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                                         800                     A1    A2     A3
                                                                 B1    B2     B3
                                         700
                                        support force (N)  600

                                         500

                                         400
                                         300
                                         200
                                            0   2    4   6    8   10   12   14  16
                                                            time (s)
                                        Figure 12. The variation of the supporting force during walking.



                                         500
                                                                 A1     A2     A3
                                                                 B1     B2     B3
                                         400
                                        TCoT (J/m)  300


                                         200
                                         100


                                          0
                                           0    1    2    3    4   5    6    7    8
                                                           gait cycles
                                   Figure 13. The value of the TCoT during walking. TCoT: Total cost of transport.


                           Table 5. The optimal supporting force and the improvement of the energy efficiency with the CEEC
                      Index   Converged supporting force (N)  Converged TCoT (J/m)  TCoT of baseline (J/m)  TCoT reduction
                      A1 & B1          487                  130              309.4           58%
                     A2 & B2           579                  181              454.7          60.90%
                     A3 & B3           682                  245              638.7          61.60%
                      CEEC: Coordinated Energy-Efficient Control.


               In the experiments, the different supporting forces were set for the support joint, whose values are selected in
               the interval with the converged supporting force as the midpoint. The selected values of constant supporting
               force and the comparison of the TCoT with the converged one are shown in Table 6. From Table 6, when the
               converged supporting force was increased or decreased, the TCoT always increased. Looking at Equations (2)-
               (4), it is intuitive that the elevation of the supporting force leads to the reduction of the energy cost. However,
               if the supporting force is bigger than the optimal one, it may cause severe slippage in the human-exoskeleton
               system. Despite the reduced energy cost, the TCoT also rises. When the supporting force is smaller than the
               optimal one, the energy cost increases without slippage, similarly causing the TCoT to increase. As a result,
               the converged supporting forces of the three control groups are optimal.



               The optimal supporting force in the table is the average final converged value in Figure 12, and the optimal
               TCoT is the average final converged value in Figure 13. Compared with the baseline, the CEEC reduced the
               TCoT by 58%, 60.9% and 61.6%, respectively. In other words, the average improvement of the energy efficiency
               can be calculated with these three values, i.e., 60.16%.
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