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Yang et al. Intell Robot 2024;4(1):107-24 I http://dx.doi.org/10.20517/ir.2024.07 Page 119

4. RESULTS AND DISCUSSION
4.1 Experimental results for the comparison with the COM’s trajectory tracking and the energy cost
First of all, the comparison of COM’s trajectories tracking performance with baseline, CMP, ESC and CEEC
during the whole walking experiments are shown in Figure 10. Note that the HEW system is moving in the
Sagittal plane; therefore, only the and positions of the COM are presented. The black solid curve is the
reference trajectory of the COM calculated from the reference joint angles based on the Equation (1), the
dashed purple curve is the COM’s trajectory with the baseline (with no supporting force and no assistance
from wheels), the solid red curve is the COM’s trajectory with the CMP (with only active assistance from
wheels and no supporting force), the dashed green curve is the COM’s trajectory with the ESC (with only
supporting force and no assistance from wheels), and the solid blue curve is the COM’s trajectory with the
CEEC (with both supporting force and assistance from wheels).

To compare the trajectory tracking of four cases, the mean squared error (MSE) of four cases relative to the
reference COM trajectories was calculated as:

1 ∑ 2 2
ˆ
ˆ
= [( − ) + ( − ) ] (16)

=1
The calculated MSE of four cases was shown in Table 4.

From the trajectory tracking comparison, we can find that in the baseline case, due to no active assistance
from the robotic walker, the human-exoskeleton system has to pull the robotic walker forward during walking,
the COM’s trajectory tracking is bad, and the final position of the COM is far away from the desired position.
In the CMP case, since there is active assistance of the wheels with the coordinated motion generated with
the reference COM trajectory, the tracking performance of the COM is good. For the ESC and CEEC cases,
since a supporting force exists, the COM’s trajectory tracking is better than the baseline, and especially for the
CEEC case, the COM’s trajectory tracking is better than the ESC case. Note that in the first several steps, the
supporting force is not optimal, and the ESC algorithm is tuning to find the optimal supporting force, which
results in a bad performance. However, after several steps of optimization, the optimal supporting force is
found, and the COM’s trajectory tracking is better. This is the reason why the MSE of CEEC is a little bigger
than the MSE of CMP.

Above all, for the COM’s trajectory tracking, CEEC is better than the ESC and baseline but worse than the
CMP. Now, let us see the energy cost during walking with these different strategies [Figure 11]. From the bars
presented in Figure 11, we can see that in the baseline case, the energy cost is much higher than in any other
method. In the CMP case, the energy cost is always similar during the walking. In ESC and CEEC cases, the
energy cost is very high at the beginning of the walking and decreases after several steps; this is because, at
the first several steps, the ESC algorithm needs to iteratively update the supporting force and find the optimal
one, which leads to a bad walking performance and high energy cost. After several steps, the energy cost is
reduced, and the CEEC is better than the ESC; this is because the CEEC not only optimizes the supporting
force but also provides horizontal coordinated walking assistance by wheels.

Overall, considering the COM’s trajectory tracking performance and the energy cost, the CEEC is the best
approach for the HEW system to finish coordinated energy-efficient overground walking.