The objective of this study is to enhance the performance of a nonlinear three-rigid-link manipulator (RLM) with a focus on trajectory tracking, robustness against disturbances and noises, and adaptability to joint flexibility. To achieve this, we have employed an optimized sliding mode controller with a proportional integral derivative (PID) sliding manifold. The tuning process involves selecting the critical gains of the controller that minimizes the integral time absolute error (ITAE), serving as the objective function (OBJF) to optimize the performance of the robot manipulator. To identify the optimal gains of the controller, we have utilized a new optimization algorithm known as memory enhanced linear population size reduction gray wolf optimization (MELGWO). The efficacy of this algorithm is compared to other existing optimization methods in the literature. Moreover, this research has delved into the impact of joint flexibility on the robot system’s performance. Encouragingly, the results demonstrate that the optimized SMC–PID with MELGWO adaptation can effectively address joint flexibility while maintaining acceptable performance levels.