Advanced quaternion forward kinematics algorithm including overview of different methods for robot kinematics

Formulisanje odgovarajućih i efikasnih algoritama kinematike robota je od suštinskog značaja za analizu i razvoj serijskih manipulatora. Kinematičko modelovanje manipulatora se najčešće vrši u Dekartovom prostoru. Međutim, usled nedostataka najzastupljenijih matematičkih operatora za definisanje orijentacije kao što su Ojlerovi uglovi i rotacione matrice, nameće se potreba za jednoznačnim, kompaktnim, računski efikasnim metodom za određivanje orijentacije. Kao rešenje ovog problema predlažu se jedinični kvaternioni kao i razvoj kinematičkih modela u prostoru dualnih kvaterniona. U ovom radu je dat pregled geometrijskih opisa i transformacija koje se mogu primeniti u okviru navedenih prostora kako bi se rešili problemi kinematike robota. Poseban akcenat je na različitim matematičkim formalizmima koji se koriste za definisanje orijentacije krutog tela, kao što su rotacione matrice, Ojlerovi uglovi, osa i ugao rotacije, jedinični kvaternioni, kao i na njihovoj uzajamnoj vezi. Prednosti kinematičkog modeliranja u prostoru kvaterniona su istaknute. Osobine jediničnih i dualnih kvaterniona se analiziraju sa stanovišta robotike. Takođe, dat je novi algoritam direktne kinematike robota u prostoru dualnih kvaterniona. Ovaj algoritam je primenjen na humanoj centrifugi koja je modelirana kao troosni manipulator.Formulation of proper and efficient algorithms for robot kinematics is essential for the analysis and design of serial manipulators. Kinematic modeling of manipulators is most often performed in Cartesian space. However, due to disadvantages of most widely used mathematical constructs for description of orientation such as Euler angles and rotational matrices, a need for unambiguous, compact, singularity free, computationally efficient method for representing rotational information is imposed. As a solution, unit quaternions are proposed and kinematic modeling in dual quaternion space arose. In this paper, an overview of spatial descriptions and transformations that can be applied together within these spaces in order to solve kinematic problems is presented. Special emphasis is on a different mathematical formalisms used to represent attitude of a rigid body such as rotation matrix, Euler angles, axis-angle representation, unit quaternions, and their mutual relation. Benefits of kinematic modeling in quaternion space are presented. New direct kinematics algorithm in dual quaternion space pertaining to a particular manipulator is given. These constructs and algorithms are demonstrated on the human centrifuge as 3 DoF robot manipulator

Advanced quaternion forward kinematics algorithm including overview of different methods for robot kinematics

Formulisanje odgovarajućih i efikasnih algoritama kinematike robota je od suštinskog značaja za analizu i razvoj serijskih manipulatora. Kinematičko modelovanje manipulatora se najčešće vrši u Dekartovom prostoru. Međutim, usled nedostataka najzastupljenijih matematičkih operatora za definisanje orijentacije kao što su Ojlerovi uglovi i rotacione matrice, nameće se potreba za jednoznačnim, kompaktnim, računski efikasnim metodom za određivanje orijentacije. Kao rešenje ovog problema predlažu se jedinični kvaternioni kao i razvoj kinematičkih modela u prostoru dualnih kvaterniona. U ovom radu je dat pregled geometrijskih opisa i transformacija koje se mogu primeniti u okviru navedenih prostora kako bi se rešili problemi kinematike robota. Poseban akcenat je na različitim matematičkim formalizmima koji se koriste za definisanje orijentacije krutog tela, kao što su rotacione matrice, Ojlerovi uglovi, osa i ugao rotacije, jedinični kvaternioni, kao i na njihovoj uzajamnoj vezi. Prednosti kinematičkog modeliranja u prostoru kvaterniona su istaknute. Osobine jediničnih i dualnih kvaterniona se analiziraju sa stanovišta robotike. Takođe, dat je novi algoritam direktne kinematike robota u prostoru dualnih kvaterniona. Ovaj algoritam je primenjen na humanoj centrifugi koja je modelirana kao troosni manipulator.Formulation of proper and efficient algorithms for robot kinematics is essential for the analysis and design of serial manipulators. Kinematic modeling of manipulators is most often performed in Cartesian space. However, due to disadvantages of most widely used mathematical constructs for description of orientation such as Euler angles and rotational matrices, a need for unambiguous, compact, singularity free, computationally efficient method for representing rotational information is imposed. As a solution, unit quaternions are proposed and kinematic modeling in dual quaternion space arose. In this paper, an overview of spatial descriptions and transformations that can be applied together within these spaces in order to solve kinematic problems is presented. Special emphasis is on a different mathematical formalisms used to represent attitude of a rigid body such as rotation matrix, Euler angles, axis-angle representation, unit quaternions, and their mutual relation. Benefits of kinematic modeling in quaternion space are presented. New direct kinematics algorithm in dual quaternion space pertaining to a particular manipulator is given. These constructs and algorithms are demonstrated on the human centrifuge as 3 DoF robot manipulator

The application of benthic diatoms in water quality assessment (Mlava River, Serbia)

The main objective of this study was to assess the ecological status of the Mlava River based on epilithic diatoms and to test the use of diatom indices as a tool for estimating the quality of flowing waters in Serbia. Quantitative analysis showed that in April Achnanthidium minutissimum was dominant at each site, except at the fi fth site, where Amphora pediculus was dominant. In July and September, Achnanthidium minutissimum, Achnanthidium pyrenaicum, Amphora pediculus, Denticula tenuis, Diatoma vulgaris, Gomphonema elegantissimum, Cocconeis pseudolineata and Cocconeis placentula var. lineata dominated. Detrended correspondence analysis (DCA) was used to detect the major patterns of variation in species composition. The first DCA axis summarizes the distribution of the diatom community, mainly through temperature, conductivity, oxygen and water hardness gradient. The second DCA axis was weakly correlated with few variables. Based on the average values of the pollution sensitivity index (IPS), commission for economical community metric (CEE) and biological diatom index (IBD), the water of the Mlava River belonged to water class I during all three seasons. Values of the diatom-based eutrophication/pollution index (EPI-D) indicated class II water quality. According to calculated trophic diatom index (TDI) values, water of the Mlava River was characterized by intermediate nutrient concentrations during three seasons. Principal components analysis was used to represent the correlation between diatom indices, and the highest correlation among the selected diatom indices is seen between EPI-D, IPS and IBD

PARP-1 and YY1 Are Important Novel Regulators of CXCL12 Gene Transcription in Rat Pancreatic Beta Cells

Despite significant progress, the molecular mechanisms responsible for pancreatic beta cell depletion and development of diabetes remain poorly defined. At present, there is no preventive measure against diabetes. The positive impact of CXCL12 expression on the pancreatic beta cell prosurvival phenotype initiated this study. Our aim was to provide novel insight into the regulation of rat CXCL12 gene (Cxcl12) transcription. The roles of poly(ADP-ribose) polymerase-1 (PARP-1) and transcription factor Yin Yang 1 (YY1) in Cxcl12 transcription were studied by examining their in vitro and in vivo binding affinities for the Cxcl12 promoter in a pancreatic beta cell line by the electrophoretic mobility shift assay and chromatin immunoprecipitation. The regulatory activities of PARP-1 and YY1 were assessed in transfection experiments using a reporter vector with a Cxcl12 promoter sequence driving luciferase gene expression. Experimental evidence for PARP-1 and YY1 revealed their trans-acting potential, wherein PARP-1 displayed an inhibitory, and YY1 a strong activating effect on Cxcl12 transcription. Streptozotocin (STZ)-induced general toxicity in pancreatic beta cells was followed by changes in Cxcl12 promoter regulation. PARP-1 binding to the Cxcl12 promoter during basal and in STZ-compromised conditions led us to conclude that PARP-1 regulates constitutive Cxcl12 expression. During the early stage of oxidative stress, YY1 exhibited less affinity toward the Cxcl12 promoter while PARP-1 displayed strong binding. These interactions were accompanied by Cxcl12 downregulation. In the later stages of oxidative stress and intensive pancreatic beta cell injury, YY1 was highly expressed and firmly bound to Cxcl12 promoter in contrast to PARP-1. These interactions resulted in higher Cxcl12 expression. The observed ability of PARP-1 to downregulate, and of YY1 to upregulate Cxcl12 promoter activity anticipates corresponding effects in the natural context where the functional interplay of these proteins could finely balance Cxcl12 transcription

Diatom species composition in the Raška river (Southwestern Serbia)

The paper presents data on the composition of epilithic diatoms in the Raška River. Samples were collected by scraping stone surfaces with a brush from 5 localities along the Raška River in April, June, August and November 2011 and March and May 2012. Diatom frustules were cleaned using cold acid method, and mounted on permanent slides. An investigation of the Raška River resulted in description of 106 diatom taxa. The most species rich genera are Navicula (10), Gomphonema (10) and Nitzschia (9), while other genera are presented with one or more species. Detailed floristic analysis of the benthic diatom flora in this river has not been conducted before. Therefore, this paper provides a groundwork for future researches. [Projekat Ministarstva nauke Republike Srbije, br. TR 037009

Procedure for definition of end-effector orientation in planar surfaces robot applications

Design of user-friendly and at the same time powerful robot programming methods is the subject of significant efforts undertaken by the international robotics community. For the purpose of facilitating robot programming, with regard to the most common present-day applications in industry, it would be useful to develop programming procedures for frequently used manipulator tasks which could be easily implemented and used as ready-made application software. Important class of industrial robot applications involves end-effector trajectories in planar surfaces. Development of robot programming language procedure intended for determination of object plane normal with respect to frame of interest, as well as programming of end-effector orientation is presented in this paper. This procedure can be used as integral part of task oriented robot programing applications as well as a procedure for explicit programming languages, and it is illustrated in practical example with the robot Lola 15