# Development and Assist-As-Needed Control of an End-Effector Upper Limb Rehabilitation Robot
## 1 Introduction
Controllers that exert the minimum required assistance to subjects are called assist-as-needed (AAN) controllers [19; 20]. AAN controllers have been used in wrist rehabilitation robots [21] and lower limb robots [22] to simulate patients to actively participate. It enables unique methods for promoting patient engagement by providing patients assistance only as-needed basis. Research result shows an assist-as-needed-based upper limb robotic training that provided intense and repetitive rehabilitation and promoted patient participation and motor performance, facilitating recovery [23]. For robot-assist training with assist-as-needed property, the impedance-based control strategies are often used to assist patients in rehabilitation training, which can increase the appliance of the robot in order to allow patients to deviate from the predetermined trajectory [24]. For example, [PERSON] et al. [25] proposed an assistance strategy based on the impedance control to provide assistance force when the patients deviate from the predetermined trajectory during rehabilitation training, which has been realized in a parallel planar rehabilitation robot. [PERSON] et al. [26] developed a planar 2-DOF(Degrees Of Freedom) rehabilitation robot based on the relationship between the interaction force of the robot and the patient and the end deviation, which realized the planar straight line and circular tracking motion of the patient and allowed the patient to deviate from the predetermined trajectory during rehabilitation training. Although this assistance strategy can allow the patient to deviate from the predetermined trajectory, the patient is limited in spatial freedom. Some studies also adopt adaptive impedance control to update the impedance parameters of the controller in real-time according to the patient's motion state [27]. Although this kind of controller could realize assistance for patients, it also restricts the spatial freedom of patients. Some scholars have done exploratory studies on increasing the patients' freedom of movement space; for example, [PERSON] et al. [28] developed a rope-driven exoskeleton rehabilitation training robot for upper limbs and added a fault-tolerant area around the predetermined trajectory to increase the patient's freedom of spatial movement. [PERSON] et al. [29] verified the feasibility of adding a plane channel around the motion trajectory in a plane based on the developed two-link plane rehabilitation robot. [PERSON] et al. [30] developed a haptic-based approach for retraining of inter-joint coordination following stroke called time-independent functional training (TIFT) and implemented this method in the ARMin III robotic exoskeleton. [PERSON] et al. [31] first quantified the characterization of the effects of modification of the upper-limb coordination in healthy subjects by imposing modification through viscous force fields distributed at the joint level. Similarly, there are many other studies that have focused on rehabilitation robots with AAN controllers [32; 33]. However, the above studies are either exploratory studies on exoskeleton type rehabilitation robots or planar upper limb rehabilitation robots, while there are few related studies that are focused on the end-effector-based upper limb rehabilitation robot that can carry on the spatial movement. In this paper, for those patients who have recovered partial upper limb motor ability, we develop a new end-effector upper limb rehabilitation robot (EULRR) that can carry on spatial movement first and then present a controller that is suitable for the assist-as-needed (AAN) training of the patients when performing the rehabilitation training. The controller enables the patient's arm to have spatial freedom by constructing a virtual channel around the predetermined training trajectory. Patients could move their arm freely in the allowed virtual channel during rehabilitation training, while the robot provides assistance when deviating from the virtual channel. Then, the AAN controller is implemented on the EULRR developed in this paper.