The tuning of the robot actuator represents many challenges to follow a predefined trajectory on account of the uncertainties of parameters and the model nonlinearity. Furthermore, the controller gains require proper optimization to achieve good performance. In this paper, the use of a modified neural network algorithm (MNNA) is proposed as a novel adaptive tuning algorithm to optimize the controller gains. Furthermore, a new mathematical modulation is introduced to promote the exploration manner of the NNA without initial parameters. Specifically, the modulation is formed by using a polynomial mutation. The proposed algorithm is applied to select the proportional integral derivative (PID) controller gains of a robot manipulator arms in lieu of conventional procedures of designer expertise. Another vital contribution is formulating a new performance index that guarantees to improve the settling time and the overshoot of every arm output simultaneously. The proposed algorithm is evaluated with different intelligent techniques in the literature, including the genetic algorithm (GA) and the cuckoo search algorithm (CSA) with PID controllers, where its superiority to follow various trajectories is demonstrated. To affirm the robustness and efficiency of the proposed algorithm, several trajectories and uncertainties of parameters are considered for assessing the response of a robotic manipulator.