Compared to serial robots, parallel robots have potential superiorities in rigidity, accuracy, and ability to carry heavy loads. On the other hand, the existence of complex dynamics and uncertainties makes the accurate control of parallel robots challenging. This work proposes an optimal adaptive barrier-function-based super-twisting sliding mode control scheme based on genetic algorithms and global nonlinear sliding surface for the trajectory tracking control of parallel robots with highly-complex dynamics in the presence of uncertainties and external disturbances. The globality of the proposed controller guarantees the elimination of the reaching phase and the existence of the sliding mode around the surface right from the initial instance. Moreover, the barrier-function based adaptation law removes the requirement to know the upper bounds of the external disturbances, thus making it more suitable for practical implementations. The performance and efficiency of the controller is assessed using simulation study of a Stewart manipulator and an experimental evaluation on a 5-bar parallel robot. The obtained results were further compared to that of a six-channel PID controller and an adaptive sliding mode control method. The obtained results confirmed the superior tracking performance and robustness of the proposed approach.