The robotic manipulator is considered one of the complex systems that include multi-input, multi-output, non-linearity, and highly coupled. The uncertainty in the parameters and external disturbances have a negative influence on the performance of the system. Therefore, the controllers that will be designed for these systems must be able to deal with these complexities and difficulties. The Proportional, Integral, and Derivative (PID) controller is known to be simple and well robust, while the neural network has a solid ability to map complex functions. In this paper, we propose six control structures by combining the benefits of PID controller with integer and fractional order and the benefits of neural networks to produce hybrid controllers for a 2-Link Rigid Robot Manipulator (2-LRRM) handling with the problem of trajectory tracking. The Gorilla Forces Troops Optimization algorithm (GTO) was used to tune the parameters of the proposed controller schemes to minimize the Integral of Time Square Error (ITSE). In addition, the robustness of the performance of the suggested control systems is tested by altering the initial position, external disturbances and parameters and carried out using MATLAB. The best performance of the proposed controllers was the Neural Network Fractional Order Proportional Integral Derivative Controller (NNFOPID).