# Development and Assist-As-Needed Control of an End-Effector Upper Limb Rehabilitation Robot
## 4 Experiments and Results
### Experiment Results  
According to the experimental results, for the testing task 1, the trajectory of the subject's hand in the Unity scene deviates from the predetermined trajectory significantly under the guidance of visual, as shown in Figures 10a and 12a, with the maximum deviation reaching 180 mm. The total interaction force between the subject and the robot's end-effector is below 5N, as shown in Figures 11a and 12a, which is caused by the error of the robot joint torque sensor (2% of the maximum error of sensor). At this time, the robot does not provide assistance force and is in a fully backward driving state, and the subject has complete spatial freedom. For testing task 2, it can be seen from Figure 10b that the trajectory of the subject is concentrated around the predetermined trajectory. Its movement deviates from the predetermined trajectory in the first 50 s and is small, and the total interactive force between the subject and the robot's end-effector is within 5 N, while the latter part deviates from the predetermined trajectory and is larger (starting from the 50 s), with the total interactive force also becoming larger, highest up to 45 N, as shown in Figure 12b. The robot will provide assistance whenever the subject's hand deviates from the predetermined trajectory during the testing. The assistance force increases with the increase in deviation distance, and the subject has limited spatial freedom. For the testing task 3, it can be seen from Figure 10c that the subject's hand moving trajectory is mainly concentrated in the virtual channel. As the radius of the virtual channel is set as 25 mm, the total interaction force between the robot end-effector and the subject's hand is about 5 N when the male subject's hand moves in the virtual channel, as shown in Figures 11c and 12c, while the total interaction force increases when the  
Figure 12: The position deviation between the subject’s hand and the desired trajectory, and the total interaction force between the participant’s hand and the robot’s handle during the three testing tasks. (**a**) the position deviation and the total interaction force for the task 1; (**b**) the position deviation and the total interaction force for the task 2; (**c**) the position deviation and the total interaction force for the task 3.  
subject's hand deviates from the virtual channel (starting from the 50 s). The total interaction force between the robot end-effector and the male subject's hand in the virtual channel is not zero because the moving velocity of the subject is not zero in reality, and the lower limits of the stiffness gradient field are not set to zero. Besides, the posture of the robot is fixed during the test. It can be seen from Figure 11 that the interactive moment between the robot and the subject's hand is within 2 N.m.  
By comparing the deviation degree of the subject in the three testing tasks and the total interaction force between the subject's hand and the robot's end-effector, it can be seen that the deviation degree of task 1 is the largest. The robot has no assistance, and the subject has fully spatial freedom. The deviation degree is small in task 2, and the robot's assistance force increases with the deviation degree. In task 3, the robot does not provide assistance force within the virtual channel, while the assistance force increases with the increase in deviation degree when moving out of the virtual channel. Compared with task 3 and task 1, the robot provides no assistance when the subject's hand is moving inside the virtual channel while provides assistance when the subject's hand deviates from the virtual channel in testing task 3. Compared with task 2 and task 3, the subject's hand in task 3 has fully spatial freedom when moving within the virtual channel. As can be seen from Figure 12b,c, the interaction force between the subject's hand and the robot's end-effector in testing task 2 and testing task 3 within 50 s is about 5 N, and the deviation degree in task 3 is significantly larger than that in task 2.