esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Discussion
### Deformation and Damage Pattern of the Pit Slope  
At present, the eastern pit slope of the Wolong Coal Mine has not yet formed an overall instability. Combining the field understanding and the numerical simulation results, it is determined that the instability and deformation process of the eastern pit slope of the Wolong Coal Mine can be divided into four stages (Figure 31). The specific description is as follows:  
The initial deformation stage  
As depicted in Sections 4.1 and 4.2, the eastern pit slope belongs to a soft-hard-interbedded anti-inclined layered rock slope with a slope structure conducive to rainwater infiltration. Moreover, the rock mass of the pit slope features a high clay mineral content  
Figure 31: Instability and failure process of the eastern pit slope in the Wolong Coal Mine: (**a**) The initial deformation stage; (**b**) The development stage of lateral shear misalignment; (**c**) The development stage of horizontal tensile-shear damage; (**d**) The slip surface development to preslip stage.  
and significant microfracture development. Consequently, the mechanical properties of the rock mass deteriorate swiftly due to the influence of rainwater. Under the influence of artificial excavation, atmospheric rainfall, and other contributing factors, the surface water permeates along the bedding and joint surfaces. This heightened groundwater activity leads to the expansion of cracks, causing stress to concentrate in the lower section of the slope (Figure 31a).  
The development stage of lateral shear misalignment  
Due to rainwater infiltration, the integrity of the rock and soil body degrades rapidly, leading to a redistribution of internal stress within the pit slope. This is evident in the swift proliferation of fissures at the rear edge of the slope (Figure 14). Under the influence of the slope's self-gravitational stress, the leading edge of the slope tilts toward the critical surface. Then, the lower rock mass is prone to shear slip misalignment, and the foot of the slope develops fissures due to stress concentration (Figure 31b).  
The development stage of horizontal tensile-shear damage  
Due to the further aggravation of the misalignment of bedding surfaces, flexural deformation of the pit slope occurs. Moreover, localized small-scale misalignment occurs at the trailing edge of the slope, and a slip surface starts to form at the upper part of the slope corner (Figure 31c).  
The slip surface development to preslip stage  
Due to the intensification of the flexural toppling deformation, shear forces within the layer become highly intense, causing the slip surface to expand further toward the upper part of the pit slope. This results in localized shallow landslides in the surface layer of loose rock and soil due to deformation (Figure 31d).  
If the deformation activity intensifies further, instability and damage to the eastern pit slope will occur when the slip surface is fully penetrated.
## 4 Numerical Examples
: _Consider the following higher order fractional integro-differential equation_  
\[\frac{1}{\sqrt{\pi}}\sum_{i=1}^{32}\sum_{j=1}^{32}a_{ij}h_{i}(x_{m})\int_{0}^{ t_{n}}h_{j}(\tau)(t_{n}-\tau)^{-0.5}d\tau=\frac{\sqrt{\pi}}{2}e^{x_{m}}-\frac{2(e-1 )t_{n}}{3}+\sum_{j=1}^{32}a_{ij}t_{n}p_{i}(1)q_{j}(1)\]1  
_subject to the initial conditions \(u(x,0)=\frac{\partial}{\partial t}u(x,0)=0.\) The exact solution is \(u(x,t)=e^{-x}t^{3/2}\). We use the Laplace Haar wavelet method at the level of resolution \(J=4\). The required discrete system is given by_  
\[\frac{1}{\sqrt{\pi}}\sum_{i=1}^{32}\sum_{j=1}^{32}a_{ij}h_{i}(x_{m})\int_{0}^{ t_{n}}h_{j}(\tau)(t_{n}-\tau)^{-0.5}d\tau=\frac{\sqrt{\pi}}{2}e^{x_{m}}-\frac{2(e-1 )t_{n}}{3}+\sum_{j=1}^{32}a_{ij}t_{n}p_{i}(1)q_{j}(1)\]2  
_with approximate solution_  
\[\frac{1}{\sqrt{\pi}}\sum_{i=1}^{32}\sum_{j=1}^{32}a_{ij}h_{i}(x_{m})\int_{0}^{ t_{n}}h_{j}(\tau)(t_{n}-\tau)^{-0.5}d\tau=\frac{\sqrt{\pi}}{2}e^{x_{m}}-\frac{2(e-1 )t_{n}}{3}+\sum_{j=1}^{32}a_{ij}t_{n}p_{i}(1)q_{j}(1)\]3  
_Figures 12 and 13 show the exact and approximate solutions for Equation (21)._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(x_{m}\) & \(t_{n}\) & **Exact Value** & **Approximate Value** & **Absolute Error** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(x_{m}\) & \(t_{n}\) & **Exact Value** & **Approximate Value** & **Absolute Error** \\ \hline
0.015625 & & 0.126968 & 0.12697 & 1.04314 \(\times\) 10\({}^{-6}\) \\
0.109375 & & 0.139448 & 0.139449 & 1.04314 \(\times\) 10\({}^{-6}\) \\
0.234375 & 0.015625 & 0.158015 & 0.158016 & 1.04314 \(\times\) 10\({}^{-6}\) \\
0.48 \begin{table}
\begin{tabular}{l c c c c} \hline \hline \(x_{m}\) & \(t_{n}\) & **Exact Value** & **Approximate Value** & **Absolute Error** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: Exact, approximate, and absolute error for different values of \(x_{m}\) and \(t_{n}\) in Example 2 with resolution \(J=4\) using HWM. \begin{table}
\begin{tabular}{l c c c} \hline \hline \(x_{m}\) & \(t_{n}\) & **Exact Value** & **Approximate Value** & **Absolute Error** \\ \hline
0.015625 & & 0.00129766 & 0.00130173 & 4.06726 \(\times\)\(10^{-6}\) \\
0.109375 & & 0.00127279 & 0.00127686 & 4.06726 \(\times\)\(10^{-6}\) \\
0.234375 & & 0.00118402 & 0.00118809 & 4.06726 \(\times\)\(10^{-6}\) \\
0.359375 & 0.015625 & 0.00103945 & 0.00104351 & 4.06726 \(\times\)\(10^{-6}\) \\
0.484375 & & 0.000852082 & 0.
# Improved YOLOv5-Based Real-Time Road pavement Damage Detection in Road Infrastructure Management
## 3 Methodology
### YOLOv5s Architecture
#### 3.1.3 Neck  
The neck can be regarded as the feature fusion network. The neck includes the Conv module, C3 module, an upsampling module, and a Concat module. The neck structure employs a fusion approach that combines top-down and bottom-up features. The bottom-up approach facilitates the effective transmission of positional data from the lower to the upper layers. The fusion of high-level and low-level features through the top-down path enhances the detection efficacy of small objects. Integrating the two paths can consolidate the characteristics of distinct detection layers originating from diverse backbone layers. The utilization of this particular structure has the potential to enhance the detection efficacy of dense objects.
# Lawn Bonitation Value as a Function of Glycine-Complexed Iron Formulation Application
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fe Dose**} & \multirow{2}{*}{**Year**} & **P** & **K** & **Ca** & **Mg** & **Na** \\ \cline{3-6}  & & & & **g\(\cdot\)kg\({}^{-1}\) d.m. & & \\ \hline \multirow{3}{*}{Control} & 2020 & 1.20 \(\pm\) 0.05 & 33.4 \(\pm\) 1.81 & 2.70 \(\pm\) 0.15 & 1.43 \(\pm\) 0.17 & 0.089 \(\pm\) 0.022 \\ \cline{2-6}  & 2021 & 1.24 \(\pm\) 0.05 & 27.4 \(\pm\) 2.59 & 3.24 \(\pm\) 1.24 & 1.34 \(\pm\) 0.23 & 0.052 \(\pm\) 0.011 \\ \cline{2-6}  & 2020-2021 & 1.22 \(\pm\) 0.05 & 30.4 a \(\pm\) 3.87 & 2.97 a \(\pm\) 0.84 & 1.39 a \(\pm\) 0.19 & 0.071 a \(\pm\) 0.026 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Variant I: \\ 60 g \\ \end{tabular} } & 2020 & 1.23 \(\pm\) 0.05 & 33.8 \(\pm\) 1.77 & 2.82 \(\pm\) 0.19 & 1.49 \(\pm\) 0.15 & 0.106 \(\pm\) 0.029 \\ \cline{2-6}  & 2021 & 1.25 \(\pm\) 0.05 & 27.4 \(\pm\) 2.55 & 3.24 \(\pm\) 1.36 & 1.32 \(\pm\) 0.18 & 0.056 \(\pm\) 0.010 \\ \cline{2-6}  & 2020–2021 & 1.24 ab \(\pm\) 0.05 & 30.6 a \(\pm\) 4.03 & 3.03 a \(\pm\) 0.90 & 1.41 a \(\pm\) 0.18 & 0.810 a \(\pm\) 0.033 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Variant II: \\ 100 g \\ \end{tabular} } & 2020 & 1.35 \(\pm\) 0.09 & 34.3 \(\pm\) 0.45 & 3.08 \(\pm\) 0.20 & 1.62 \(\pm\) 0.15 & 0.148 \(\pm\) 0.085 \\ \cline{2-6}  & 2021 & 1.33 \(\pm\) 0.10 & 29.7 \(\pm\) 1.57 & 4.77 \(\pm\) 2.99 & 1.53 \(\pm\) 0.25 & 0.057 \(\pm\) 0.008 \\ \cline{2-6}  & 2020–2021 & 1.34 b \(\pm\) 0.09 & 32.0 a \(\pm\) 2.73 & 3.93 a \(\pm\) 2.11 & 1.58 a \(\pm\) 0.19 & 0.102 a \(\pm\) 0.073 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Variant III: \\ 140 g \\ \end{tabular} } & 2020 & 1.36 \(\pm\) 0.10 & 35.0 \(\pm\) 0.65 & 3.17 \(\pm\) 0.25 & 1.62 \(\pm\) 0.13 & 0.147 \(\pm\) 0.082 \\ \cline{2-6}  & 2021 & 1.33 \(\pm\) 0.10 & 29.8 \(\pm\) 1.71 & 4.75 \(\pm\) 3.16 & 1.52 \(\pm\) 0.27 & 0.054 \(\pm\) 0.006 \\ \cline{2-6}  & 2020–2021 & 1.35 b \(\pm\) 0.09 & 32.4 a \(\pm\) 3.07 & 3.96 a \(\pm\) 2.18 & 1.57 a \(\pm\) 0.20 & 0.101 a \(\pm\) 0.073 \\ \hline \multicolumn{6}{c}{Standard Deviation} & 0.088 & 3.36 & 1.60 & 0.198 & 0.054 \\ \hline \multicolumn{6}{c}{Variation Coefficient, \%} & 6.835 & 10.7 & 46.1 & 13.3 & 60.8 \\ \hline \multicolumn{6}{c}{The same markings (a,b) mean no statistically significant changes (\(p\geq 0.05\)).} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Effect of Fe fertilization on the macroelement content in plants.
# Substrate-Integrated Waveguide Microwave Sensor for Water-in-Diesel Fuel Applications
## 4 Simulation of Cross-Slot SIW Applicator as Sensor Water-in-Diesel Background  
To evaluate the cross-slot SIW applicator performances as a water-in-fuel sensor, the measured dielectric constants of the five samples were imported into the simulation CST Studio Suite(r) software. A similar investigation to that reported in Section 3 was performed, showing that the same SIW structure could be employed with a water-in-diesel background, allowing a promising performance without further refinement. In other words, the dielectric constant of air and the real part \(\epsilon^{\prime}\) of the diesel dielectric constant at the considered frequencies \(f\) are sufficiently close.  
In fact, Figure 12 illustrates the modulus of the scattering parameters \(S_{11}\) (solid curves) and \(S_{21}\) (dotted curves) as a function of the frequency \(f\) for air (black curve) and pure diesel (blue curve) backgrounds. The impedance matching with \(|S_{11}|=-18\) dB at the frequency \(f=9.5\) GHz for the diesel background is good enough.  
The percentage change on the modulus of the scattering parameter \(S_{21}\), obtained by simulating the diesel sample (i) in contact and (ii) placed at the distance \(d_{air}=0.1\) mm from the top metallic layer, is below \(\Delta S_{21}=9\%\). However, the distance \(d_{air}\) can be eliminated in practical application after an easy mechanical optimization.  
The percentage change in the modulus of the scattering parameter \(S_{21}\) obtained by simulating the diesel sample in contact with the top metallic layer and the radiating slots (iii) filled with diesel and (iv) filled with air is of the order of \(\Delta S_{21}=1.3\%\). Additionally, this error can be eliminated by a direct contact of the applicator with diesel flux.  
Figure 12: Cross-slot SIW applicator. Modulus of the simulated scattering parameters \(S_{11}\) (solid curves) and \(S_{21}\) (dotted curves) as a function of the frequency \(f\) for air (black curves) and pure diesel (blue curves) backgrounds.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Description** \\ \hline \(L_{sub}\) & 35 mm & Substrate length \\ \(W_{sub}\) & 25 mm & Substrate width \\ \(L_{guide}\) & 20 mm & SIW length \\ \(W_{guide/2}\) & 6.9 mm & Half SIW width \\ \(\bar{W}_{feed}\) & 4.7 mm & Microstrip line width \\ \(L_{feed}\) & 7.5 mm & Microstrip line length \\ \(W_{slot}\) & 0.2 mm & Slot width \\ \(L_{slot}\) & 4.9 mm & Slot length \\ \(gap\) & 0.2 mm & Gap distance \\ \(s\) & 0.75 mm & Center–center distance of vias \\ \(d\) & 0.5 mm & Vias diameter \\ \hline \end{tabular}
\end{table}
Table 5: Optimized geometric parameters of the designed cross-slot SIW applicator.  
The simulated sensor sensitivity can be calculated as  
\[\frac{\Delta|S_{21}|}{\Delta\rho}=1.39\;\mathrm{mdB/ppm}\;\text{@}\;9.2\;\mathrm{GHz}\]  
The coefficient of determination is \(R^{2}=0.85\), which is quite good.
## 5 Conclusions  
In this paper, we propose a pedestrian flow tracking and statistics algorithm for front-down monocular camera. The algorithm relies on convolutional neural network for real-time pedestrian detection, and uses Kalman filter linear motion model and data association algorithm to track pedestrian targets. Finally, a counting method based on virtual blocks is proposed to complete pedestrian flow statistics. We use real scene videos to evaluate the counting performance of the algorithm. At the same time, we compare the detection and tracking performance of the algorithm with other algorithms using a public dataset, MOT 2015, which proves the effectiveness of the algorithm. The experiment results show that the algorithm has good accuracy and real-time performance, and has high application value. Although the algorithm has achieved good results, there are still some shortcomings, which need further improvement. Since the accuracy of the algorithm will be affected when the pedestrian is seriously occluded, future work is to further improve the tracking accuracy of the algorithm in the case of serious occlusion by means of optical flow and re-identifying appearance model.  
\begin{table}
\begin{tabular}{l l r r r r r r r r} \hline \hline
**Sequence** & **Algorithm** & **MOTA** & **IDF1** & **MOTP** & **MT** & **ML** & **FP** & **FN** & **ID Sw** \\ \hline \multirow{4}{*}{KITTI-19} & MDP\_Subcnn & 40.9 & 61.8 & 68.1 & 0.242 & 0.081 & 1143 & 1965 & 51 \\  & DMT & 45.7 & 55.5 & 72.8 & 0.306 & 0.097 & 884 & 1946 & 72 \\  & Sort & 29.1 & 46.4 & 68.4 & 0 & 0.258 & 855 & 2852 & 79 \\  & PFS(our) & 37.8 & 46.4 & 69 & 0.274 & 0.129 & 1327 & 1890 & 109 \\ \hline \multirow{4}{*}{Venice-1} & MDP\_Subcnn & 42.6 & 48.4 & 76 & 0.353 & 0.235 & 729 & 1867 & 21 \\  & DMT & 32.4 & 38 & 70.9 & 0.294 & 0.412 & 527 & 2538 & 18 \\  & Sort & 24.7 & 24.4 & 69.7 & 0.118 & 0.471 & 485 & 2888 & 62 \\  & PFS(our) & 43.7 & 40.1 & 75.8 & 0.294 & 0.176 & 435 & 2071 & 64 \\ \hline \multirow{4}{*}{TOTAL} & MDP\_Subcnn & 47.5 & 55.7 & 74.2 & 0.3 & 0.186 & 8631 & 22,969 & 628 \\  & DMT & 44.5 & 49.2 & 72.9 & 0.347 & 0.221 & 8088 & 25,335 & 684 \\ \cline{1-1}  & Sort & 33.4 & 40.4 & 72.1 & 0.117 & 0.309 & 7318 & 32,615 & 1001 \\ \cline{1-1}  & PFS(our) & 48.1 & 45 & 74.7 & 0.327 & 0.15 & 8422 & 22,074 & 1372 \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._  
Figure 8: Tracking result on 2 DMOT15 dataset.  
**Author Contributions:** Conceptualization, M.H.; Methodology, M.H.; Software, M.H.; Validation, M.H., B.H. and Z.C.; Formal Analysis, M.H.; Investigation, M.H.; Resources, B.H. and Z.C.; Data Curation, M.H.; Writing-Original Draft Preparation, M.H.; Writing-Review and Editing, H.L.; Visualization, M.H.; Supervision, H.L.; Project Administration, H.L.; Funding Acquisition, H.L.  
**Funding:** This research was funded by Hainan Heaven Reward Security Technology Co. Ltd.  
**Conflicts of Interest:** The authors declare no conflict of interest.
# Driver Fatigue Detection Based on Residual Channel Attention Network and Head Pose Estimation
## 4 Experiments and Results
### Selection of the Over-Angle  
The objective of this section is to determine whether the head pose is in an over-deflection state through the pitch, yaw, and roll of the head. In reality, we cannot directly obtain the Euler angle of the head and we just need to know whether the head is too deflected. In Section 3.1, this article constructed 10 one-min videos simulating the change of the driver's head posture and marked each frame. If the head Euler angle is too deflected, it is annotated as 1, and if the head Euler angle is in a normal state, it is annotated as \(-1\). Therefore, the purpose of this section is to obtain the angle (over-angle) at which the head posture is too deflected. When the Euler angle output by EPnP exceeds this angle, it is considered that the head posture is too deflected.  
According to [14], the normal state of the head Euler angle is \([-20^{\circ},\,20^{\circ}]\). This value is related to the different methods used by different researchers. Therefore, this paper dynamically tests the situation of over-angles 16 to 25. The test results are shown in Figure 8.  
Figure 8 shows missed detection or wrong detection under different over-angles. It can be seen that when the pitch over-angle is \(20^{\circ}\), missed detection and wrong detection is the least. Therefore, the pitch over-angle should be set to \(21^{\circ}\). That is, when the pitch angle is between \([-21^{\circ},\,21^{\circ}]\), the head pitch angle is normal. Similarly, the yaw over-angle should be set to \(20^{\circ}\) and the roll over-angle should be set to \(20.5^{\circ}\). Figure 9 shows the results of using this set of over-angles to analyze one of the 1-min videos.  
There are six graphs, from top to bottom, in Figure 9. The red curve of the first graph is the pitch output by EPnP. The blue line segment is binarized using the pitch over-angle. If it exceeds the over-angle, the pitch is too deflected. The second graph is the ground truth of the pitch angle. This line segment is the result of manual annotation. Other graphs are the test results of yaw and roll.  
Figure 8: Missed detection and wrong detection frames of different over-angles. The left image is of the pitch over-angle. The middle image is of the yaw over-angle. The right image is of the roll over-angle.
###### Abstract  
(1) Background: Musculoskeletal conditions show increasing prevalence and high economic/human burden. Recovery for hip or knee surgery may require more than 26 weeks, while universally accepted rehabilitation guidelines are missing. Provided that multisensory-based training enhances motor learning, the study aims to verify if visuomotor training accelerates the recovery of lower limb motor function after orthopedic surgery. (2) Methods: Post-surgery subjects were randomly assigned to receive visuomotor training as an add-on to the conventional physical therapy (VTG), or receive the conventional therapy alone (CG). Subjects performed 40 one-hour training sessions in 8 weeks. The primary endpoint was the improvement in the Lower Extremity Functional Scale (LEFS) over the minimally clinical important difference (MCID) at 4 weeks post-randomization. The secondary endpoint included pain reduction. (3) Results: Eighteen patients were equally distributed into the VTG and CG groups. While LEFS and pain scores significantly improved in both groups, the VTG exceeded the LEFS MCID by 12 points and halved the pain value after the first 4 weeks of treatment, while the CG reached the endpoints only after treatment end (p = 0.0001). (4) Conclusions: Visuomotor training offers an innovative rehabilitation approach that accelerates the recovery of lower limb motor function in patients undergoing orthopedic surgery.  
msculoskeletalal; visuomotor training; sensory-motor training; osteoarthritis; fractures; orthopedic rehabilitation; post-surgery +
Footnote †: journal: Applied Sci.
# Enhanced Teaching-Learning-Based Optimization Algorithm for the Mobile Robot Path Planning Problem
## 3 TLBO and DE Algorithms
### De  
The DE approach is a stochastic and swarm-based optimization algorithm [24]. It begins with a random initial population consisting of a number of target individuals. The population evolves by means of mutation and crossover and selection operators. The detailed operations of a classical DE are as follows:  
(1) Mutation operation  
The mutation operation in the DE approach is utilized to generate a mutant vector associated with each target individual in the current population. Given a candidate solution, \(x\), its associated mutant vector, \(v\), can be produced by taking one of the following strategies.  
\[\text{DE/rand}/1\ v=x_{r_{1}}+F\cdot(x_{r_{2}}-x_{r_{3}}) \tag{6}\] \[\text{DE/rand}/2\ v=x_{r_{1}}+F\cdot(x_{r_{2}}-x_{r_{3}})+F\cdot(x _{r_{4}}-x_{r_{5}})\] (7) \[\text{DE/best}/1\ v=x_{best}+F\cdot(x_{r_{2}}-x_{r_{3}})\] (8) \[\text{DE/best}/2\ v=x_{best}+F\cdot(x_{r_{2}}-x_{r_{3}})+F\cdot(x _{r_{4}}-x_{r_{5}})\] (9) \[\text{DE/current}-\text{to}-\text{best}/1\ v=x+F\cdot(x_{best}-x )+F\cdot(x_{r_{1}}-x_{r_{2}}) \tag{10}\]  
where \(x_{r_{1}}\sim x_{r_{5}}\) are randomly selected individuals and \(x_{best}\) represents the current best solution. Meanwhile, the scaling factor, \(F\), is used to control the differential variation between two individuals.  
(2) Crossover operation  
The DE algorithm employs a crossover operation to generate candidate offspring in order to the increase population diversity. In this regard, a candidate offspring, \(u\), is produced by combing solution information from each pair of a target vector, \(x\), and its associated mutant vector, \(v\). The scheme can be described as follows:  
\[u_{d}=\left\{\begin{array}{ll}v_{d}&rand(0,1)\leq CR\\ x_{d}&\text{otherwise}\end{array}\right. \tag{11}\]  
where \(d\in\{1,2,\cdots,D\}\), and \(rand(0,1)\) is a random number in the interval \([0,1]\). Symbols \(x_{d}\), \(v_{d}\), and \(u_{d}\) represent the \(d-\)th gene in the individual vectors \(x\), \(v\), and \(u\), respectively. The crossover probability, \(CR\), is utilized to control the proportion of genes copied from target and mutant vectors.  
(3) Selection operation  
The selection operation in the DE algorithm employs a one-to-one greedy selection to determine whether the candidate offspring, \(u\), can replace its parent individual, \(x\). Solution \(x\) will be replaced by \(u\) once that \(u\) performs equally or even better than \(x\).
## 4 Experimental Setup and Results
### Evaluation of the Proposed Teleoperation System  
The operator arbitrarily controlled the master device by directly applying the external wrench force to the end-effector, and its positional command was used as the input for the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Mean (mm)** & **SD (mm)** & **RMS (mm)** \\ \hline X axis & \(-\)0.4253 & 2.2046 & 2.2446 \\ Y axis & \(-\)0.7673 & 0.9058 & 1.1869 \\ Z axis & 0.6157 & 0.4005 & 0.7344 \\ Magnitude & 1.0718 & 2.4169 & 2.6432 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Measured error of the EE on the trajectory.  
Figure 9: Comparison of the (**a**) position value and (**b**) applied wrench force according to the different virtual systems.  
slave device through data communication. Furthermore, the positions of the master and the slave device were simultaneously measured using the OTS in real time.  
Figure 10 shows a comparison of results for the end-effector positions of the master and slave devices in Cartesian space. The maximum absolute values of the position tracking error between the master and slave device were measured as 3.21, 1.38, and 2.54 mm for the \(X,~{}Y\), and \(Z\) axis, respectively. The average standard deviation and RMS of the measured errors are shown in Table 4. The measured time delay of the developed teleoperation system was 35 ms. From the comparison, it is evident that the slave CDPR smoothly followed the master CDPR during teleoperation. However, the magnitude of each position was slightly different because of a geometric error caused by neglecting the size of the pulley in the kinematic equation used in order to minimize the computation time and because of the designed scale factor regarding the spatial workspace volume.  
Figure 11 shows a snapshot of the teleoperation system experiment conducted by the master and slave device through the admittance control. The red dotted lines in each figure represent the initial reference line of the slave CDPR device end-effector, and some of the paths are shown in Figure 10. Green dotted lines in each figure represent the initial reference line of the master CDPR haptic device end-effector. As a result, the master CDPR haptic device on the user's desk was able to control the slave CDPR according to the user-entered motion with visual supervising of an operator.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Mean (mm)** & **SD (mm)** & **RMS (mm)** \\ \hline \(X\) axis & 0.2191 & 0.7625 & 0.7933 \\ \(Y\) axis & 0.0284 & 0.4276 & 0.4285 \\ \(Z\) axis & \(-\)0.5852 & 0.9966 & 1.1556 \\ Magnitude & 0.6255 & 1.3257 & 1.4657 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Measured error of the EE on the teleoperation.  
Figure 10: Result of the master–slave control in the developed teleoperation system: (**a**) in 3D space; (**b**) in 2D space \(X,~{}Y\), and \(Z\) axis.