With more links, manipulator systems become substantially more effective and valuable, however at the expense of more complexity. In this study, the performance of a multi-input and multi-output highly rigid three-link robotic manipulator system (TLRMS) using a fractional-order nonlinear proportional, integral, and derivative (FONPID) controller for trajectory tracking along with X and Y positional movement are analyzed. The performance of the FONPID controller is carefully investigated and results are compared to the nonlinear proportional, integral, and derivative (NPID) as well as traditional proportional, integral, and derivative (PID) controllers. The cuckoo search algorithm (CSA) is used to optimize controller gains by choosing the minimum objective function criterion (Jmin) which is the combination of the weighted sum of the integral of absolute error (IAE) and integral of absolute change in controller output (IACCO) values. The analysis's findings conclusively show that the FONPID controller performs better in trajectory tracking. This study advances fractional-order control techniques, especially when applied to sophisticated manipulator systems.