Intelligent Controller for Robot Manipulator

This paper suggests an intelligent controller to control the manipulator movement in an environment of two and three – dimensional. The fuzzy logic controller of planning structure locally approach constructs of multi-unit. The aim is to transmit or guide the manipulator from the elected to a desired configuration. Modeling, scenarios and simulations are presented clearly in two dimensions and three dimensions together with their analysis which be done using MATLAB software. In addition, the results of the robot navigation in two-dimensional environments also compared with the results of the navigation in three-dimensional environments to clarify the strength of the suggested intelligent controller, where results (in rad) for the third link for both two and three- dimensional environments are minimum: and in the scenario 1 also minimum results in scenario 2 as the following: 0 0060 and 0 0000. Simulation results indicate this manipulator successfully reached the desired goal configuration.


INTRODUCTION
he arm of robotic is utilized to pick and place object at locations are set in a given hemispherical three dimensional space. The mechanism of pick and place finds it applications in the field of electronics industry, consumer goods industry, military and food industry [1].
Traditional control methods require near complete knowledge of a robot's nonlinear dynamics in order to generate effective control signals. Obtaining accurate model parameters consumes time, expense, and loses accuracy over time. Robot path planning is an important part of the development of autonomous systems [2][3][4]. The low cost, fast response, real-time ability is good and unnecessary knowledge the accurate sample of the model to control it and meet the real-time demands for planning the motion of the robot are benefits of fuzzy control [5,6]. Fuzzy system illustrated in Figure (1) [7].  [7]. Some previous researchers dealt with the subject of robot strategies for navigation system as follows: Tawfik M. A. et al [8] presented a three-dimensional continuous autonomous chaotic system, Basic properties of the presented system were analyzed by means of Lyapunov T exponent spectrum, Poincar'e mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore the cited chaotic system was implemented in robotics field for coverage area purposes, where it's used to generate chaotic motion for mobile robot that's guarantee of scanning the whole connected workspace as an example of advantage of this system. Hussein Z. D. et al [9] suggested a study for optimal performance of a robot to be used in human surgery (Laparoscope device). The optimal performance was obtained by using genetic algorithm method to choose the optimal path planning in the working area. The robot used was the Lab-Volt Servo Robot System. Wei and Shimin [10] presented three-dimensional planning the path using NNT networks for a robot manipulator. They reported that it is complex to find a good path when the robot is in a complex dynamic change condition. Algorithms for the device to perform path planning and trajectory prediction were described. Dubey et al [1] suggested evolutionary process to optimize robot manipulators task time. Tasks can be planned with relative to joints of robot / relative to end effector of robot.
Aljarboua [11] presented a distance transform based on geometric algorithm of planning the path with vision capability suitable for robots. Ramírez and Rubiano [12] presented the forward kinematic model for industrial manipulator three degrees of freedom with a multiple applications.
Fani and Shahraki [13] suggested an individual FOPID controller is applied in order to control each link. Three evolutionary optimization algorithms included particle swarm optimization (PSO), genetic algorithm and estimation of distribution algorithm, are compared from optimal coefficients determination point of view.
Albert, Koh, Chen et al., [14] presented application and the formulation of a genetic algorithm based on strategy for the calculations of optimizing joint angles in a given search space for three armed planar manipulator structure that would contribute to a quality and a productive way of material processing and handling. In this paper, the suggested approach effectiveness is validated through simulations. It meets the real-time demands for planning robot motion in environments of two -dimensional and three -dimensional.

Theory of the Fuzzy Inference System
Mamdani and Sugeno are the most widely used methods in fuzzy inference to determine the fuzzy intersection operation. The operators of minimum and product are the fuzzy rules. Every output of fuzzy unit can be calculated by utilizing the gravity center (COG) defuzzification method [15,16], this method is used for the defuzzification: Where is the consequent center membership function of rule ( ). means the area under the membership function.

Suggested Method
In this section, the suggested system has been described and illustrated. To make the design more comprehensive and expanded, the structure is applied into two environments of twodimensional and three -dimensional.
The suggested fuzzy logic controller is to control the robot manipulator motion where this robot arm consists of three links. Each link produces depending on the input and on the current value , Where means error between the goal value and which represents the input2 to the first fuzzy unit and n the number of link, similar to units two and three of fuzzy logic controller. Figure (2) shows the overall structure of navigation robot arm applied in two different cases environments as illustrated below where, in two dimensional environment and three dimensional environment respectively.

Figure (2): Overall structure
The variables (inputs) of fuzzy system are angle parameters, where illustrated in Figure (3).

Figure (3): Fuzzy inference system for calculating the required change of joints angle for each link
The mathematical equations for the suggested method in equation (2) and equation (3): ... (2) Then the output of controller (the required change of joint angle) can be easily computed by the following: Outputs of fuzzy unit 1, 2 and 3 respectively. The require change of joints angle.

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Where, means Desired Configuration also called which means Goal Configuration. By using Mamdani method and center of gravity in equation (1), For example rule 1: When (Error Negative Far i.e. negative value of membership function) and (Current value of joint1 angle is Left i.e. negative value of membership function) then the output (will be Negative Far i.e. negative value) also try and error used in each one.
As example below part of rules of first unit of fuzzy control in two -dimensional environment: If Error is NFar and Current value of joint1 angle is Left then Output1 is NFar If Error is NFar and Current value of joint1 angle is Right then Output1 is NAverage If Error is NAverage and Current value of joint1 angle is Below then Output1 is NClose If Error is NAverage and Current value of joint1 angle is Right Positive then Output1 is NFar If Error is NClose and Current value of joint1 angle is Right Positive then Output1is NClose If Error is NClose and Current value of joint1 angle is Below then Output1 is PClose The surface viewer of this link is shown in Figure (

Figure(4): The surface viewer of first link
Also part of rules of second unit of fuzzy control in two -dimensional environment: If Error is NAverage and Current value of joint2 angle is PFar then Output2 is NClose If Error is NClose and Current value of joint2 angle is PAverage then Output2 is NFar If Error is PClose and Current value of joint2 angle is NFar then Output2 is NClose If Error is PClose and Current value of joint2 angle is NClose then Output2 is NClose If Error is PClose and Current value of joint2 angle is PClose then Output2 is PClose If Error is PAverage and Current value of joint2 angle is NClose then Output2 is PClose The surface viewer of this link is shown in Figure (5).

Figure(5): The surface viewer of second link
Moreover, part of rules of third unit of fuzzy control in three -dimensional environment as example: If Error is NFar and Current value of joint3 angle is PFar then Output3is NFar If Error is NAverage and Current value of joint3 angle is NClose then Output3 is NMedium If Error is NAverage and Current value of joint3 angle is PFar then Output3is NClose If Error is NClose and is Current value of joint3 angle NAverage then Output3 is NFar If Error is PClose and is Current value of joint3 angle NFar then Output3 is NClose If Error is PClose and is Current value of joint3 angle NClose then Output3 is NClose Where N is Negative for example NFar means Negative Far and so on. The surface viewer of this link is shown in Figure (6).

Figure (6): The surface viewer of third link
Moreover, below Figure (7) shows part of fuzzy rule table that suggested in this paper for robot navigation in two and three dimensional environments respectively.

Continued
Inputs (Current value of joints angle and error). Where, the range of universe of discourse equal to the value from -6.283 to 6.283 for the first input but the second input the universe of discourse equal to the value from -3.141 to 3.141 all these value in rad.
Output (The required change of joints angle). Where the range of universe of discourse equal to the value from -0.05 to 0.05 rad.

Input 1
Input 2 Output

Simulations Results and Discussions
To test the overall system of Figure (2), Table (1) and Table (4) below show the specifications of scenario 1 and scenario 2 of robot arm navigation in two and three dimensional environment respectively. Additionally, the results of the system structure of navigation in two and three dimensional are illustrated in Table (3) and Table (6) respectively. Table (2) and Table (5) clarify comparison between desired configuration and reached configuration for both scenario 1 and scenario2 respectively. Inputs (Current value of joints angle and error). Where, the range of universe of discourse equal to the value from -6.283 to 6.283 for the first input but the second input the universe of discourse equal to the value from 0 to 6.283 all these value in rad.
Output (The required change of joints angle). Where, the range of universe of discourse equal to the value from -0.0157 to 0.0157 rad.  Applying the same mechanism of Figure (8 Eng. &Tech.Journal, Vol.34,Part (A), No.13,2016 2558 (10), (11), (12) and (13) show the arm navigation in three -dimensional environment, moreover all viewer directions such as 3 D view, axial view, side view and top view respectively. Figure (14) the simulation results of scenario 1.

Figures
, and mean Link1, Link2 and Link3 respectively.  Eng. &Tech.Journal, Vol.34,Part (A), No.13 More inclusive, we take another scenario by taking different values as clarified in Table (3) and the numerical results in Table (

Table )5(: Comparison between desired configuration and reached configuration
Furthermore robot arm navigates in three-dimensional as shown in Figure (17).  From tables of simulation results for both two-dimensional and three-dimensional environment the robot arm reached successfully to desired configuration with ( 0 0 0 ) minimum error value in navigation in two-dimensional environment after minimum iterations of program (455 and 505) However, three-dimensional navigation is more complex to explain, although it may enable more accurate.

CONCLUSIONS
This paper includes two essential parts. In the first one, navigate the robot arm in twodimensional environment and the second one, navigate the robot arm in three dimensional environment. To prove and evaluate the performance of the arm, two scenarios for both environment applied so the results show that the problem solved for these structures by using intelligent controller. This algorithm is useful and applicable when dealing with intelligent controller. In this work, robot arm has been successfully reached to the desired configuration when the navigation in two and three-dimensional environments. Moreover a comparison has been made between them. Where, navigation in these environments exhibits good results where the results of reaching the goal ( 0 0 0 ) after minimum iterations of program was minimum values in navigation in two-dimensional environment and good performance, while the navigation in three-dimensional the program iterations was larger than in two-dimensional environment (455 and 505 in two-dimensional, 1000 and 1200 in three-dimensional) but also the error remain acceptable with minimum value ( 0 0 ). However, 3D navigation is more difficult to interpret, although it may enable greater precision.