# Hardware Development and Safety Control Strategy Design for a Mobile Rehabilitation Robot
## 5 Experimental Validation
### Unloading Force Control of AMBSS  
For AMBSS's linear actuator controller design, the adjusted force must be smooth and slow to ensure a comfortable and safe interaction between the device and the subject. Therefore, the fifth-degree polynomial function describes the supporting load trajectory. The initial [i.e., \(y_{d}^{\text{load}}(t=0)\), \(\dot{y}_{d}^{\text{load}}(t=0)\), and \(\dot{y}_{d}^{\text{load}}(t=0)\)] and final [i.e., \(\dot{y}_{d}^{\text{load}}(t=t_{f})\) and \(\dot{y}_{d}^{\text{load}}(t=t_{f})\)] variations achieved were set as 0. The fifth-degree polynomial function is present as follows:  
Figure 4: MRR’s control system architecture diagram. \[y_{d}^{force}(t)= \begin{cases}f_{h}\bigg{[}10\Big{(}\frac{t}{f_{f}}\Big{)}^{3}-15 \Big{(}\frac{t}{f_{f}}\Big{)}^{4}+6\Big{(}\frac{t}{f_{f}}\Big{)}^{5}\bigg{]},&0 \leq t<t_{f}\\ f_{h}&,\ t_{f}\leq t\end{cases}  \tag{32}\]  
where \(f_{h}\) is the target unloading force, \(t_{f}\) is the runtime of AMBSS, \(y_{d}^{force}(t)\) denotes the force tracking trajectory and \(t\) is the running time. The experiments involved assessments of the AMBSS using the ILESO-PSMC in the following experiments. The parameters used for the ILESO-PSMC in the experiments are presented in Table 1. Figure 5 shows the control block of the AMBSS containing the ILESO-PSMC, where \(y_{d}^{force}\) is the target load trajectory described by the fifth-degree polynomial function expressed in Equation (32). \(y^{force}\) is the support force of the right linear actuator, and \(y^{force_{i}}\) is the support force of the left linear actuator. The ILESO-PSMC outputs the PWM signal to \"PWM Transform\", denoted as \(u_{AMBSS}\) for the right and left linear actuators. Then, the PWM control signal \(u_{PWM}\) was calculated adopting the PWM transformation function to convert the LESO-PSMC output into a PWM signal. The PWM transformation function is expressed as follows:  
\[u_{PWM}=\left\{ \begin{array}{ll}u_{AMBSS}\times T_{PWM}\times 100\%&\text{ }text{ },\ if\ u_{AMBSS}>0\\ |u_{AMBSS}|\times T_{PWM}\times 100\%&\text{ down, }\ if\ u_{AMBSS}<0\\ 0&\text{stop, }\ if\ u_{AMBSS}=0\end{array} \right. \tag{33}\]  
where \(T_{PWM}\) is the period of the carrier wave, \(u_{AMBSS}\) is the controller output of the ILESO-PSMC, and \(u_{PWM}\) is the PWM duty cycle of the linear actuators. The control voltage of the linear actuator is \(V=24\times u_{PWM}\). If \(u_{\text{AMBSS}}>0\), the linear actuator moves upward; if \(u_{AMBSS}<0\), the linear actuator moves downward; and if \(u_{AMBSS}=0\), the linear actuator ceases. The ILESO-PSMC provides control signals to the linear actuator at a sampling rate of 100 Hz. Therefore, 0.01 s was used as the carrier wave period in this unloading force control. Two linear actuators excited by the PWM signal controlled the output support forces of ABWSS. In practice, the ILESO-PSMC provides unanimous PWM signals for both side linear actuators; thus, the AMBSS could run smoothly. The input of the LESO was the average of the measured outputs of the two load cells. Two healthy subjects with no history of disability--a woman with a weight of 47.5 kg and a height of 1.5 m and a healthy man with a weight of 88 kg and a height of 1.68 m--participated in the experimental evaluation. We performed experiments with different bodyweight unloading forces for the AMBSS, mainly 15%, 20%, 25%, and 40% weight support. Two bodyweight support control strategies--static and dynamic unloading force control--were adopted in \begin{table}
\begin{tabular}{c c c c c c} \hline Control parameters & \(S_{0\_AMBSS}\) & \(w_{1\_AMBSS}\) & \(K_{P\_AMBSS}\) & \(K_{D\_AMBSS}\) & \(\lambda_{h\_AMBSS}\) & \(\gamma_{AMBSS}\) \\  & 15 & 5 & 10 & 7 & 9 & 15 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of the ILESO-PSMC with PWM for the AMBSS experiment. Figure 5: Control block of the AMBSS. the first experimental project to evaluate the availability of the AMBSS. The static unloading force control was tested when the AMBSS was stationary.