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Task and Motion Planning for a 7-DOF serial robot containing only revolute joints needs a fast and numerically stable inverse kinematics solution. The analytical methods are real-time, but they are robot dependent. Although the numerical methods based on inverse differential kinematics can solve the inverse kinematics problem (IKP) of 7R robots with arbitrary geometric parameters, their numerical stability is insufficient. Moreover, it is time-consuming for them to converge to a single solution that depends on the initial guess. The main innovation of this article is the development of a practical method for solving the IKP of general 7R robots. The proposed method can find multiple solutions and is also faster than the numerical method. It combines symbolic preprocessing, Sylvester dialytic elimination, and eigendecomposition. First, according to the Denavit-Hartenberg convention of geometric representation, a general kinematics model of a 7R manipulator is established. Secondly, the joint variables are separated by symbolic preprocessing, and then two symbolic matrices are obtained. After numerical substitution, a square matrix of polynomial coefficients is computed through Gaussian and Sylvester dialytic elimination. Finally, utilizing the eigendecomposition of the matrix restructured from the square matrix, the values of some variables are obtained, and then the remaining variables are solved by back-substitution. The simulation and experimental data are analyzed. The comparison results verify that the proposed method applies to solving the IKP of general 7R robots and is almost real-time, effective, and numerically stable.

The inverse kinematics problem involves the study that the inverse kinematics solver needs to calculate the values of the joint variables given the desired pose of the end-effector of a robot. However, to apply to seven-degree-of-freedom robots with arbitrary configuration, analytical methods need to fix one joint and set an increment when the current value fails to solve the inverse kinematics problem. Although numerical methods based on inverse differential kinematics are efficient in solving the inverse kinematics problem of seven-degree-of-freedom robots with arbitrary geometric parameters, they are deficient in numerical stability and time-consuming for convergence to one solution governed by the initial guess. In order to reduce the execution time of an inverse kinematics solver, this article introduces a speedup method for analytical and numerical methods, which can improve their performance.

Coal is one of the most important sources in China. The separation of coal and gangue is a key link in coal mining, and its intellectualization promotes the intelligent development of coal mining. But it is difficult to sort coal and gangue quickly and accurately because of some reasons, such as fast running speed of belt, different shapes and sizes of gangue, and so on. To solve the problem, an online flexible sorting model based on multi-information fusion is proposed. We use a near-infrared camera to identify coal and gangue, and combine it with a depth camera to obtain the height and pose information of gangue. Besides, we analyze the factors that affect the trajectory of gangue before and after pneumatic separation, deduce the theoretical formula of horizontal movement distance of gangue pneumatic separation, establish the mathematical model of gangue flexible sorting, and carry out experiments of pneumatic separation with different shapes and sizes of gangue. Experimental data is used to realize error compensation of the model. Finally, experimental results verify that the gangue flexible sorting model improve the accuracy of gangue sorting effectively and sort gangue with different shapes and sizes accurately despite the high-speed movement of belt.

In Streptococcus thermophilus, EpsC is a polysaccharide co-polymerase which is involved in determining the chain length of EPS synthesized by the Wzx/Wzy-dependent pathway. Our previous study found that there was a positive correlation between transcription level of epsC and molecular weight of EPS in S. thermophilus 05-34. To further investigate the effects of EpsC on EPS biosynthesis, this gene was over-expressed in S. thermophilus 05-34 in this study. Reverse transcription qPCR and Western blotting confirmed the successful transcription and translation of epsC in 05-34, respectively. The yield of EPS was not affected by the over-expression of EpsC. Gas chromatography-mass spectrometry (GC-MS) showed that the monosaccharide composition was still composed of galactose and glucose in a molar ratio of 1.0:0.8, whereas high performance gel permeation chromatography (HPGPC) indicated that the molecular weight of EPS was increased from 4.62 × 105 Da to 9.17 × 105 Da by the over-expression of EpsC. In addition, S. thermophilus 05epsC which could produce higher molecular weight EPS improved the viscoelasticity and water-holding capacity of yogurt, but significantly reduced the level of syneresis in yogurt. In summary, these results indicated that homologous over-expression of EpsC in S. thermophilus could increase the molecular weight of EPS and improve the microrheological or physical properties of yogurt.

Glycosyltransferases are key enzymes involved in the assembly of repeating units of exopolysaccharides (EPS). A glycosyltransferase generally consists of the N-terminal and the C-terminal domain, however, the functional role of these domains in EPS biosynthesis remains largely unknown. In this study, homologous overexpression was employed to investigate the effects of EpsFN, a truncated form of rhamnosyltransferase EpsF with only the N-terminal domain, on EPS biosynthesis in Streptococcus thermophilus 05-34. Reverse transcription qPCR and Western blotting analysis confirmed the successful expression of epsFN in 05-34 at the transcription and translation level, respectively. Further analysis showed that the monosaccharide composition and yield of EPS were not affected by the overexpression of epsFN, whereas the molecular mass decreased by 5-fold. Accordingly, the transcription levels of genes involved in EPS biosynthesis, including chain-length determination gene epsC, were down-regulated by 5- to 6-fold. These results indicated that the N-terminal domain of EpsF alone could influence the molecular mass of EPS, probably via lowering the concentration of sugar precursors, which may lead to decreased expression of genes responsible for chain-length determination.