African vultures optimization-based hybrid neural network–proportional-integral-derivative controller for improved robot manipulator tracking

Rigid robotic manipulators encounter several challenges in trajectory tracking control, including low accuracy and poor stability, resulting from uncertainties, external disturbances, and parameter variations. To address these issues, this study proposes two hybrid controllers that integrate the strengths of proportional-integral-derivative (PID) control with neural network (NN) methods for a three-link rigid robotic manipulator. These hybrid structures are the NN–PID controller and the self-tuning NN with PID (STNN–PID) controller. Their performance is compared against that of a conventional PID controller. To optimize control performance metrics, such as the integral time square error (ITSE), the parameters of the proposed controllers were tuned using the African vultures optimization algorithm. MATLAB was used to evaluate the effectiveness. Robustness tests were performed by varying the initial conditions, introducing external disturbances, and modifying system parameters. The NN–PID controller achieved ITSE values of 0.28919 × 10−4, 0.064321, and 0.001164, respectively, while the STNN–PID controller yielded values of 3.54549×10−4, 3.526199, and 0.883710, respectively. Moreover, when all these conditions were applied simultaneously, the NN–PID controller achieved an ITSE of 0.073968, compared to 2.672754 for the STNN–PID controller. These results demonstrate that the NN–PID controller outperforms the other controllers across all testing conditions. These findings confirm that the NN–PID controller is the most effective controller in terms of tracking accuracy, stability, and robustness across all test scenarios.