamaludin Jalani2c, Mohd Razali Md Tomari1d 1ADvanced Mechatronics Research Group (ADMIRE), Faculty of Electrical and Electronic Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Malaysia. 2Department of Electrical Engineering Technology, Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Malaysia. E-Mail: amohammadafifayob@gmail.com, bshazwani@uthm.edu.my, cjamalj@uthm.edu.my, dmdrazali@uthm.edu.my  ABSTRACT This paper presents the inverse kinematics analysis of the five degree of freedom (DOF) Mitsubishi Melfa RV-2AJ industrial robot. The proposed method is used specifically for controlling the z-axis Cartesian position. The kinematics problem is defined as the transformation from the robot’s end-effector Cartesian space to the joint angle of the robotic arms. An analytical solution using trigonometry illustration is presented to describe the relation between the position of the robot end-effector to each of the robot joints. Several lab experiments to validate the established kinematics equations have been conducted. In this study, the developed kinematics solutions were found to be accurate to approximately 99.83% compared to the real robot. These findings have significant implication for developing a kinematic simulation model that can be used to evaluate position and force control algorithm.  Key words: Inverse kinematics  Mitsubishi Melfa RV-2AJ  Pythagoras’s theorem    INTRODUCTION Robotics technology is at the convergence of diverse branch of knowledge that one must realize to successfully express the motion of complex robotic systems. At present, incorporation of human in the process is fundamental for a rapid setup, programming and robot system maintenance. Therefore, before any robotic system is associated to a specific workplace, a simulation approach is often needed to provide deep understanding upon the control framework and its behavior. By simulating the robot and its environment, the human can consistently improve the overall system, reduce the build cost, and eliminate the risks the robot might exerts on the user. The Mitsubishi RV-2AJ robot as shown in Figure 1 has been chosen as a case study as it thecnically offers the best performance as a small, compact and powerful articulated-arm robot in its class. The robot operates using AC servomotors that can produce a maximum speed of 2100 mm/s with a repeatability of ±0.02 mm. The high precision motors with integrated absolute position encoders consistently ensure reliable and maintenance-free operation (Esa, Ibrahim, Mustaffa, & Majid, 2011).  The maximum payload of the robot is rated at 2 kg and thus is exceptionally sufficient for low payload handling, placing and separating small parts. Another prominent applications that are worth mentioning include quality control and handling samples in medical and other laboratories. Since the robot is able to cover horizontal motion of up to 410 mm (with the gripper pointed downwards), it is also ideal for applications where a small and compact robot needs to be installed directly next to or even in any automated system.    Figure 1: RV-2AJ at work in cramped quarters. (Mitsubishi Electric, 2009).  Taking into consideration the way the five jointed robot arm of the RV-2AJ is engineered, the mechanical structure is designated as anthropomorphic articulate (having human-like characteristics). Every single joint has one freedom of rotation around its own axis. The motion axes for the model are assigned with their own nomenclature as follows: base rotation for Joint 1, shoulder rotation for Joint 2, elbow rotation for Joint 3, wrist pitch for Joint 4, and wrist roll for Joint 5. Figure 2 shows the assigned naming convention. VOL. X, NO. X, XXXXXXXX ARPN Journal of Engineering and Applied Sciences  ©2006-2013 Asian Research Publishing Network (ARPN). All rights reserved. ISSN 1819-6608 2    Figure 2: RV-2AJ robot arm joints.  Table 1 lists the maximum working envelope for each joint of the robotic arm while Table 2 lists the link distance between those joint. Each link has its own range limitation allocated by the manufacturer so that the arm will not move beyond the range and thus damaging the servo motor. The complete dimensions of the link frames, the distance between the joints and the robot work envelope are given in Figure 3.  Table 1: Rotation range for RV-2AJ. (Mitsubishi Electric, 2002). Joint Angle Range 1: Waist rotation -150° to +150° 2: Shoulder rotation -60° to +120° 3: Elbow rotation -110° to +120° 4: Wrist pitch -90° to +90° 5: Wrist roll -200° to +200°  Table 2: Link distance for RV-2AJ. (Mitsubishi Electric, 2002). Link Distance 1: Waist to shoulder 300 mm 2: Shoulder to elbow 250 mm 3: Elbow to wrist 160 mm 4: Wrist to end 72 mm   Figure 3: Dimensions of RV-2AJ robot. (Mitsubishi Electric, 2002). Inverse kinematics of RV-2AJ robot The inverse kinematics study consists of determining the joint angles of a robot from its specified end-effector Cartesian position. The analysis of this inverse kinematics for the robot mechanical structures is vital to realize the mechanical system, allowing the development of further studies and applications.  In the past, previous researchers have established different method for developing inverse kinematics of the RV-2AJ robot than the one being discussed in this paper. Such is by implementing an iterative algorithm based on Jacobian transpose matrix (Haklidir & Tasdelen, 2009). However, for no reasonable justification, the kinematic model was developed only up to the first three joints (instead of five) and no experiments result were showed at all to verify the accuracy of the model. As a result of the limited DOF and the unknown accuracy, the position of the end-effector will always be ambiguous. Several other researches have also developed the inverse kinematics solution for the RV-2AJ, but again the accuracy of the models were not proven by any approach (Coman, Balan, Donca, & Verdeş, 2011; Coman, Stan, Manic, & Balan, 2009; Šljivo, 2013). On that account, this paper addresses this matter thoroughly with comparison to experimental results in order to validate the accuracy of the developed model. In addition, considering that the proposed method in this paper is limited to just controlling the z-axis Cartesian position of the robot, the process is much simpler and straightforward to develop compared to other conventional method from previous researchers.  Pythagoras’s theorem in inverse kinematics problem In order to solve the inverse kinematics problem for the 5-axis RV-2AJ robot using Pythagoras’s theorem, a conclusion has been made in which that the solution is not applicable for the wrist roll of the robot. This is because the rotation of the wrist roll does not have any influence on the end-effector Cartesian position. Therefore, the joint angle of the wrist roll is not considered. Referring to the top view of the robot as shown in Figure 4, the waist joint angle of  can be easily resolved. Additionally, it can be seen that wherever the robot moves in any Cartesian position that is permissible for the robot, the waist joint angle could always be calculated by using the same technique that will be discussed in this section.   Figure 4: Determining waist angle at joint 1. VOL. X, NO. X, XXXXXXXX ARPN Journal of Engineering and Applied Sciences  ©2006-2013 Asian Research Publishing Network (ARPN). All rights reserved. ISSN 1819-6608 3   Since the robot posture resulted in Figure 4 produces a right-angled triangle that involves the angle at first joint, the following Pythagoras’s theorem applies:   (1) Hence,  can be calculated as follows:   (2) Before the same theorem is applied to identify the subsequent joint angles of the robot, the initial condition of the wrist pitch has to be configured as shown in Figure 5 so that the wrist pitch is always perpendicular to the ground level at all times during the experiments. To achieve the required setting, both the elbow and the wrist pitch were inclined at +90° while the shoulder is at 0° respectively.   Figure 5: RV-2AJ robot with wrist pitch at vertical position.  Figure 6 shows an example position to acquire the shoulder joint angle of  to  of the robot. The law of sine will be used in this section as the following equation:   (3) The length of  is obtained by using the known sides of the triangle using relevant Pythagoras’s theorem as follows:  (4) The law of cosine relates the lengths of the sides of a triangle to the cosine of one of its angles. Hence we can get :   (5)   (6)   Figure 6: Determining angle at shoulder joint,  to wrist joint, .  Since the joint angle of each link of the robot is based on the previous link inclination, hence:  (7) Substitute the calculated  to equation (3) to acquire  and :  (8)   (9) Next, to solve the following triangle, we get:  (10) Since both  and  are within their right-angled triangle, this yields to:  (11) For the next section of the triangle, we get:  (12) with:  (13) Calculating  from (12), we have:  (14)  VOL. X, NO. X, XXXXXXXX ARPN Journal of Engineering and Applied Sciences  ©2006-2013 Asian Research Publishing Network (ARPN). All rights reserved. ISSN 1819-6608 4   Consequently, the remaining joint angles of  and  can be obtained as follows:  (15)  (16)  (17) Results and analysis  The inverse kinematics of the RV-2AJ robot has been implemented and simulation study has been performed using the MATLAB program. To find out the angle at joint 1, several random positions of the x-axis position, Px and the y-axis position, Py were taken. For experimental results of finding the joint angles at joint 2 to joint 4, the Cartesian coordinates for the end-effector of the robot were set in a way that Px is fixed at 302.45 mm while Py is fixed at 0 mm at all time. However, it should be noted that the applied inverse kinematics method is still applicable when there are any movements anywhere in these axes. The experiment variable, which is the z-axis position, Pz of the robot end-effector changes from 397.35 mm down to 207.36 mm with 10 mm reduction (±1-3 mm) for each sample taken. The desired Cartesian coordinates of the robot were manually controlled via the teach pendant and the joint angles of the robot were directly obtained from its display panel. Comparison between simulation and experiment results are analyzed in this section. In order to fully validate the workability of the developed inverse kinematics method, data taken from the experiments were categorized into three possible configurations.  Determining  To determine the first joint angle,  of the RV-2AJ robot, the end-effector was placed in different Cartesian positions such as in Figure 4. Comparison for both simulation and experimental results were recorded in Table 3. The error produced is found to be approximately 0.196%.   Table 3: Comparison between simulation and experimental results for determining . No. of test Px (mm) Py (mm) Simulation (degree) Experiment (degree) Difference (degree) Error (%) 1 -0.02 0  0  0 0 0 2 224.52 156.22  34.83  34.83 0 0 3 63.37 14.74  13.0943  13.09 -0.0043 -0.43 4 50.73 56.5  48.0801  48.08 -0.0001 -0.01 5 247.56 -93.02  -20.594  -20.59 0.004 0.4 6 7.04 -140.77  -87.137  -87.14 -0.003 -0.3 7 24.77 -25.69  -46.0445  -46.05 -0.0055 -0.55 8 -41.65 65.76  -57.6513  -57.65 0.0013 0.13 9 -60.48 -49.01  39.0196  39.02 0.0004 0.04 10 -37.99 -67.95  60.791  60.79 -0.001 -0.1  First configuration for determining , , and  The first configuration for the conducted experiments to find the joint angles at joint 2 to joint 4 took place when the wrist joint of the robot was located above the shoulder joint as featured in Figure 7. By implementing the developed inverse kinematics method, identical end-effector positions from the robot have been used in MATLAB simulation and the results were recorded.   Figure 7: RV-2AJ robot at first configuration.  The comparison between the simulation and experimental results are presented in Table 4. The average error for , , and  over the 10 data readings are 0.34%, 0.82%, and 2.28% respectively.   Table 4: Comparison between simulation and experimental results for first configuration. No. of test Pz (mm) Simulation (degree) Experiment (degree) Difference (degree) Error (%) 1 397.35  35.7386  35.73 -0.0086 -0.86  66.3738  66.39 0.0162 1.62  77.8877  77.86 -0.0277 -2.77 2 387.34  36.3252  36.32 -0.0052 -0.52  68.9218  68.93 0.0082 0.82  74.753  74.73 -0.023 -2.3 3 377.35  37.0279  37.02 -0.0079 -0.79  71.2709  71.28 0.0091 0.91  71.7012  71.67 -0.0312 -3.12 4 367.35  37.84  37.84 0 0  73.4453  73.45 0.0047 0.47  68.7147  68.69 -0.0247 -2.47 VOL. X, NO. X, XXXXXXXX ARPN Journal of Engineering and Applied Sciences  ©2006-2013 Asian Research Publishing Network (ARPN). All rights reserved. ISSN 1819-6608 5   5 357.35  38.7597  38.76 0.0003 0.03  75.443  75.45 0.007 0.7  65.7973  65.78 -0.0173 -1.73 6 347.36  39.7787  39.78 0.0013 0.13  77.2742  77.28 0.0058 0.58  62.947  62.93 -0.017 -1.7 7 337.34  40.8968  40.89 -0.0068 -0.68  78.9515  78.96 0.0085 0.85  60.1518  60.13 -0.0218 -2.18 8 327.36  42.1013  42.1 -0.0013 -0.13  80.4676  80.48 0.0124 1.24  57.4311  57.41 -0.0211 -2.11 9 317.37  43.3936  43.39 -0.0036 -0.36  81.8342  81.84 0.0058 0.58  54.7721  54.75 -0.0221 -2.21 10 307.35  44.7725  44.77 -0.0025 -0.25  83.0556  83.06 0.0044 0.44  52.1719  52.15 -0.0219 -2.19  Second configuration for determining , , and  For the second configuration experiment, the wrist joint of the robot was placed horizontally equal to the shoulder joint. By realizing this Cartesian position of the robot, the robot configuration in Figure 8 was achieved.    Figure 8: RV-2AJ robot at second configuration.  The simulation and experiment results from this particular position are presented in Table 5. The error produced for , , and  are 0.40%, 1.24%, and 1.84% respectively.      Table 5:  Comparison between simulation and experimental results for second configuration. Pz (mm) Simulation (degree) Experiment (degree) Difference (degree) Error (%) 300  45.8340  45.83 -0.0040 -0.40  83.8576  83.87 0.0124 1.24  50.3084  50.29 -0.0184 -1.84  Third configuration for determining , , and  The wrist joint of the robot was assigned to be lower than the shoulder joint for the third configuration. Detail posture of the robot is given in Figure 9.   Figure 9: RV-2AJ robot at third configuration.  The results for the third region data readings between the MATLAB simulation and experiment are compared in Table 6. The average error for , , and  readings are 0.17%, 0.45%, and 1.49% respectively.  Table 6: Comparison between simulation and experimental results for third configuration. No. of test Pz (mm) Simulation (degree) Experiment (degree) Difference (degree) Error (%) 1 297.35  46.2268  46.22 -0.0068 -0.68  84.1273  84.14 0.0127 1.27  49.6459  49.63 -0.0159 -1.59 2 287.36  47.7548  47.75 -0.0048 -0.48  85.048  85.05 0.002 0.2  47.1972  47.18 -0.0172 -1.72 3 277.36  49.3517  49.35 -0.0017 -0.17  85.8292  85.83 0.0008 0.08  44.8192  44.8 -0.0192 -1.92 4 267.38  51.0099  51.01 1E-04 0.01  86.4649  86.47 0.0051 0.51  42.5253  42.51 -0.0153 -1.53 5 257.36  52.7349  52.73 -0.0049 -0.49  86.959  86.96 0.001 0.1 VOL. X, NO. X, XXXXXXXX ARPN Journal of Engineering and Applied Sciences  ©2006-2013 Asian Research Publishing Network (ARPN). All rights reserved. ISSN 1819-6608 6    40.3061  40.29 -0.0161 -1.61 6 247.37  54.5104  54.51 -0.0004 -0.04  87.3081  87.31 0.0019 0.19  38.1816  38.17 -0.0116 -1.16 7 237.34  56.3442  56.34 -0.0042 -0.42  87.5145  87.52 0.0055 0.55  36.1412  36.13 -0.0112 -1.12 8 227.35  58.2175  58.22 0.0025 0.25  87.5768  87.58 0.0032 0.32  34.2057  34.19 -0.0157 -1.57 9 217.34  60.1371  60.14 0.0029 0.29  87.4956  87.5 0.0044 0.44  32.3673  32.35 -0.0173 -1.73 10 207.36  62.0894  62.09 0.0006 0.06  87.2716  87.28 0.0084 0.84  30.639  30.63 -0.009 -0.9  Comparison with other method To compare the accuracy of the developed inverse kinematic model, another conventional method of using inverse matrix multiplication (Niku, 2011) has been established and the results are shown in Table 7. For this comparison,  represents the total summation of ,  and  which should theoretically produced 180°. Based on these findings, it is clear that the method discussed in this paper is more accurate.  Table 7: Comparison between Pythagoras’s simulation and inverse matrix simulation results. No. of test Pz (mm) Pythagoras’s Simulation (degree) Inverse Matrix Simulation (degree) 1 277.36  180.00  179.9828 2 287.36  180.00  179.9828 3 297.35  180.00  179.9885 4 300.00  180.00  179.9885 5 307.35  180.00  179.9828 6 317.37  179.99  179.9828 7 327.36  180.00  179.9885  CONCLUSION  In this paper, the inverse kinematic equations for the joint angle of the RV-2AJ industrial robot arm with regards to the end-effector position have been derived. It can be seen that the developed inverse kinematics solution provides approximately 97.72% to 99.83% accuracy identical to the robot itself. On the other hand, the errors produced from the conducted experiments (when compared to the simulations) were possibly because of the robot calibration issue and mechanical properties that contributes to slightly false data readings whenever the robot arms were moved.   ACKNOWLEDGEMENT  This work was supported by Ministry of Education and Universiti Tun Hussein Onn Malaysia under Research Acculturation Grant Scheme Vot R032.  REFERENCE Coman, M., Balan, R., Donca, R., & Verdeş, D. (2011). Optimization of the Control for the RV-2AJ Serial Robot. Romanian Review Precision Mechanics, Optics and Mechatronics, (39), 149–152. Retrieved from http://www.incdmtm.ro/editura/documente/pag. 149-152 COMEFIM 10 COMAN.pdf  Coman, M., Stan, S., Manic, M., & Balan, R. (2009). Design, Simulation and Control in Virtual Reality of a RV-2AJ Robot. In 2009 35th Annual Conference of IEEE Industrial Electronics (pp. 2026–2031). IEEE. doi:10.1109/IECON.2009.5414922  Esa, M. F. M., Ibrahim, H., Mustaffa, N. H., & Majid, H. A. (2011). The Mitsubishi MelfaRxm middleware and application: A case study of RV-2AJ robot. In 2011 IEEE Conference on Sustainable Utilization and Development in Engineering and Technology (STUDENT) (pp. 138–143). IEEE. doi:10.1109/STUDENT.2011.6089341  Haklidir, M., & Tasdelen, I. (2009). Modeling, simulation and fuzzy control of an anthropomorphic robot arm by using Dymola. Journal of Intelligent Manufacturing, 20(2), 177–186. doi:10.1007/s10845-008-0227-9  Mitsubishi Electric. (2002). MELFA Industrial Robots - Specifications Manual.  Mitsubishi Electric. (2009). MELFA Industrial Robots. Consistent Quality - Precise Control.  Niku, S. B. (Saeed B. (2011). Introduction to robotics : analysis, control, applications. Hoboken, NJ: Wiley.  Šljivo, D. (2013). SIMULATION OF A 5-AXIS RV-2AJ ROBOT. 17th International Research/Expert Conference, ”Trends in the Development of Machinery and Associated Technology”, (September). Retrieved from http://tmt.unze.ba/zbornik/TMT2013/098-TMT13-096.pdf  

Nondestructive quantitative analysis of water potential of tomato leaves using online hyperspectral imaging system

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