Abstarct: In this thesis, a nonlinear optimal control problem is investigated on the two-lixnk artist robot manipulator. The maximum difference in between robots are their mechanical parts and how to control them. Minimizing the tracking error and tracking control are important purpose and considerable in control systems. In this study, particle swarm optimization algorithm(PSO) is used to design the optimal controller. Applying the particle swarm optimization algorithm is useful for highly complex systems in optimization problems because the PSO is easy to be implemented and independent of the model. The PSO results the optimal control baxse on optimization control parameters. In this algorithm, the optimal value of control parameters are determined by minimizing the cost function, and the integral square of errors (ISE) as a performance criteria. In this case, the performance of PSO algorithms such as an improved PSO (IPSO), an improved PSO using fuzzy logic (F-PSO), a linearly decreasing inertia weight of PSO (LWD-PSO) and a nonlinearly decreasing inertia weight of PSO (NDW-PSO) are compared in terms of parameter accuracy and convergence speed. As a result, the simulation results show that the F-PSO approach presents a better performance in the tracking control of robot manipulators than other algorithms.