To address the issues of poor human-robot interaction compliance caused by fixed impedance parameters and insufficient dynamic disturbance compensation in traditional upper limb rehabilitation robots, this study proposes an impedance model-based interactive control strategy. First, an adaptive robust controller was designed to compensate for system uncertainties including model parameters and external disturbances. Second, an adaptive impedance parameter regulator was developed to overcome the compliance deficiency induced by fixed impedance parameters, which dynamically adjusts impedance parameters by establishing correlations between patient exertion levels, robot motion states, and impedance parameters. Trajectory tracking simulation results demonstrate that compared with conventional PD control, the proposed adaptive robust control reduces NRMSD of shoulder and elbow joint trajectories by 35.20% and 63.31%, respectively, under dynamic disturbance conditions. Active compliance simulations reveal that the system can dynamically adjust training trajectories based on patient exertion levels and track them effectively. Compared with variable impedance control using PD compensation, the proposed adaptive robust compensation-based variable impedance control achieves 70.79% and 54.53% reductions in shoulder and elbow joint NRMSD, respectively. These results indicate that the proposed control scheme not only enhances compliance but also exhibits superior robustness, effectively meeting the requirements for patient rehabilitation training.