Robotic rehabilitation for ankle injuries offers several advantages in terms of precision, force accuracy, and task-specific training. While the existing platform-based ankle rehabilitation robots tend to provide a rotation center that does not coincide with the actual ankle joint. In this paper, a novel bio-inspired ankle rehabilitation robot was designed, which is wearable and can keep the participant's shank be stationary. The robot is redundantly actuated by four motors in parallel to offer three ankle rotation degrees-of-freedom (DOFs) with sufficient range of motion (ROM) and force capacity. To control the robotic rehabilitation device operated in a repetitive trajectory training manner, a model-free robust control method in form of iterative feedback tuning (IFT) is proposed to tune the robot controller parameters. Experiments were performed on the parallel ankle rehabilitation platform to investigate the efficacy of the design and the robustness of the IFT technique under real-life rehabilitation scenarios.