esa-sceva/satcom-chunk-collection huggingface dataset:
# An Integrated Dictionary-Learning Entropy-Based Medical Image Fusion Framework
## 4 Experiments and Analysis
### Image Quality Comparison
#### 4.2.4 Average Performance of Nine Image Fusion Comparative Experiments  
Table 4 shows the average objective evaluations of nine image fusion comparative experiments. The proposed IDLE obtains the largest value in \(Q^{AB/F}\), MI, and VIF among 10 image fusion methods. Although BSD gets the largest value in AG and EI, the block effect seriously affects the quality of the fused image. The average objective evaluations prove that the proposed IDLE has the best overall performance in three types of image fusion experiments.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **AG** & **EI** & \(\mathbf{Q^{AB/F}}\) & **MI** & **VIF** \\ \hline BSD & **5.5369** & **56.6304** & 0.3293 & 1.8758 & 0.2837 \\ DWT & 5.4205 & 55.1206 & 0.3585 & 1.2852 & 0.2471 \\ DT-CWT & 4.4082 & 45.0176 & 0.4376 & 1.6371 & 0.2847 \\ CS-DCT & 3.6498 & 36.8703 & 0.3974 & 1.8496 & 0.2745 \\ KSVD-OMP & 3.6265 & 39.9752 & 0.5382 & 1.8416 & 0.2984 \\ MFR & 5.1247 & 52.1774 & 0.5653 & 2.0934 & 0.3204 \\ SRDL & 4.9845 & 5.1983 & 0.5537 & 1.9416 & 0.3279 \\ JPC & 5.2903 & 55.0743 & 0.6149 & 1.9773 & 0.3395 \\ MST-SR & 4.0817 & 44.1942 & 0.5142 & 1.9237 & 0.3076 \\ Proposed IDLE & 5.2374 & 53.9238 & **0.6291** & **2.1045** & **0.3426** \\ \hline \hline \end{tabular}  
* The highest result of each objective metric is marked in bold-face.  
\end{table}
Table 4: Average Objective Evaluations of Nine Image Fusion Comparative Experiments.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **AG** & **EI** & \(\mathbf{Q^{AB/F}}\) & **MI** & **VIF** \\ \hline BSD & **5.8505** & **59.7385** & 0.7180 & 1.5139 & 0.2951 \\ DWT & 4.6099 & 57.2050 & 0.6397 & 1.3106 & 0.2766 \\ DT-CWT & 3.8157 & 37.3078 & 0.7079 & 1.6847 & 0.3212 \\ CS-DCT & 3.0988 & 31.6784 & 0.3601 & 1.4818 & 0.2695 \\ KSVD-OMP & 2.7215 & 38.1780 & 0.6497 & 1.6565 & 0.2898 \\ MFR & 4.5781 & 51.8703 & 0.7174 & 1.7067 & 0.3196 \\ SRDL & 4.8603 & 51.3517 & 0.7219 & 1.6973 & 0.3244 \\ JPC & 4.7361 & 52.5702 & 0.7196 & 1.7102 & 0.3227 \\ MST-SR & 3.8729 & 43.7209 & 0.6173 & 1.5927 & 0.2681 \\ Proposed IDLE & 4.7295 & 52.0081 & **0.7317** & **1.7192** & **0.3265** \\ \hline \hline \end{tabular}  
* The highest result of each objective metric is marked in bold-face.  
\end{table}
Table 3: Objective Evaluations of MRI-SPECT Image Fusion Comparative Experiments.
# Integration of Deep Learning Vision Systems in Collaborative Robotics for Real-Time Applications
## 3 Materials and Methods
### Deep Learning  
Deep learning is a branch of Machine Learning (ML) that seeks to learn high-level abstractions from data [15]. It uses Artificial Neural Networks (ANNs), which are computer representations of human neurons. These networks are made up of several layers that work together to produce optimal results, enabling the extraction of characteristics from datasets and subsequent learning [16]. The scope of this field ranges from the automotive industry and autonomous driving [17] to all manufacturing tasks, such as assembly [18], automatic sorting [19; 20], quality inspection [21; 22], stock management in the supply chain [23], and object detection [10; 22]. In addition, its impact can also be seen in the healthcare industry [24], the agricultural sector [25], the detection of monetary fraud [26], and cybersecurity [27; 28].  
Despite all these benefits, it should be emphasized that since DL is a branch of ML and ML, in turn, is a branch of AI, the evolution of deep learning is due not only to the computational capacities available and the inherent cost reduction [28] but also essentially to the evolution of AI algorithms that allow computers to learn and improve automatically with experience, without being explicitly programmed [29].  
There are several algorithms that can be used in ML, including K-Nearest Neighbors, which is used for both classification and regression using metrics such as Euclidean distance, cosine, or Manhattan distance, or the Naive Bayes algorithm based on Bayes' Theorem, among others. Variations such as Gaussian, Multinomial, and Bernoulli Naive Bayes are commonly used for different types of data distributions, however the Naive Bayes algorithm will not be the most suitable for cobots due to its non-linear behavior [30].  
One-Stage Detectors  
Since this project requires fast inference times and low computational power, single-phase detectors will be the main focus. In the following lines, we will discuss two models that fit this criterion, RetinaNet and YOLO.
# A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms
###### Abstract  
The system identification problem becomes more challenging when the parameter space increases. Recently, several works have focused on the identification of bilinear forms, which are related to the impulse responses of a spatiotemporal model, in the context of a multiple-input/single-output system. In this framework, the problem was addressed in terms of the Wiener filter and different basic adaptive algorithms. This paper studies two types of algorithms tailored for the identification of such bilinear forms, i.e., the Kalman filter (along with its simplified version) and an optimized least-mean-square (LMS) algorithm. Also, a comparison between them is performed, which shows interesting similarities. In addition to the mathematical derivation of the algorithms, we also provide extensive experimental results, which support the theoretical findings and indicate the good performance of the proposed solutions.  
adaptive filter; Kalman filter; optimized LMS algorithm; bilinear forms; system identification 1
# An Optimization Framework for Wind Farm Design in Complex Terrain
## 3 Optimization Framework
### Constraints
Given the grid sizes along the \(x\) and \(y\) directions are \(\Delta x\) and \(\Delta y\), the TRI at grid \((x_{i},\ y_{j})\) can be computed based on its elevation and the elevation values of the eight surrounding grids as:\[\text{TRI}(x_{i},\,y_{j})=\,\frac{1}{8}\left\{\frac{\left[\text{z}(x_{i},\,y_{j})- \text{z}(x_{i+1},\,y_{j})\right]^{2}}{\Delta x^{2}}+\frac{\left[\text{z}(x_{i}, \,y_{j})-\text{z}(x_{i-1},\,y_{j})\right]^{2}}{\Delta x^{2}}\right.\]  
\[\left.+\frac{\left[\text{z}(x_{i},\,y_{j})-\text{z}(x_{i},\,y_{j+1})\right]^{2 }}{\Delta y^{2}}+\frac{\left[\text{z}(x_{i},\,y_{j})-\text{z}(x_{i},\,y_{j-1}) \right]^{2}}{\Delta y^{2}}+\frac{\left[\text{z}(x_{i},\,y_{j})-\text{z}(x_{i+ 1},\,y_{j+1})\right]^{2}}{\Delta x^{2}+\Delta y^{2}}\right. \tag{15}\]  
For the wind farm site in Figure 1a, the TRI map calculated in Equation (15) is shown in Figure 3a. Note that the grid sizes are chosen as \(\Delta x=\Delta y=25\) m in this study according to the default setting of WAsP, which makes the total number of grids in the rectangle area shown in Figure 1 as 38,801. In the current framework, the constraints on TRI and mean wind speed, \(v^{mean}\), are considered. Note that the mean wind speed values on the grids, \(v^{mean}(x_{i},\,y_{j})\), can be imported from wind resource assessment tools or calculated based on the sector wise wind resource parameters, i.e., Weibull-A, Weibull-k, and frequency. For an arbitrary site, linear interpolation is used to find the value of TRI and \(v^{mean}\). Thus, constraints on TRI and mean wind speed can be written as:  
\[\text{TRI}_{max}-\text{TRI}(x_{i},\,y_{i})\geq 0,\quad\text{for}\ i=1,2,\, \ldots,\,N_{\text{wt}}, \tag{16}\]  
\[v^{mean}(x_{i},\,y_{i})-v^{mean}_{min}\geq 0,\quad\text{for}\ i=1,2,\, \ldots,\,N_{\text{wt}}. \tag{17}\]  
where \(\text{TRI}_{max}\) is the allowed maximal TRI and \(v^{mean}_{min}\) is the allowed minimal mean wind speed. For the wind farm site in Figure 1, the feasibility of each grid, \((x_{i},\,y_{j})\), can then be estimated as \(F(x_{i},\,y_{j})\) based on the first and third types of constraints, i.e., constraints defined in Equations (13), (16) and (17). Note that \(F(x_{i},\,y_{j})\), with a value of 1 (true) or 0 (false), means whether the given site, \((x_{i},\,y_{j})\), is a feasible site to install a turbine, i.e., a site satisfies the constraints on inclusive/exclusive boundaries and bounds of certain site condition variables. The map of \(F(x_{i},\,y_{j})\) is shown in Figure 3b. Note that the black area in this figure denotes the feasible area. Compared with the feasible area defined by Equations (13) and (14), the bounds on TRI and \(v^{mean}\) help to reduce the feasible grids from 12,150 to 9218, representing a 24.13% reduction in the feasible design space. This reduction can help certain optimization algorithms, such as RS, to limit the search space and converge faster.
# Lithium-Ion Battery Capacity Prediction with GA-Optimized CNN, RNN, and BP
## 3 Related Algorithms
### Evaluation Parameters  
In this paper, five different metrics--Mean Squared Error (_MSE_), Root Mean Squared Error (_RMSE_), Normalized Root Mean Squared Error (_NRMSE_), Mean Absolute Error (_MAE_), and Squared Correlation (\(R^{2}\))--will be used to measure the similarity between the predictions generated by the proposed system and the actual values. These metrics serve to evaluate the system's performance from various perspectives. The calculations for these metrics will be conducted using the formulas provided in Equations (6)-(10).  
\[MSE=\frac{1}{N}\sum_{i=1}^{N}(x_{i}-\hat{x}_{i})^{2} \tag{6}\]  
\[RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_{i}-\hat{x}_{i})^{2}} \tag{7}\]  
\[NRMSE=\frac{\sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_{i}-\hat{x}_{i})^{2}}}{\max(x_{ i})-\min(x_{i})} \tag{8}\]  
\[MAE=\frac{1}{N}|x_{i}-\hat{x}_{i}| \tag{9}\]  
Figure 10: RNN architecture.  
\[R^{2}=\left(\frac{\sum{(x_{i}-\text{mean}(x))(\hat{x}_{i}-\text{mean}(\hat{x}))}}{ \sqrt{\sum{(x_{i}-\text{mean}(x))}^{2}\sum{(\hat{x}_{i}-\text{mean}(\hat{x}))} ^{2}}}\right)^{2} \tag{10}\]  
where \(x_{i}\) is the true value, \(\hat{x}_{i}\) is the predicted value, N is the number of cycles, \(\text{max}(x_{i})\) is the largest true value, \(\text{min}(x_{i})\) is the smallest true value, \(\text{mean}(x)\) is the mean of the true values, and \(\text{mean}(\hat{x})\) is the mean of the predicted values.
## 2 Theory Background
### Support Vector Machine  
SVM is a machine-learning algorithm based on the structural risk minimization principle of statistical learning theory [33]. For the two-class problem, SVM maps the non-linear separable problem in low-dimensional space to high-dimensional space through a certain non-linear kernel function mapping, making it linear separable. The core of SVM is to seek a hyper plane in high-dimensional space as the segmentation of two classifications to ensure the minimum classification error rate.  
Figure 2: Time–frequency spectrum plane division corresponding to the characteristic frequency band energy entropy method.  
For a given training sample \(\{(x_{i},y_{i})\},(i=1,2,3,\ldots,n),x_{i}\in\mathbf{C}^{d},y_{i}\in\{-1,1\}\), where \(d\) represents the dimension of the space, \(y_{i}\) is the pattern label of \(x_{i}\). The hyper plane can be described as:  
\[\omega\bullet x+k=0, \tag{16}\]  
where, \(\omega\) and \(k\) represent the weighting vector and the bias, respectively.  
The optimal classification plane in the feature space can be constructed by solving the following quadratic programming problem:  
\[\left\{\begin{array}{l}\min\!L(\omega)=\frac{1}{2}\|\omega\|^{2}+C\sum\limits \limits_{i=1}^{n}\xi_{i}\\ \text{s.t.}\,y_{i}\bullet(\omega x+k)\geq 1-\xi_{i},i=1,2,\ldots,n\end{array} \right., \tag{17}\]  
where, \(C\) is a penalty factor which can indicates the penalty level for classification errors and \(\xi_{i}\) represents a slack factor. According to quadratic programming, Equation (16) is equivalent to solve the following optimization problem:  
\[\left\{\begin{array}{l}\max W(\lambda)=\sum\limits_{i=1}^{n}\lambda_{i}- \frac{1}{2}\sum\limits_{i,j=1}^{n}\lambda_{i}\lambda_{j}y_{i}y_{j}K(x_{i},x_{ j})\\ \text{s.t.}\sum\limits_{i=1}^{n}\lambda_{i}y_{i}=0,0\leq\lambda_{i}\leq C,i=1,2,\ldots,n\end{array}\right., \tag{18}\]  
where \(\lambda_{i}\) is Lagrange multiplier and \(K(x_{i},x_{j})\) represents the kernel function. The optimal classification decision function can be derived as:  
\[f(x)=\text{sgn}\left(\sum\limits_{i=1}^{n}\lambda_{i}y_{i}K(x_{i},x)+k\right). \tag{19}\]  
To deal with multi-class fault diagnosis problems, 'one-against-others' SVM algorithm illustrated in [30] is adopted in this paper.
# Feature Point Identification in Filtel Weld Joints Using an Improved CPDA Method
## 3 Feature Points Extraction Method in Fillet Welding  
### Image Pre-Processing  
The pre-processing of the acquired image primarily involves performing a threshold segmentation, which aims to separate the light stripe information from the original image and minimize the influence of background on image processing. In the image (Figure 1c) that was captured with the developed sensing system, pixels can be mainly separated into two classes: the background with dark lightness, and the laser line with bright lightness. As shown in the histogram of a captured image with the resolution of 2592 \(\times\) 1944 pixels in Figure 2a, a total number of 4.7 \(\times\) 10\({}^{6}\) pixels are in black (grayscale value from 0 to 10) while 1.6 \(\times\) 10\({}^{4}\) pixels are in white (grayscale value from 245 to 255). Other pixels with different grayscale values (the average number of pixels is 865) are an order of magnitude lower than these two classes. Therefore, the simple but effective [PERSON]'s method [32] is implemented to calculate an optimal threshold \(T\) (marked by a red line in the histogram in Figure 2a) by maximizing the variance between two classes of pixels to separate the laser line from the background. Pixels (\(u\), \(v\)) in the image with grayscale values below the threshold \(T\) are set to 0, while pixels with grayscale values equal to or above the threshold \(T\) remain as themselves. The process can be summarized as follows:  
\[f(x,y)=\left\{\begin{array}{l}0,\,f(u,v)<T\\ f(u,v),\,f(u,v)\geq T\end{array}\right. \tag{2}\]  
Figure 2: Laser stripe processing. (**a**) Threshold calculation; (**b**) laser center line determination; (**c**) original image; (**d**) pre-processed image; (**e**) center line extraction.  
Compared with the original image, the pre-processed image in Figure 2c,d shows that the gray-scale features become more pronounced after the image pre-processing. The interference image features caused by the metal reflection can be effectively filtered out. The brightness information of the laser stripe area can be better retained, which provides favorable conditions for the subsequent center extraction of laser fringe.
## 4 Experimental Results and Discussion
### Parameter Sensitivity Analysis of the Proposed PL-MSMM  
Finally, a hyperparameter sensitivity experiment was conducted for the proposed PL-MSMM. The training dataset consisted of 20 randomly selected samples from each class, and the test dataset consisted of 20 randomly selected samples. Hyperparameter \(C\) was adjusted as follows: \(\{0.01,0.1,1,10,100,200,300,400,500,600\}\). The accuracy of the PL-MSMM on the current dataset is shown in Table 5 and Figure 8.  
The experimental results show that the performance of the PL-MSMM is sensitive to hyperparameter \(C\). The choice of hyperparameters depends on the performance of the model in terms of the evaluation metrics. The influence parameter \(p\) on accuracy was also analyzed; the accuracy performance under different \(p\) values is shown in Table 6 and Figure 9.  
The experimental results show that hyperparameter \(p\) has an impact on the model's performance. Consequently, we need to choose an appropriate \(p\) value to obtain the best performance based on the specific application scenario and dataset.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Testing**} & \multicolumn{3}{c}{**Training**} \\ \hline
**Method** & **Noise** & **Accuracy (\%)** & **Precision (\%)** & **F1-Score (\%)** & **Accuracy (\%)** & **Precision (\%)** & **F1-Score (\%)** \\ \hline \multirow{2}{*}{MSMM} & Clean & 98.11 & 98.17 & 98.14 & 98.07 & 98.12 & 98.09 \\  & SPN & 96.49 & 96.65 & 96.57 & 98.45 & 98.5 & 98.48 \\ \hline \multirow{2}{*}{PL-MSMM} & Clean & 98.67 & 98.70 & 98.68 & 98.74 & 98.77 & 98.76 \\  & SPN & 97.67 & 97.75 & 97.71 & 98.19 & 98.23 & 98.21 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance comparison of PL-MSMM and MSMM with or without noise using 10-fold cross-validation.
## 2 Motivations and Contributions  
The main contribution of researchers around the world is to provide new innovative information to society, government, and different educational sectors in their respective domains. Many researchers had motivated and contributed to the significant problem of LU/LC prediction analysis. The LU/LC change detection for past, present, and future analysis has been a key research topic to understand the environmental change on the earth's surface. Hence, LU/LC feature extraction has emerged as an essential research aspect, and therefore, the standard and accurate methodology for LU/LC classification and prediction should be made. By use of satellite system technology, we can perform our research on LU/LC change analysis. The main need of this research is to assist the landscape management, government officials, forest department, and urban planners to take action to protect the earth's environment. From the brief survey on different classification and prediction algorithms, we have found that the sustainable growth of the LU/LC environment for the time-series data requires an accurate classification and prediction map, which was considered the strong motivation for our study. The main contributions of our work are as follows:  
* The novel Vision Transformer-based Bidirectional long-short term memory (Bi-LSTM) model is proposed for predicting the LU/LC changes of Javadi Hills, India.
* The use of the LST map with the Vision Transformer-based LU/LC classification map provides the main advantage in achieving good validation accuracy with less computational time during the process of LU/LC prediction analysis through the Bi-LSTM model.
* The impacts of the Multi-Satellite System (LISS-III multispectral with the Landsat TIRS, RED, and NIR bands) on the proposed LU/LC prediction model for Javadi Hills, India, are analyzed.
* Explainable Artificial Intelligence (XAI), an application-based explanation, is also introduced for validating the predicted results through the Google Earth Engine platform of Google Cloud so that the predicted results will be more informative and trustworthy to the urban planners and forest department to take appropriate measures in the protection of the environment.
###### Abstract  
This paper investigates the direction identification of micro-cracks with nonlinear components generated by Lamb wave with frequency-mixing technique. Three-dimensional finite element simulations were carried out to investigate the interaction mechanism between Lamb wave signals and micro-cracks. Upon re-visiting the conventional Lamb wave excitation signal with two kinds of fundamental frequencies (f\({}_{1}\) and f\({}_{2}\)), it was found to be possible to generate new types of frequencies (f\({}_{1}\)\(\pm\) f\({}_{2}\)) at the sideband if nonlinear sources existed in the plate. A pulse inversion method was used to extract the sideband frequency for nonlinear ultrasonic detection. By arranging piezoelectric chip arrays around the micro-crack, the acoustic nonlinearity parameter \(\beta\) related to the fundamental frequency and the sideband frequency for different micro-crack directions was calibrated. It was shown that \(\beta\) varied for different crack directions, which provides useful information about the scattering features of the nonlinear Lamb wave interacting with the micro-crack to characterize its directivity. Moreover, the scattering degree defined with the relative nonlinear parameter \(\beta^{\prime}\) of the micro-crack in different directions was investigated in detail by changing the size of the micro-crack. The outcomes showed that the forward scattering signal of the crack had a greater amplitude, whereas the backscattering signal had a smaller amplitude compared with the scattering signals in other directions from micro-cracks. In addition, the signal scattering degree in the forward direction from micro-cracks increased with the increasing micro-crack length, but decreased with increasing crack width. Furthermore, for the buried crack, the forward scattering degree of Lamb wave from micro-crack decreased as crack was buried deeper in plate. In summary, the findings of this study can help to further advance the use of nonlinear Lamb wave with the frequency-mixing technique for identifying the direction of micro-cracks.  
nonlinear Lamb wave; frequency mixing; pulse inversion; direction identification 2020; 10.2135; doi:10.3390/app10062135
# Task-Oriented Evaluation of the Feasible Kinematic Directional Capabilities for Robot Machining
## 2 Materials and Methods
### Translational and Rotational Manipulability
However, how can translational capabilities be managed separately from the rotational and also keep control over a rotational subspace? If we add another constraint that requires joint velocities to be projected onto the null space of \(J_{R}\) (\(J_{T}\)), the translational (rotational) manipulability polytope in the strong sense can be obtained, which enables the analysis of purely translational (rotational) motions. In order to graphically represent the translational (rotational) manipulability polytope in the strong sense, it is necessary to find the intersection between the joint velocity polytope \(Q\) and the null space \(N(J_{R})(N(J_{T}))\), i.e., \(Q\cap N(J_{T})\) (\(Q\cap N(J_{R})\)). The mapping of such joint velocities to the task space forms a translational (rotational) manipulability polytope in the strong sense \(P_{strong}^{T}(P_{strong}^{R})\), with the shape depending on the dimension of the considered null space:  
\[P_{strong}^{T}=\left\{v\in\mathbb{R}^{3}\right|v=J_{T}\hat{\theta},\ \left\|\hat{\theta}\right\|_{\infty}\leq 1,\ J_{R}\hat{\theta}=0\right\} \tag{20}\]  
\[P_{strong}^{R}=\left\{\omega\in\mathbb{R}^{3}\right|\omega=J_{R}\hat{\theta}, \ \left\|\hat{\theta}\right\|_{\infty}\leq 1,\ J_{T}\hat{\theta}=0\right\} \tag{21}\]  
The translational manipulability polytope \(P_{strong}^{T}\) is depicted in \[v_{2}=\left\|{{{I}_{T}^{\dagger}}{{\hat{u}_{T}}}}\right\|_{\infty}^{-1} \tag{16}\]0 A comparison with the polytopes \(P^{twist}\), \(P_{\infty}^{T}\), and \(P_{2}^{T}\) is shown in Figure 3b,c. The polytope \(P_{strong}^{T}\) is quite  
\[v_{2}=\left\|{{{I}_{T}^{\dagger}}{{\hat{u}_{T}}}}\right\|_{\infty}^{-1} \tag{16}\]1 Example of a manipulability polytope representation based on the 3 DOF planar manipulator: (a) Joint velocity polytope \(Q\), the minimum \(L_{\infty}\) norm solution of joint velocities represented by \(Q_{\infty}^{T}\), and the least \(L_{2}\) norm solution of joint velocities represented by \(Q_{2}^{T}\); the task space polytopes \(P^{twist}\), \(P_{\infty}^{T}\), and \(P_{2}^{T}\) in the isometric view (b), and in the top view (c). reduced in comparison to the polytopes \(P_{\infty}^{T}\) and \(P_{2}^{T}\). The joint velocity solution under the constraint \(J_{R}\dot{\theta}=0\) and (8), i.e., \(\left\|\dot{\theta}\right\|_{\infty}\leq 1\), is illustrated by \(Q_{strong}^{T}\) in Figure 3a. The translational (rotational) manipulability polytope in the strong sense \(P_{strong}^{T}\) (\(P_{strong}^{R}\)) allows for a complete separation of the translational and rotational capability analyses since only pure translational (rotational) movement is being considered at a time. What if a robot task requires a simultaneous motion with synchronized translational and rotational end-effector velocities, as in the case of robot surface machining? For this purpose, a solution will be derived in the following.