## 3 Modified NDT Intervention  
The motor control system can repeat the NDT intervention after receiving the triggering signals from the gait detection system. In previous studies [14; 15; 16], we concluded that the therapists cued a subject's right (left) pelvis when they observed the subject's left (right) HS during the NDT rehabilitation, as illustrated in Appendix A. Therefore, we designed the motor control system to automatically repeat this pattern. When detecting a HS, the detection system sent a triggering signal to the motor control system on the opposite side, which tracked the following force command:  
\[F(t)=\frac{(\overline{F}_{\max}-\overline{F}_{\min})}{2}\times\sin(2\pi ft)+ \frac{(\overline{F}_{\max}+\overline{F}_{\min})}{2} \tag{1}\]  
where \(\overline{F}_{\max}\) and \(\overline{F}_{\min}\) represent the maximum and the minimum forces, respectively, while \(f\) is the frequency. Based on previous experiences [14; 15; 16], we set \(\overline{F}_{\max}=6\) lb, \(\overline{F}_{\min}=1\) lb, and \(f=\)1 Hz in the experiments. Since gait symmetry is critical for walking rehabilitation, we analyzed the asymmetry of the swing phase [32], defined as follows:  
\[Asym_{SP}(\%)=\frac{SP_{paretic}-SP_{non-paretic}}{SP_{paretic}}\times 100\% \tag{2}\]  
where \(SP_{non-paretic}\) and \(SP_{paretic}\) represent the proportion of the swing phase on the paretic side and the non-paretic side, respectively. Since stroke patients tend to have hemipareresis and a longer swing time on the paretic side, we applied \(Asym_{SP}\) to evaluate the rehabilitation effectiveness and regarded the training as effective if \(Asym_{SP}\) approached zero. We recruited 10 healthy subjects for the experiments. The subjects' data are provided in Table 3. A rehabilitation gaiter was attached to one knee joint on each subject to limit the joint movements and to mimic stroke gaits. Each subject received the tests by the \(\mathrm{A-B-\overline{A}}\) procedures, where \(\mathrm{A,\ B,\ and\ \overline{A}}\) represented the before-treatment, during-treatment, and after-treatment periods, respectively. The subjects first walked on their own once down a 20 m corridor (A). They then received NDT training twice by the trainer on the 20 m corridor (B), and they finally walked on their own down the 20-m corridor once (\(\overline{A}\)). Their gait data were recorded, as illustrated in Appendix B, to evaluate the training effects. Figure 5: Rehab gaiter and IMUs’ location. The experimental results are shown in Table 4, where imp% represents the percentage improvement of the training compared to before the training (stage A). As shown in Table 4, the asymmetry of the swing phases of 9 of the 10 subjects was improved after the treatment (\(\overline{\text{A}}\) stage). A possible reason is that subject H9 had a light body weight and may have had insufficient muscle strength to push the movable trainer. Generally, the NDT intervention is effective in improving \(Asym_{SP}\). Apart from the gait symmetry, the locomotion of the pelvis is also important for maintaining walking stability [25, 26, 27]. During each step, the pelvis rotates forward on the side of the swinging limb. The axis of this rotation is the hip joint of the stance leg, which undergoes internal rotation. As the pelvis forms a bridge between the two hips, it reduces the angle of intersection of the thighs to reduce the vertical descent of the trunk. As mentioned previously, pelvis rotation conserves energy during the normal gait and allows people to walk at a comfortable pace. Therefore, we further analyzed the subjects' pelvic rotation during the NDT training.