## 1 Introduction  
Since the introduction of PID controllers, a great number of methods such as trial-and-error, D-partitioning, Ziegler-Nichols, and pole placement have been developed for the gain tuning of PID controlled systems [1]. Nonetheless, most of these direct methods have been developed for linear, time invariant systems and require extensive knowledge of the system and its frequency response in order to be employed efficiently. Due to these facts, various meta-heuristic optimization methods have been used for the gain tuning of PID controllers for nonlinear systems such as robotic systems. More specifically, evolutionary algorithms such as genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO) have been very popular for PID tuning of various systems [2].  
Recent research suggests that meta-heuristic algorithms such GA, DE, and PSO produce consistently better results than conventional tuning techniques with DE outperforming the other algorithms in results and computational cost [3].Furthermore, [PERSON] [2], in a comparison of the three algorithms, concluded that GA falls into local minima with greater tendency than the other algorithms, while PSO tends to result in higher density of solutions within the solution space with DE being closely comparable to PSO.  
Comparing PSO with GA, controllers tuned by the PSO method were found to be more efficient, with the PSO exhibiting better performance and a higher convergence rate than GA [4]. This can be attributed to PSO's ability to avoid premature convergence to local minima and therefore provides higher quality solutions [5]. Similarly, in [6] DE was found to produce better tuning results than the GA with the authors, however noting that for high order systems, the results of both optimization techniques were quite similar. Furthermore, controllers optimized by DE performed better than the PSO tuned equivalents, leading to the conclusion that DE can be more robust than PSO [7]. However, it should be noted that the performance of each optimization algorithm is also subject to the optimization problem itself as demonstrated in [8].  
In our previous research, the concept of position domain (PDC) was introduced in the form of PD and PID control types [9; 10; 11], with its main feature being its good contour tracking efficiency when compared to pre-existing control schemes in time domain. The main idea behind PDC is the discretization of the system into master and slave motions, with the use of the master motion as reference for the slave motions instead of time [9; 10; 11].  
In this paper, the performance of GA, DE and PSO are studied for the gain tuning of a position domain PID controller (PDC-PID). The controller is tasked with contour tracking of a 3R planar serial robotic manipulator on the end-effector level. The robotic manipulator is used to track two different contours, one is linear and the one is nonlinear, for which different optimized control gains are generated. Furthermore, the optimizations are executed under various fitness functions for a large variation in performance criteria.  
The rest of this paper is organized as follows: Section 2 summarizes the concept of position domain control and the PDC-PID controller. Section 3 synopsizes optimization algorithms to be compared. Section 4 describes the details of optimization, and Section 5 exhibits some optimized results for contour tracking of the end-effector of a robotic manipulator. Finally, Section 6 provides some conclusions.