esa-sceva/satcom-chunk-collection huggingface dataset:
# Research on the A* Algorithm for Automatic Guided Vehicles in Large-Scale Maps
## 2 A* Algorithm and Analysis of Its Problems
### Overview of the A* Algorithm
#### 2.1.2 Conceptual Illustration of the A* Algorithm in Practical Applications
Ideally, the heuristic function \(h(n)\) should be as close as possible to the actual shortest distance so that the algorithm can target and expand those nodes leading to the optimal path faster. In practice, \(h(n)\) is often estimated using geometric metrics such as Manhattan distance or Euclidean distance, which provide more accurate estimates in empty, unobstructed space. However, it is worth noting that these simple distance formulas are often ineffective in complex environments, especially in scenarios where numerous obstacles are present, by ignoring the effects of obstacles. Therefore, in order to enhance the applicability of the A* algorithm in complex environments, researchers have continued to explore more refined heuristic functions with the aim of reflecting the cost of the actual path more accurately. Furthermore, a crucial principle is that the estimate of \(h(n)\) must always be less than or equal to the actual shortest distance from n to the goal node. This constraint ensures that the A* algorithm is always able to follow the optimal path or at least guarantees that the found is a feasible path. In other words, even if the estimate of \(h(n)\) is biased, as long as it does not exceed the true value, the A* algorithm is guaranteed to find the shortest path from the start to the end [32]. This feature makes the A* algorithm widely used and respected in path planning, game AI, robot navigation, and many other fields.
# Sorghum Flour: A Valuable Ingredient for Bakery Industry?
## 3 Results and Discussion
### Amino Acid Composition
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Amino Acids** & **Sorghum Seed flour** & \begin{tabular}{c} **Whole Wheat** \\ **Seed flour** \\ \end{tabular} & \begin{tabular}{c} _p-Value (t-Test)_ \\ \end{tabular} \\ \hline \multirow{8}{*}{\
\begin{tabular}{c} Essential amino \\ acids \\ \end{tabular} } & Arginine & \(3.65\pm 0.18\) & 4.30 \(\pm\) 0.54 & 0.123 \\  & Leucine & \(12.84\pm 0.66\) & \(6.69\pm 0.65\) & \(<\)0.0001 \\  & Valine & \(4.76\pm 0.24\) & 4.46 \(\pm 0.43\) & 0.347 \\  & Lysine & \(2.1\pm 0.40\) & \(2.56\pm 0.73\) & 0.391 \\  & Phenylalanine & \(4.65\pm 0.18\) & 4.63 \(\pm 0.16\) & 0.909 \\  & Isoleucine & \(3.65\pm 0.14\) & \(3.14\pm 0.23\) & 0.029 \\  & Threonine & \(2.77\pm 0.20\) & \({}^{\mathrm{a}}\) & \(2.73\pm 0.42\) & 0.888 \\  & Histidine & \(1.88\pm 0.54\) & \(2.40\pm 0.47\) & 0.272 \\ \hline \multirow{8}{*}{
\begin{tabular}{c} Dispensable amino \\ acids \\ \end{tabular} } & Glutamic ac. & \(19.93\pm 0.50\) & 26.20 \(\pm\) 0.46 & \(<\)0.0001 \\  & Glycine & \(3.1\pm 0.19\) & 4.21 \(\pm\) 0.27 & 0.004 \\  & Serine & \(4.1\pm 0.43\) & 4.63 \(\pm\) 0.55 & 0.260 \\  & Proline & \(8.41\pm 0.41\) & 10.50 \(\pm\) 0.43 & 0.003 \\  & Aspartic ac. & \(5.54\pm 0.50\) & 3.31 \(\pm\) 0.31 & 0.002 \\  & Alanine & \(8.41\pm 0.44\) & 3.31 \(\pm\) 0.37 & \(<\)0.0001 \\  & Tyrosine & \(2.99\pm 0.17\) & 1.57 \(\pm\) 0.30 & 0.0019 \\  & Methionine & \(1.88\pm 0.14\) & 1.65 \(\pm\) 0.12 & 0.009 \\  & Cysteine & \(1.33\pm 0.04\) & 2.31 \(\pm\) 0.07 & \(<\)0.0001 \\ \hline \hline \end{tabular} Note: \({}^{\mathrm{a,b}}\) The results are expressed as mean \(\pm\) standard deviation. Different letters in the same row indicate significant diferences (_i_-Test, _p_\(<\) 0.05).  
\end{table} 
Table 4: Amino acids composition of sorghum and whole wheat flours (g amino acid/100 g protein). Figure 2: Chemical scores of amino acids of sorghum and whole wheat seeds. Note: \({}^{*}\), \({}^{**}\) Correlations significant at _p_\(<\) 0.05, _p_\(<\) 0.01, and _p_\(<\) 0.001, respectively. An appreciable correlation was reported between the chemical scores determined in this way and the values obtained by biological tests for protein quality [33]. It can be seen in Figure 2 that both sorghum and wheat protein are a rich source of isoleucine, leucine, and valine. The most limited amino acid is lysine, followed by phenylalanine, threonine, and methionine.
## 3 Results and Discussion
### Total Phenolic Content and Antioxidant Activity  
Phenolic compounds are the widely found secondary metabolites in plants. Phenolic acids and flavonoids are the major phenolic compounds. In general, phenolic compounds play a role in the protection of an organism against the actions of reactive oxygen species [54]. Polyphenols are compounds with antioxidant, anticancer, antiviral, antibacterial, and antimicrobial activities [55]. Recently, [PERSON] et al. [56] found that \(p\)-coumaric acid, \(p\)-coumaric acid 4-O-hexoside, apigenin 7-glucoside, and quercetin-O-pentosyl-hexoside are the main phenolics in PL. The total phenolic content in wheat flour was 0.35 mg GAE/g DM, whereas PL contained 21 mg GAE/g DM. Antioxidant activity was expressed by the EC\({}_{50}\) index of PL, which was 6.23, 3.61, and 5.28 mg DM/mL for the ABTS, CHEL, and RED assays, respectively. EC\({}_{50}\) values for wheat flour were 356.7, 34.1, and 132.8 mg DM/mL, respectively. The incorporation of PL into wheat bread increased the phenolic content in the enriched samples (Figure 4). A significant (\(p<0.05\)) and positive linear relation (\(r=0.99\)) was found between PL and the TPC. PB5 extracts were characterized by about threefold higher content of phenolics (0.84 mg GAE/g DM) compared with the control bread (0.23 mg GAE)/g DM). An increase in the phenolic content enhanced the antioxidant activity of the enriched bread. Various antioxidants show substantially different efficiencies in food due to different molecular structures. Therefore, standardized analytical methods are used in the assessment of the antioxidant activity of food [57]. The results of the present study suggested that PL contain antioxidants with a broad spectrum of action. Furthermore, ABTS, CHEL, and RED assays showed a significant decrease in EC\({}_{50}\) with an increasing amount of PL in the bread recipe, which shows an increase in the antioxidant activity of bread. The highest decrease in EC\({}_{50}\) was found for ABTS-neutralizing activity (from 326 mg DM/mL for CB to 112 mg DM/mL for PB5), and the lowest was found for CHEL (from 32.3 mg DM/mL to 23.1 mg DM/mL). Statistically significant correlations (\(p<0.05\)) were observed between the addition of PL and ABTS-neutralizing activity, CHEL, and RED (\(r=0.97\), 0.98, and 0.97, respectively). Studies also observed that PL increased the TPC and antioxidant activity of different kinds of food, such as pasta [19; 43] and beans [58]. [PERSON] et al. [59] analyzed the phenolic profile and bioactivity of hydroethanolic extracts from PL samples obtained from 25 cultivars and found that apigenin and kaempfer were the most abundant phenolic compounds, demonstrating antioxidant and antimicrobial activity against fungi and bacteria. Moreover, 29 flavonoid glycosides were found in the aqueous extract of PL, and apian, a diglycoside of the flavone apigenin, was the dominant compound responsible for the antioxidant activity of PL [60].
## 3 Results and Discussion
### Char Morphology Analysis Flame Retardant Coatings  
#### 3.11.1 SEM Analysis  
The micro-morphologies of the char layers after calorimeter test for F0, F1, F2 and F3 composites were investigated by SEM. Figure 13a-d shows the morphology on the surface of F0, F1, F2, and F3 samples at a 3000\(\times\) magnification level. Figure 12a shows that the surface of the char layer for the F0 sample (the sample without ZrO\({}_{2}\) NPs) contains large holes. The char layer with large holes of micron size did not provide protection against fire. The char morphology of F1, F2, and F3 formulations in Figure 12b-d indicates that large holes and cracks gradually reduced the addition of ZrO\({}_{2}\) NPs (1%, 2%, and 3%). The holes and cracks that are formed in the F0 char may be due to the release and flow of volatile gases into the flame zone.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Code** & **Decomposition Temp.\(\approx\) (\({}^{\circ}\)C)** & **Char Residue (\%) at 800 \({}^{\circ}\)C** \\ \hline APP & 363.8 & 61.5 \\ Boric Acid & 154.4 & 55.2 \\ Chitosan & 303.8 & 31.6 \\ Epoxy Resin and Hardener & 373.4 & 6.6 \\ Mixture & 364.5 & 0.0 \\ \({}^{\star}\) Zirconia & - & 92.7 \\ F0 & 241.2 & 18.1 \\ F1 & 337.0 & 32.4 \\ F2 & 340.6 & 35.1 \\ F3 & 348.5 & 37.5 \\ \hline \hline \end{tabular}  
* Experiment was conducted from ambient temperature to 800 \({}^{\circ}\)C. In between, the component did not decompose.  
\end{table}
Table 4: Thermal stability results of the flame retardant components and formulation samples.
# Remote Sensing-Based Multilayer Perceptron Model for Grassland Above-Ground Biomass Estimation
## 5 Results and Analysis
### Model Accuracy Evaluation and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data Type** & **Metrics** & **RF** & **XGBoost** & **SVR** & **MLR** & **GBDT** & **MLP** \\ \hline \multirow{3}{*}{Vegetation index} & \(R^{2}\) & 0.6080 & 0.5790 & 0.4300 & 0.4900 & 0.5880 & 0.6510 \\  & \(RMSE\) (\(g\)/m\({}^{2}\)) & 47.453 & 48.244 & 58.835 & 55.307 & 50.913 & 44.222 \\  & \(rRMSE\) (\%) & 41.867 & 42.537 & 51.752 & 48.688 & 44.872 & 39.061 \\ \hline \multirow{3}{*}{Vegetation index + Meteorological factor} & \(R^{2}\) & 0.6770 & 0.6630 & 0.7010 & 0.5460 & 0.6140 & 0.6720 \\  & \(RMSE\) (\(g\)/m\({}^{2}\)) & 44.650 & 45.579 & 42.987 & 52.927 & 48.827 & 45.006 \\  & \(rRMSE\) (\%) & 38.775 & 39.582 & 37.331 & 45.963 & 42.403 & 39.084 \\ \hline \multirow{3}{*}{Vegetation index + Meteorological factor + Terrain factor} & \(R^{2}\) & 0.7040 & 0.7130 & 0.7030 & 0.5080 & 0.6430 & 0.7460 \\  & \(RMSE\) (\%) & 42.754 & 42.099 & 42.817 & 55.093 & 46.915 & 39.627 \\ \cline{1-1}  & \(rRMSE\) (\%) & 37.128 & 36.560 & 37.183 & 47.844 & 40.742 & 34.413 \\ \hline \multirow{3}{*}{Vegetation Index + Meteorological factor + Terrain factor + RoMSE (\%)} & \(R^{2}\) & 0.7080 & 0.7230 & 0.5300 & 0.5900 & 0.6580 & 0.7650 \\ \cline{1-1}  & \(RMSE\) (\%) & 42.453 & 41.354 & 53.835 & 50.307 & 45.913 & 38.066 \\ \cline{1-1}  & \(rRMSE\) (\%) & 36.867 & 35.913 & 46.752 & 43.688 & 39.872 & 33.058 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Precision evaluation indexes of each model under different combinations of characteristic variables. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **R\({}^{2}\)** & **RMSE (g/m\({}^{2}\))** & **rRMSE (\%)** \\ \hline Random Forest Regression (RF) & 0.708 & 42.453 & 36.867 \\ Extreme Gradient Boosting (XGBoost) & 0.723 & 41.354 & 35.913 \\ Support Vector Machine Regression (SVR) & 0.530 & 53.835 & 46.752 \\ Multiple Linear Regression (MLR) & 0.590 & 50.307 & 43.688 \\ Gradient Boosting Decision Tree (GBDT) & 0.658 & 45.913 & 39.872 \\ Multilayer Perceptron (MLP) & 0.765 & 38.066 & 33.058 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Model accuracy evaluation. rRMSE = 33.058%), outperforming all five traditional machine learning models across all evaluation metrics. The MLP model demonstrated significantly higher accuracy than traditional algorithms, with an R\({}^{2}\) of 0.765 compared to 0.723 for XGBoost, 0.708 for RF, and lower values for other models. To assess whether these performance differences were statistically significant, a paired \(t\)-test was conducted at \(\alpha\) = 0.05. The results showed that the MLP's R\({}^{2}\) was significantly higher than XGBoost (\(p\) = 0.023), RF (\(p\) = 0.018), SVR (\(p\) < 0.001), MLR (\(p\) < 0.001), and GBDT (\(p\) = 0.035). This indicates that the accuracy improvement of MLP is not due to random chance but reflects its superior ability to capture complex relationships between input variables and AGB. Figure 3: Comparison of model accuracy.
Due to the close relationship between CL and eating quality, the feasibility of HSI for evaluating the CL of fresh chicken meat should also be studied. Therefore, the prime focus of this study was to investigate visible and near-infrared (VNIR) HSI to assess and visualize CL of fresh broiler breast fillets. The specific objectives of the present study were to: (1) generate the reasonable regions of interest (ROIs) most closely related to CL information; (2) build qualitative relationships between the spectra and pre-assigned high-CL and low-CL groups; (3) select and identify the important wavelengths that carry the most useful information; and (4) develop image processing algorithms to generate pixel-level and fillet-level classification maps for visualizing the CL of chicken fillets.
# A Survey of of Side-Channel Attacks and Mitigation for Processor Interconnects
## 2 Interconnect and Network-on-Chip
Routers on the processor are commonly referred to as stops and, depending on the organization of the processor interconnect, can also be referred to as ring stops [20] or mesh stops [21; 22]. Nodes of the NoC composed of stops and processing elements on the processor are called tiles. Tiles on the processor are differentiated based on the processing elements they contain, such as core tiles and IMC tiles [33]. As shown in Figure 1, a core tile contains a CPU core (including L1 and L2 caches), an LLC slice, and a stop. The LLC slice comprises data, a directory (snoop filter), and a control unit called Cache/Home Agent (CHA), responsible for maintaining cache coherence among blocks. The stop handles injection, forwarding, and receiving of traffic in the interconnect. It is also known as a node router or station. An IMC tile includes a stop and an integrated memory controller, which connects to off-chip DRAM modules. The NoC interconnect architecture employs a packet-based communication approach. Requests or responses sent to caches or off-chip memory are divided into packets, which are then transmitted and injected into the network. Flit is the smallest unit of flow control in the NoC. A packet can consist of one or more flits. For instance, when a load instruction at the core tile at position \(s\) in Figure 2 is executed, it \(\bigoplus\) first checks the private cache and \(\bigoplus\) LLC cache, and if there is a cache miss, the required data must be fetched from memory. Therefore, \(\bigoplus\) a memory fetch request message is created and sent to the network interface (NI) over the appropriate virtual network. The NI transforms it into a network packet based on the packet format, filters the packet, and \(\bigoplus\) sends it into the network via the local router. The network \(\bigoplus\) is then responsible for routing these packets to their destination, which is the IMC tile at position d. Packets can be routed along the same path or different paths, depending on the routing protocol. The NI at position \(d\)\(\bigoplus\) receives flits and creates packets based on them, then \(\bigoplus\) forwards the request to the IMC, and finally \(\bigoplus\) initiates the memory fetch request. Figure 1: Mesh interconnect architecture of an Intel 16-core processor.
## 2 Materials and Methods
### Data Management and Statistical Analysis  
Heart rate and SmO\({}_{2}\) data were exported to Garmin Connect online software (v.2022) where visual inspection of each participant's files allowed each stage of each trial to be identified. The primary identification determination was the running cadence (steps/min), with the secondary evaluation as the pace (min/km), as shown in Figure 1. Once time points were visually identified, the 1-min average heart rate and SmO\({}_{2}\) were taken. The maximum heart rate for each trial was determined as the highest 5 s average heart rate within the 8-min intense running stage.  
Based on previous research, exercise at \(-\)14 \({}^{\circ}\)C alters performance after insulative clothing is removed, and thus, we estimated that to see an effect of cold air exposure in \(-\)15 \({}^{\circ}\)C cold air, at least 8 subjects were required (ES = 0.5, \(\alpha\) = 0.05; \(\beta\) = 0.8) [23]. Since knowledge about sex differences in cold exposure is very limited, a similar number of females and males were included in the study.  
The primary evaluation of the data set was performed with Q-Q plots for outlier identification. Group-level data are expressed as the means and standard deviations (SDs). Normal distribution, sphericity and homogeneity were determined with a Shapiro-Wilk test, [PERSON]'s W-test, and Levene test, respectively. All data met these assumptions. We used a mixed model ANOVA design (sex [between] \(\times\) condition [within]x time point[within]) for HRavg, MVC, SmO2 VL, SmO2 VM, heavy legs, cold discomfort and thermal state scale values. Distance and HRmax were analyzed with mixed measures ANOVAs as (sex [between] \(\times\) condition [within]). In case of a significant effect, post hoc Bonferroni analyses were used to identify the significant pairwise group differences. For all analyses, the statistical significance level was set at \(\alpha\) = 0.05 (two-tailed). To assess the effect size of the mixed model ANOVAs, the partial eta squared was used, assuming a strong effect from \(\eta_{\mathrm{p}}\)2 \(>\) 0.14 and a medium effect between \(\eta_{\mathrm{p}}\)2 = 0.06 and \(\eta_{\mathrm{p}}\)2 = 0.14 [37]. In post hoc power analyses, the result was considered meaningful if the power was greater than 0.8 (1-\(\beta\) \(>\) 0.8). Data in tables are presented as means \(\pm\) standard deviations, with data in figures as means and standard errors. Data management and analysis was performed with Excel (Microsoft Corporation, Seattle, WA, USA, 2018), Jamovi version 2.3 (The Jamovi Project, Sydney, Australia, 2022), and power was calculated using G*Power version 3.1.9.7.
## 4 Results and Discussion
### Sensitivity of the Proposed Approach to the Parameter Settings
The metrics have been evaluated by using the cosine distance and \(N_{bin}=50\) histogram bins.
## 5 Feature Extraction
### Complex Correlation Measure  
Calculation of the Complex Correlation Measure (CCM) does not require the explicit plotting of the Poincare plot. The calculation is performed over the original time series of the vibration signal denoted \(X=\{x_{1},x_{2},x_{3},...,x_{N}\}\) as well as their delayed version \(X_{\tau}\). The \(i\) window includes the points denoted \(a(x_{i},y_{i})\), \(b(x_{i+1},y_{i+1})\) and \(c(x_{i+2},y_{i+2})\) where \(y_{i}=x_{i+\tau}\). With this information, Equations (5) and (6) are evaluated. The CCM of the vibration signals was calculated for \(\tau\) varying between 1 and 50. An example of this feature set is shown in Figure 17 for a signal extracted from the healthy class \(P1\) and for the faulty class \(P2\). In general the amplitude of the CCM feature is higher for the faulty class when compared to the normal class.
# Sources of Extraterrestrial Rare Earth Elements: To the Moon and Beyond
## 5 Lunar Resources
### Other Potential Lunar Resources
#### 5.3.4 Aluminum  
Aluminum (Al) is widely used throughout society today in fuselages of aircraft, food and beverage packing containers, packaging, kitchen utensils and beer kegs, to name but a few. It is the most abundant metal in Earth's crust (\(\sim\)8%) where it is mined from bauxite and cryolite ores. The lunar highlands are however comparatively enriched with between 10 and 18 wt % Al due to the abundance of anorthitic plagioclase feldspar, from which Al could be extracted [24; 26; 141].
# Void Hole Avoidance for Reliable Data Delivery in IoT Enabled Underwater Wireless Sensor Networks
## 6 Simulation Results
### Performance Comparison  
For performance evaluation, simulations are executed by comparing our proposed schemes with the WDFAD-DBR protocol. We evaluate our proposed schemes against WDFAD-DBR in terms of average PDR, energy tax, end-to-end delay and APD. The simulation results after comparison with WDFAD-DBR are shown in Figures 7-10.
## 4 All-Silicon Photodetector Structures
### TPA-Based Devices
The avalanche process in APDs amplifies the weak IR two-photon absorption photocurrent, thereby greatly improving the sensitivity of the autocorrelation measurement. More recently, TPA in all-silicon bulk detectors has been exploited for a novel profilometry technique at \(\lambda=1.55\) um [84]; compared with conventional profilometry, TPA has a much wider dynamic range without the need for high-speed devices or complicated computation. [PERSON] _et al._[85] fabricated a hemispherical nearly-intrinsic silicon TPA photodetector operating at a wavelength of 1.3 um and emitted from a CW laser. The detector was made of nearly-intrinsic silicon crystal with a resistivity of 6,000 \(\Omega\)/cm and made into a hemisphere with a radius of 3 mm. The silicon hemisphere was used as both a detector and a solid immersion lens (SIL) in the experiments. The bottom of the detector is (110) plane, on which aluminum electrodes were evaporated. The electrodes consisted of concentric circular and annular metal contacts with a spacing of 0.15 mm and a radius of 0.5 mm for the central electrode. The contacts between the aluminum and the silicon hemisphere are considered to be ohmic contacts. Because TPA substantially occurs in the vicinity of the focused spot (the center of the hemisphere), the concentric electrodes collect the photo-excited carriers efficiently. The responsivity of the detector was about 2 \(\mu\)A/W at 1,300 nm and 1 V of applied bias. This silicon photodetector is easy to fabricate and is useful in autocorrelation for measuring ultra-short laser pulses with wavelengths in the region of 1.2-2.1 um.
# Strategies and Challenges in Detecting XSS Vulnerabilities Using an Innovative Cookie Collector
## 1 Introduction
### Cross-Site Scripting (XSS) Attacks: Characteristics and Analysis
#### 1.1.1 Key Characteristics  
_Injection of malicious code:_ attackers insert JavaScript or other client-side scripting into web pages viewed by other users [3].  
_Browser execution:_ the injected code is executed in victims' browsers with the privileges of the legitimate website [4].  
_Trust exploitation:_ XSS leverages the trust relationship between a user and a website [5].
# Object-Environment Fusion of Visual System for Automatic Pear Picking
## 3 Results
### Picking Pose Estimation Experiment  
#### 3.3.1 Evaluation Metrics  
Three metrics were used to evaluate picking pose estimation: the success rate (\(SR\)), the mean error (\(MeanE\)), and the median error (\(MedE\)) of the picking position. The \(SR\) is affected by two factors. The first is whether the \(MeanE\) is less than 5 cm. The second is whether there is at least one collision-free picking candidate. The formulas for the calculation of the \(SR\), \(MeanE\), and \(MedE\) are as follows [29; 35; 36]:  
Figure 14: Instance segmentation results of Mask R-CNN(ResNet-50) under different conditions.  
Figure 12: Instance segmentation results of YOLOv5 under different conditions.  
Figure 13: Instance segmentation results of YOLOv8 under different conditions.  
\[SR=\frac{\sum\limits_{i=1}^{N}\mathbf{f}(\Delta d_{i})\cdot S_{i}}{N}\times 100\% \tag{12}\]  
\[MeanE=\frac{\sum\limits_{i=1}^{N}\mathbf{f}(\Delta d_{i})}{N} \tag{13}\]  
\[MedE=\mathbf{median}(\{\Delta d_{1},\dots,\Delta d_{N}\}) \tag{14}\]  
\[\mathbf{f}(\Delta d_{i})=\begin{cases}0,\Delta d_{i}>5\;\text{cm}\\ 1,\Delta d_{i}\leq 5\;\text{cm}\end{cases} \tag{15}\]  
\[\Delta d_{i}=\sqrt{\left(x_{i}^{est}-x_{i}^{gt}\right)^{2}+\left(y_{i}^{est}-y _{i}^{gt}\right)^{2}+\left(z_{i}^{est}-z_{i}^{gt}\right)^{2}} \tag{16}\]  
where \(N\) represents the number of tests, and \(\Delta d_{i}\) represents the Euclidean distance between the estimated and real values of the picking position in the \(ith\) experiment. \(S_{i}\) is a binary symbol, where 0 indicates that there is no collision-free candidate, and 1 indicates that there is at least one collision-free candidate. \(\mathbf{median}(\cdot)\) represents the median operation. \((x_{i}^{est},y_{i}^{est},z_{i}^{est})\) and \((x_{i}^{gt},y_{i}^{gt},z_{i}^{gt})\) are the estimated and real values of the picking position.