# Probabilistic Sensitivity Amplification Control for Lower Extremity Exoskeleton
## 4 Experiment and Discussion
### Flat Walking Experiment  
In the experiment, the pilot is asked to naturally swing his left leg, as shown in Figure 11. The control algorithms compared in the experiment are SAC [10], SAC + Qlearning [27], SAC + CMA-ES and our proposed algorithm.  
The tracking performances of the knee joint and the hip joint are given in Figure 12a,b. Since the hidden states \(\theta_{1},\theta_{2}\) are identified, the single exoskeleton leg can follow the human motion in real time. Furthermore, owing to the CMA-ES algorithm, the evolution of the sensitivity factor \(\alpha\) for the hip joint is shown in Figure 12c, along with the evolution for the knee joint presented in Figure 12d. To be more specific, the updated distribution is derived from the contributions of 15 samples selected from 20 candidates. The lower bound and upper bound are set to be three and 10, respectively, according to experimental experience. Furthermore, from Figure 12c, the sensitivity factor of the hip joint increases as the pilot puts down his leg, which means that the HRI force decreases, and the exoskeleton does not need too much additional torque from the pilot. Consequently, setting a fixed sensitivity factor is not a  
Figure 10: Cross-validation of the learned identification model. For the purpose of verifying the learning result of the identification model, we conduct a cross-validation with 600 successive data pairs. The state-space inferences of the hip joint, ground truth and the prediction error are presented in the above figure.  
Figure 9: Evaluation of \(m\) GPs (\(m=10\)). According to the distributed framework, the ten GPs share the same hyper-parameters. (**a**) GP1; (**b**) GP2; (**c**) GP3; (**d**) GP4; (**e**) GP5; (**f**) GP6; (**g**) GP7; (**h**) GP8; (**i**) GP9; (**j**) GP10.  
good option. Moreover, compared with the hip-joint sensitivity factor, the knee-joint sensitivity factor almost keeps a lower one, fluctuating around four. The reason for this situation is that the interaction between the thigh and the exoskeleton is more compliant than the interaction between the shank and the exoskeleton. Therefore, the sensitivity of the hip joint is better than that of the knee joint.  
In order to assess the control performance of our proposed algorithm, we compare the HRI force of four algorithms as shown in Figure 13. Since there is no sensor mounted between the pilot and exoskeleton, the HRI force is estimated by the disturbance observer. From intuition, the pilot feels more comfortable with less interaction force in the walking pattern. Therefore, the control performance  
Figure 11: Flat walking experiment. (**a**) Initial ground contact; (**b**) heel rise; (**c**) initial swing; (**d**) middle swing; (**e**) terminal swing; (**f**) heel strike; (**g**) full ground contact. The interaction between the pilot and the exoskeleton is made possible with the compliant cuff. Moreover, the pilot is asked to naturally sway his left leg.  
Figure 12: Tracking performances and evolution of sensitivity factors. (**a**) Tracking performance of the hip joint; (**b**) tracking performance of the knee joint; (**c**) evolution sensitivity factor of the hip joint; (**d**) evolution sensitivity factor of the knee joint.  
may be evaluated from the information of the interaction force. As we all know, the ideal control performance is that the interaction force is zero, which means that the exoskeleton can follow the human motion perfectly.  
Thus, to quantitatively evaluate the four control schemes, we compute the RMSE of the HRI of each joint. From Table 1, compared with the SAC control scheme, both SAC + Qlearning and SAC + CMA-ES own lower RMSE in both joints, since both algorithms learn an adaptive sensitivity factor. Furthermore, a small difference is shown in Table 1 between the SAC + Qlearning, as well as SAC + CMA-ES, and SAC + CMA-ES performs a little better. Moreover, a significant reduction of RMSE can be seen in Table 1 in our proposed algorithm, which is nearly two-times less than the other control schemes.