**1. Introduction**

The robot Inverse Kinematics problem involves finding the joints' variable values that match input parameters of position and direction of the end effector [1]. These matched variable values will ensure that subsequent robot control will follow the desired trajectory. This is one of the important issues in the robotic field because it is related to other aspects such as motion planning, dynamic analysis and control [2]. Traditionally, there are several methods to resolve inverse kinematics problem

for robots such as: geometry method is the method using geometric and trigonometric relationships to solve; the iterative method is often required inversion of a Jacobian matrix, etc. However, when applying these methods to solve the IK problem for robots, especially with redundant robots, it is often much more complicated and time-consuming. The reason is the nonlinearity of the formulas and the geometry between the workspace and the joint space. In addition, the difficult point is in the singularity, the multiple solutions of these formulas as well as the necessary variation of the formulas corresponding to the changes of different robot structures [3–5].

In addition to those existing methods of solving the IK problems, in recent years, the application of meta-heuristic optimization algorithms has become increasingly common. 8 optimization algorithms applied in [5] in the cases of a single point or a whole trajectory endpoint. The simulation results showed that the PSO algorithm can effectively solve the IK problem. In [6] the authors used algorithms such as ABC, PSO, and FA to solve the inverse kinematic requirement for Kawasaki RS06L 6-DoF robot in the task of picking and place objects. Ayyıldız et al. compared the results of all IK tests for a 4-DOF serial robot using 4 different algorithms: PSO, QPSO, GA and GSA [7]. Two versions of the PSO algorithm have been used to solve the IK problem for robots with a number of degrees of freedom from 9 to 180 [8]. In recent research [9], Malek et al. used PSO algorithm to handle inverse kinematics for a 7-DoF robot arm manipulator. The study mentioned both the requirements for the location and the direction of the endpoint, however, it only solved for 2 different end effector positions. Laura et al., in [10] used DE algorithm for the IK problem of 7-DoF robot. The problem was solved for specific points, but the quality evaluation parameters such as endpoint position deviation, execution time as well as the values of the joints' variable did not reach impressive quality. Ahmed El-Sherbiny et al. [11] proposed to use ABC variant algorithm for solving inverse kinematics problem in 5 DoFs robot arm. Serkan Dereli et al. [12] used a quantum behave partial algorithm (QPSO) for a 7-DoF serial manipulator and compare the results with other techniques such as firefly algorithm (FA), PSO and ABC.

In this study, the self-adaptive control parameters in Differential Evolution (ISADE) algorithm, that developed [13, 14] by authors, was applied to solve the problem of inverse kinematic for a 7-DOF serial robot. To compare the results, this IK problem was also handled by applying DE and PSO algorithms. In addition, the study also compared the results in the application of the above algorithms with the search space improvement of joints' variables (Pro-ISADE, Pro-PSO and Pro-DE) [15].

> The homogeneous transformation matrix can be used to obtain the forward kinematics of the robot manipulator, using the DH parameters in Eq. (1) [17].

**Joint** *θ***(rad) d(mm) a(mm) α(rad)** 1 -π <*q*<sup>1</sup> <π *d*<sup>1</sup> = 500 0 - π/2 2 -π/2 <*q*2<π/6 0 *l*<sup>2</sup> = 200 π/2 3 -π/2 <*q*<sup>3</sup> <2π/3 0 *l*<sup>3</sup> = 250 - π/2 4 -π/2<*q*<sup>4</sup> <π/2 0 *l*<sup>4</sup> = 300 π/2 5 -π/2<*q*<sup>5</sup> <π/2 0 *l*<sup>5</sup> = 200 - π/2 6 -π/2<*q*<sup>6</sup> <π/2 0 *l*<sup>6</sup> = 200 0 7 -π/2 <*q*<sup>7</sup> <π/2 *d*7=5 *l*<sup>7</sup> = 100 0

*Use Improved Differential Evolution Algorithms to Handle the Inverse Kinetics Problem…*

*Cθ<sup>i</sup>* �*Sθ<sup>i</sup>* 0 *ai*

*nx sx ax x*<sup>5</sup> *ny sy ay y*<sup>5</sup> *nz sz az z*<sup>5</sup> 000 1

(1)

(2)

*SθiC*α*<sup>i</sup> CθiC*α*<sup>i</sup>* �*S*α*<sup>i</sup>* �*diS*α*<sup>i</sup>*

*SθiS*α*<sup>i</sup> SθiS*α*<sup>i</sup>* �*C*α*<sup>i</sup>* �*diC*α*<sup>i</sup>* 0 00 1

The position and orientation of the end-effector can be determined by Eq. (2):

*Ti*�1*<sup>i</sup>* ¼

**Figure 1.**

**Table 1.** *D-H parameters.*

**21**

*The 7-DFO robot Scheme and coordinate systems used in the study.*

*DOI: http://dx.doi.org/10.5772/intechopen.97138*

where S and C denote the sine and cosine functions.

*T*<sup>07</sup> ¼ *T*<sup>01</sup> ∗ *T*<sup>12</sup> ∗ *T*<sup>23</sup> ∗ *T*<sup>34</sup> ∗ *T*<sup>45</sup> ∗ *T*<sup>56</sup> ∗ *T*<sup>67</sup> ¼

The remainder of the paper is divided into the following sections: Section II describes the experimental model. The theory of the PSO, DE and ISADE algorithms as well as the algorithms with improved search area, Pro-PSO, Pro-DE and Pro-ISADE, will then be presented in Section III. Section IV covers scenarios and object functions that will be applied to calculate the IK. The results after applying the algorithm are shown and compared in Section V. Finally, the conclusions are outlined in Section VI.
