# Hardware Development and Safety Control Strategy Design for a Mobile Rehabilitation Robot
## 5 Experimental Validation
### Lower Limb Exoskeleton Gait Trajectory Tracking Control  
During the initial rehabilitation phase, the LES assists the subject in walking in a passive mode according to a given gait trajectory. Model-based control depends on the accuracy of the system models, while model-free methods have limitations in dealing with disturbance issues, as is the case with standard PID strategies. Under the premise of safety, the main target of the LES is to track a given gait trajectory with high precision under external disturbances. The ILESO-PSMC can estimate the unknown disturbances of the LES and eliminate the effect on the designed controller to achieve both safety and good trajectory tracking performance. It is critical to knowing the gait cycle of a healthy person walking over-ground for LES-assisted gait continuous passive motion (CPM) training therapy. A complete gait cycle in a healthy person is defined as the progression of movement of one leg returning to a specific angle. The normal person's gait trajectory required for this study was derived from the Clinical Gait Analysis [17]. With a gait period of two seconds, the continuous variation in the rotation angle over time was determined by the Fourier series fitting method, providing the following two continuous rotation angle functions for the hip and knee joints [32]:  
\[\begin{split}& f_{ knee}(t)=28.1-17.7\cos(3.1t)+11.2\sin(3.1t)+1.2\cos(6.3t)-17.2\sin(6.3t)-1.9\cos(9.4t)\\ &+3.5\sin(9.4t)+0.7\cos(12.6t)+1.2\sin(12.6t)-0.1\cos(15.7t)-0.7 \sin(15.7t)\text{ for the knee.}\end{split} \tag{34}\]  
and  
\[\begin{split}& f_{hip}(t)=12.7-14.6\cos(3.1t)-19.6\sin(3.1t)+2.7 \cos(6.3t)-3.3\sin(6.3t)-0.7\cos(9.4t)\\ &+1.8\sin(9.4t)+0.2\cos(12.6t)+0.1\sin(12.6t)\text{ for the hip,}\end{split} \tag{35}\]  
Figure 10a,b show the regular gait-training cycle for the experiments, described as angle trajectories, for the knee and hip, respectively, during the standard two-second gait period. The period of gait training is modifiable. For example, the gait period can be adjusted to two times the standard reference gait-training period for 4 seconds of gait training. We suppose the LES to be a decoupled system; therefore, the interaction of the knee and hip joints will be considered as external disturbances in the controller design [32]. Therefore, four direct-current servo motor modules drive the LES for over-ground gait  
Figure 9: Dynamic bodyweight unloading force control of ILESO\(-\)PSMC, 20% (93.1 N) and 40% (186.2 N) of female subject body weight (845.5 N). (**a**) Unloading force tracking response; (**b**) unloading force tracking error; (**c**) duty cycle of PWM.  
CPM training. Each direct-current servo motor module includes a direct-current servo motor and its driver. The LES uses four ILESO-PSMCs, tracking a gait trajectory captured from a healthy human by regulating four direct-current servo motors. Figure 11 shows the single joint control block of the LES. In the second experiment, the required gait tracking trajectories for each joint of the LES were derived by extending the period of fitting expression to 5 seconds. The reference angle trajectories for the knee and hip joints were calculated using Equations (34) and (35). The ILESO-PSMC is shown in Equation (28) as \(u(t)=u_{LES}\). A trial-and-error method was used to select control parameters for accuracy and compliance. The parameters of ILESO-PSMCs for the direct-current servo motors were chosen as shown in Table 2.  
within the interval of (\(-\)0.4, 0.5). Figures 12c and 13c show the current control signal of the ILESO-PSMC for the right knee and hip joint, respectively.