Abstract: In this study, we addressed the problem of trajectory tracking control for a two-degree-of-freedom wrist-joint upper-limb rehabilitation exoskeleton robot with unknown model information. A novel model-free prescribed-time control framework based on prescribed-time high-order control barrier functions is proposed. The developed approach simultaneously guarantees prescribed-time convergence and strict satisfaction of safety constraints without relying on an accurate dynamic model. In practical rehabilitation scenarios, obtaining an accurate dynamic model of the human–robot system is extremely difficult because of the complex physical interactions, significant parameter uncertainties, time-varying external disturbances, and variations in human parameters among different patients. To solve this problem, a second-order ultra-local model was constructed to describe the system dynamics. In this model, the uncertainties, external disturbances, and human–robot interaction torques are unified into a lumped disturbance term. Furthermore, radial basis function (RBF) neural networks are incorporated to estimate the lumped disturbances online in real time, enabling a fully model-free control implementation without requiring prior knowledge of system dynamics. Based on this formulation, a prescribed-time sliding-mode control strategy based on state transformation was designed to ensure that the desired motion trajectories are rapidly and stably tracked by the system states. Specifically, by utilizing the controller, the tracking errors between the states and described trajectories can be forced to zero within a predefined time bound, which can be explicitly assigned according to practical rehabilitation requirements. It should be noted that the convergence time is independent of the initial conditions, thereby ensuring uniform transient performance even when the system starts from different or unfavorable initial states. To enhance the safety of the rehabilitation training process further, a prescribed-time high-order control barrier function was constructed that explicitly incorporates safety constraints into the controller design. This formulation explicitly encodes the state constraints and guarantees that the system states are driven into the safe set within a prescribed time and remain there thereafter, even when starting from outside. In contrast to existing barrier Lyapunov function-based methods, the proposed approach relaxes the requirement of the initial conditions by allowing the system states to start outside the safe set and ensuring their convergence within a prescribed time. The optimal control law satisfying the safety constraints is solved by incorporating the Karush–Kuhn–Tucker (KKT) conditions. As a result, the proposed method ensures that the system states not only converge to the desired trajectories within the prescribed time but also enter and remain within the safe set in a guaranteed manner, achieving both transient safety and long-term forward invariance. The global stability of the closed-loop system and forward invariance of the safe set were rigorously established using the Lyapunov stability theory, providing strong theoretical guarantees for the proposed approach. Numerical simulation results were obtained to validate the effectiveness of the proposed strategy. The results demonstrate that the system states converge within the prescribed time bound, regardless of the initial conditions, even when the initial states lie outside the safe set. Comparative studies under sudden disturbances further highlight the superiority of the proposed control barrier function in terms of maintaining safety. In addition, compared with finite- and fixed-time control schemes, the proposed method not only accelerates the convergence process but also provides a flexible and user-defined convergence time.