## 1 Introduction  
A manipulator robot is the most useful and popular robot type, so has been acquiring importance in recent years [1]. The manipulator robot has been increasingly used more and more, especially in industrial and manufacturing applications like packaging, welding, etc. It also is associated with all life fields, especially in personal assistance where it works instead of a human hand. The manipulator must have good accuracy and high precision [2]. There are numerous methods to solve the trajectory generation problem, and many key methods were studied such as cell decomposition [3], mathematical program [4], skeleton [5] and boundary following methods. In order to design the performance of planning, more than one planning approach, like the APF decomposition method on aircraft [6] needs to be utilized. Since the introduction of the proportional-integral-derivative (PID) controllers, many algorithms were used such as trial-and-error, Ziegler-Nichols, pole placement and D-partitioning methods. All of these algorithms have been adopted for tuned PID controllers on the elastic joints [7]. In addition, all of these algorithms have been used in frequency response of linear time invariant systems. These algorithms require a good knowledge of the system, and therefore, many meta-heuristic optimization approaches have been used to gain tuned controllers for linear and nonlinear robotic manipulator systems. There are many optimization algorithms such as differential evolution (DE), genetic algorithms (GA) and particle swarm optimization (PSO) which have been used for PID tuning of robotic systems. At present, the DE algorithm gives better results for the PID-PDC controller in linear and nonlinear contour tracking [8]. The previous researches concluded that the meta-heuristic algorithms produce better results than traditional tuning techniques (in time domains), to tune the position domain PID controller. The principal work of the position domain controller (PDC) was presented for PD and PID controllers [9]. The principal idea of the position domain controller is to describe the system in slave motions and master motions. Master motions were considered as reference to the slave motion instead of time. The optimization method is defined for the configuration space and is based on an obstacle-dependent Gaussian model predictive control to avoid obstacles [10], and to move to the goal point by APF which is velocity dependent [11]. The APF needs to be developed by many algorithms such as proximity maneuvering, formation-flying, large angle slew maneuvers, and small spacecraft formation [12]. To build an efficient path for the manipulator robot, it is important to define the frame transformation and solve the inverse kinematics. In inverse kinematics, all joint variables of the manipulator are considered as a function of goal configuration of the end-effector. A basic principle of APF is best described when adding an attractive potential field with a repulsive potential field as a local minimum formation to trap a maneuvering object in many configurations [13]. The basic idea of the APF algorithm for manipulator path planning was to consider the manipulator movement while considering obstacles as bodies [14]. The famous applications of the collision-free trajectory lie in unmanned aerial vehicles (UAVs) which used a dynamic artificial potential field (D-APF) [15], industrial manipulator robots, and robotics in medical applications. There are a lot of research studies regarding the manipulator to perform the trajectory with obstacle avoidance. To avoid obstacles, external sensors or technology must be added to the robot [16]. Spatial mapping was proposed for nonlinear and linear distances [17]. In the APF, realize real-time avoidance path planning was enhanced against a randomly moving obstacle. The bidirectional APF method was proposed for obstacle avoidance [18]. In [19], the APF method was enhanced to obtain collision-free paths in a 3D space by using sliding mode techniques.