Abstract: For the upper limb rehabilitative and assisted movement, a pneumatic artificial muscle (PAM) compliantly actuated assistive robot for the elbow joint is developed. The hysteresis and nonlinearity of pneumatic artificial muscles significantly reduce the motion accuracy of the system. The robustness of common hysteresis compensation methods based on offline identification against the variation of the system configuration is low. Therefore, an adaptive hysteresis compensation method is proposed in this paper, which integrates the direct inverse modeling approach and the modified adaptive projection (MAP) algorithm. Based on the direct inverse modeling approach, the Prandtl-Ishlinskii model is utilized to construct the inverse hysteresis model, i.e., the hysteresis compensator. MAP algorithm is used to complete the online parameter identification of the inverse hysteresis model. By the proposed method, the offline modeling and inversion are avoided, and the on-site tuning of the controller parameters in tracking different trajectories is also eliminated. Experimental results demonstrate the effectiveness of the proposed method in hysteresis compensation compared with PID (proportional-integral-derivative) controller and adaptive projection (AP) algorithm. The setting time and overshoot of the transient process are significantly better comparing with the above mentioned methods. The closed-loop system can accurately track different types of trajectories, such as step trajectory and sinusoidal trajectory with a descending amplitude.