Cardiopulmonary resuscitation refers to the process of sending oxygen and blood to the body's vital organs during cardiac arrest. For this reason, designing and controlling an accurate robot is crucial to saving the lives of patients. This study aims to optimize two nonlinear robust controllers for the first time for the parallel manipulator for cardiopulmonary resuscitation to reduce overshoot, increase accuracy, increase convergence speed, and increase robustness to destructive factors affecting the precision of the robots. The paper first presents the kinematics and dynamics of a translational parallel manipulator robot. Then, to reduce the difference between the practical and simulation results, the paper presents a nonlinear model under uncertainties, disturbances, and noise. Then, the ONSTSMC awaiting the uncertainty band is designed to eliminate the singularity problem and increase the accuracy and robustness to destructive factors, as well as improve stability using the Lyapunov principle. Furthermore, the results of applying this robust controller to the robot are compared with the results of a non-singular terminal sliding mode controller without considering the uncertainty band, a conventional sliding mode controller, and a PID controller for the same model. The developed controller exhibits better performance in terms of accuracy and convergence time even when external and internal destructive factors are present. The accuracy is 0.21 mm and the convergence time is 0.7 seconds when compared with PID. Furthermore, it is approximately 0.17 mm and 0.4 seconds faster compared with conventional sliding mode controllers.