# FES Control of a Finger MP Joint with a Proxy-Based Super-Twisting Algorithm
## 5 Experiments  
### Experiment Setup  
The Ethics Committee of the School of Engineering at Kyushu University approved the experiments (Approval no. 2021-02), which were meticulously conducted with strict adherence to protocols. The experiment setup is illustrated in Figure 1, which includes an Arduino microprocessor (Arduino Mega, the manufacturer is Laplace, located in Miyagi, Japan), a driver (L298n), electrodes (IVES ELR-6211), and a joint angle acquisition unit (CP45 Single-turn Potentiometer). Six volunteers, \(A,B,C,D,E,F\), four females and two males ranging in age from 18 to 60 years, participated in the study. Preliminary experiments revealed that electrical stimulation elicited a more sensitive response in the MP joint of the index finger than other finger joints; therefore, this joint was selected for further investigation to enable clearer comparison between different control methods. The location of each participant's Flexor digitorum superficialis muscle, responsible for flexion movement, and Extensor digitorum muscle, responsible for extension movement, were identified on their arm's surface, as these target muscles are located relatively superficially. Surface electrode patches provided by OGWellness (model ELR-615) were used after simple adjustments were made to their positions upon application; if no motion response was observed upon current application, electrodes were slightly relocated within close proximity until a motion response was achieved in the finger.  
As studied in our previous research [42], the biphasic wave can effectively stimulate the nerve-muscles, and thus, leads to joint movements. Therefore, a stimulation signal is employed in experiments with alternating positive and negative square waves. The magnitude of the stimulation voltage remains constant, i.e., \(V_{max}\) or \(V_{min}\), followed a zero voltage of with constant duration of 50 \(\upmu\)s. By changing the duration of the square wave with the input \(\mu\), the actual average voltage is changed and its magnitude of the actual average voltage determines the amount of joint motion and the sign of \(u\) determines the motion direction. In the experiments, the output \(\mu\) of the PSTA is as the actuation input, i.e., \(\mu\) us with the saturation level \(F=150\) us, i.e., \(|\mu|\leq F=150\) us, and the feedback of the joint angle \(x=\theta\) as the output is sampled by an analog angle sensor, one analog potentiometer, with a period of \(5\,\)ms from the Analog Pin of the Arduino equipped with ADC device. As shown in (7), we have adjusted the gain \(F=150\) us according to practical actuation saturation levels. For \(\kappa_{1}\) and \(\kappa_{2}\), we set \(\kappa_{1}=1.5\sqrt{L}\) and \(\kappa_{2}=1.1L\) based on literature about STA. Due to its insensitivity to gain overestimation, we increased \(L\) until tracking error convergence was achieved. Regarding \(\kappa_{3}\) in (7), we tuned it through trial and error to ensure there was no overshooting in experiments.  
The proposed PSTA for the MP joint control is shown in Figure 1, where the PSTA implemented in the Arduino board and \(\mu\) is calculated in a real-time manner with \(h=25\) ms. Then, the stimulation signal with a duration of \(\mu\) us is generated by the Arduino board to the motor driver connected with an external power supply. The outputs of the two motor drivers are transmitted to electrode patches that are applied to the index finger extensor muscle group, i.e., Channel 1, and the index finger flexor muscle group, i.e., Channel 2, respectively. One circular potentiometer, CP45 Single-turn Potentiometer, as the encoder with a resolution of \(0.35^{\circ}\) is placed at the MP joint of the index finger. To prevent the wrist from rotating with the index finger, a fixation device is also placed on the wrist, as shown in Figure 1.