## 3 Results and Discussion  
### Objective Measures  
The MR-subspace-based motion-mapping HRI technique was compared to Baseline and MR direct control schemes across two tasks. Results in Tables 1 and 2 show the data and statistical findings. The analysis rejected the null hypothesis (H0) that the MR-subspace-enhanced spatial motion mapping approach for telemanipulation and the other typical teleoperation modules have identical effects on task performance (Table 1). In contrast, the results indicated that the MR subspace motion-centric HRI approach significantly outperformed both the 2D Baseline and the MR SpaceMouse HRI schemes on both tasks for all pairwise comparisons (Table 2). Guiding a robotic hand-arm system using the natural arm motion mapping through the MR subspace improved task performance for both tasks. The F value for the HRI factor of overall task completion time and its related significance level and the magnitude of the effect (Partial Eta Squared) in the Greenhouse-Geisser correction showed that the mean aggregate task completion time for each HRI module was statistically significantly different (F(1.875, 43.128) = 303.197; \(p\) < 0.001; Partial = 0.93). The pairwise comparisons indicated that aggregate time significantly decreased from the Baseline (M = 298.66) compared to the MR SpaceMouse module (M = 221.15) and the MR subspace module (M = 156.03). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Measure**} & \multicolumn{1}{c}{**Partial Eta Squared**} & \multicolumn{1}{c}{**F**} & \multicolumn{1}{c}{**\(p\)**} & \multicolumn{1}{c}{**MRS-MRD**} & \multicolumn{1}{c}{**MRS-B**} & \multicolumn{1}{c}{**MRD-B**} \\ \hline Pick-and-place (s) & 0.87 & F(1.382, 31.778) = 148.198 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 \\ \hline Assembly (s) & 0.76 & F(1.553, 35.725) = 74.080 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 \\ \hline Aggregate Time (s) & 0.93 & F(1.875, 43.128) = 303.197 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 \\ \hline Physical Demand & 0.45 & F(1.971, 45.339) = 18.478 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & 0.387 \\ \hline Mental Demand & 0.59 & F(1.995, 45.874) = 32.638 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & 0.002 \\ \hline NASA TLX & 0.76 & F(1.663, 38.247) = 74.408 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 \\ \hline Usefulness & 0.41 & F(1.846, 42.449) = 15.794 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & 1.000 \\ \hline Ease of Use & 0.69 & F(1.832, 42.133) = 50.205 & \textless{}0.001 & \textless{}0.001 & \textless{}0.001 & 0.299 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: One-way ANOVA statistics for all measures. B, MRD, and MRS denote Baseline, MR SpaceMouse, and MR subspace, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Baseline**} & \multicolumn{1}{c}{**MRD**} & \multicolumn{1}{c}{**MRS**} \\ \hline
**Measure** & **Mean** & **Std.Dev** & **Mean** & **Std.Dev** & **Mean** & **Std.Dev** \\ \hline Pick-and-place (s) & 136.06 & 20.72 & 98.27 & 17.00 & 58.52 & 9.75 \\ \hline Assembly (s) & 162.60 & 23.61 & 122.88 & 16.84 & 97.51 & 12.18 \\ \hline Aggregate Time (s) & 298.66 & 26.42 & 221.15 & 23.39 & 156.03 & 17.19 \\ \hline Physical Demand & 76.04 & 11.32 & 70.88 & 11.51 & 55.63 & 12.54 \\ \hline Mental Demand & 81.38 & 13.29 & 68.46 & 11.12 & 54.54 & 13.15 \\ \hline NASA TLX & 75.81 & 6.23 & 66.89 & 5.39 & 51.92 & 8.15 \\ \hline Usefulness & 2.83 & 1.17 & 3.08 & 1.10 & 4.75 & 1.33 \\ \hline Ease of Use & 2.67 & 0.87 & 3.25 & 1.39 & 5.50 & 0.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical results for objective and subjective measures for each method compared. MRD and MRS denote MR SpaceMouse and MR subspace, respectively. Overall, the aggregate task completion time was reduced by 48% compared to the 2D Baseline module and 29% compared to the MR SpaceMouse module.