The use of exoskeleton robots is increasing due to the rising number of musculoskeletal injuries. However, their effectiveness depends heavily on the design of control systems. Designing robust controllers is challenging because of uncertainties in human-robot systems. Among various control strategies, Model Predictive Control (MPC) is a powerful approach due to its ability to handle constraints and optimize performance. Previous studies have used linearization-based methods to implement robust MPC on exoskeletons, but these can degrade performance due to nonlinearities in the robot's dynamics. To address this gap, this paper proposes a Robust Nonlinear Model Predictive Control (RNMPC) method, called multi-stage NMPC, to control a two-degree-of-freedom exoskeleton by solving a nonlinear optimization problem. This method uses multiple scenarios to represent system uncertainties. The study focuses on minimizing human-robot interaction forces during the swing phase, particularly when the robot carries unknown loads. Simulations and experimental tests show that the proposed method significantly improves robustness, outperforming non-robust NMPC. It achieves lower tracking errors and interaction forces under various uncertainties. For instance, when a 2 kg unknown payload is combined with external disturbances, the RMS values of thigh and shank interaction forces for multi-stage NMPC are reduced by 77 and 94 percent, respectively, compared to non-robust NMPC.