Robot-aided physical therapy should encourage subject's voluntary participation to achieve rapid motor function recovery. In order to enhance subject's cooperation during training sessions, the robot should allow deviation in the prescribed path depending on the subject's modified limb motions subsequent to the disability. In the present work, an interactive training paradigm based on the impedance control was developed for a lightweight intrinsically compliant parallel ankle rehabilitation robot. The parallel ankle robot is powered by pneumatic muscle actuators (PMAs). The proposed training paradigm allows the patients to modify the robot imposed motions according to their own level of disability. The parallel robot was operated in four training modes namely position control, zero-impedance control, nonzero-impedance control with high compliance, and nonzero-impedance control with low compliance to evaluate the performance of proposed control scheme. The impedance control scheme was evaluated on 10 neurologically intact subjects. The experimental results show that an increase in robotic compliance encouraged subjects to participate more actively in the training process. This work advances the current state of the art in the compliant actuation of parallel ankle rehabilitation robots in the context of interactive training.