Effective computation of singularities of parametric affine curves

AbstractLet k be a field of characteristic zero and f(t),g(t) be polynomials in k[t]. For a plane curve parameterized by x=f(t),y=g(t), Abhyankar developed the notion of Taylor resultant (Mathematical Surveys and Monographs, Vol. 35, American Mathematical Society, Providence, RI, 1990) which enables one to find its singularities without knowing its defining polynomial. This concept was generalized as D-resultant by Yu and Van den Essen (Proc. Amer. Math. Soc. 125(3) (1997) 689), which works over an arbitrary field. In this paper, we extend this to a curve in affine n-space parameterized by x1=f1(t),…,xn=fn(t) over an arbitrary ground field k, where f1,…,fn∈k[t]. This approach compares to the usual approach of computing the ideal of the curve first. It provides an efficient algorithm of computing the singularities of such parametric curves using Gröbner bases. Computational examples worked out by symbolic computation packages are included

Representation and control of coordinated-motion tasks for human-robot systems

It is challenging for robots to perform various tasks in a human environment. This is because many human-centered tasks require coordination in both hands and may often involve cooperation with another human. Although human-centered tasks require different types of coordinated movements, most of the existing methodologies have focused only on specific types of coordination. This thesis aims at the description and control of coordinated-motion tasks for human-robot systems; i.e., humanoid robots as well as multi-robot and human-robot systems. First, for bimanually coordinated-motion tasks in dual-manipulator systems, we propose the Extended-Cooperative-Task-Space (ECTS) representation, which extends the existing Cooperative-Task-Space (CTS) representation based on the kinematic models for human bimanual movements in Biomechanics. The proposed ECTS representation can represent the whole spectrum of dual-arm motion/force coordination using two sets of ECTS motion/force variables in a unified manner. The type of coordination can be easily chosen by two meaningful coefficients, and during coordinated-motion tasks, each set of variables directly describes two different aspects of coordinated motion and force behaviors. Thus, the operator can specify coordinated-motion/force tasks more intuitively in high-level descriptions, and the specified tasks can be easily reused in other situations with greater flexibility. Moreover, we present consistent procedures of using the ECTS representation for task specifications in the upper-body and lower-body subsystems of humanoid robots in order to perform manipulation and locomotion tasks, respectively. Besides, we propose and discuss performance indices derived based on the ECTS representation, which can be used to evaluate and optimize the performance of any type of dual-arm manipulation tasks. We show that using the ECTS representation for specifying both dual-arm manipulation and biped locomotion tasks can greatly simplify the motion planning process, allowing the operator to focus on high-level descriptions of those tasks. Both upper-body and lower-body task specifications are demonstrated by specifying whole-body task examples on a Hubo II+ robot carrying out dual-arm manipulation as well as biped locomotion tasks in a simulation environment. We also present the results from experiments on a dual-arm robot (Baxter) for teleoperating various types of coordinated-motion tasks using a single 6D mouse interface. The specified upper- and lower-body tasks can be considered as coordinated motions with constraints. In order to express various constraints imposed across the whole-body, we discuss the modeling of whole-body structure and the computations for robotic systems having multiple kinematic chains. Then we present a whole-body controller formulated as a quadratic programming, which can take different types of constraints into account in a prioritized manner. We validate the whole-body controller based on the simulation results on a Hubo II+ robot performing specified whole-body task examples with a number of motion and force constraints as well as actuation limits. Lastly, we discuss an extension of the ECTS representation, called Hierarchical Extended-Cooperative-Task Space (H-ECTS) framework, which uses tree-structured graphical representations for coordinated-motion tasks of multi-robot and human-robot systems. The H-ECTS framework is validated by experimental results on two Baxter robots cooperating with each other as well as with an additional human partner

Convergence Properties of Analytical Target Cascading

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77196/1/AIAA-2002-5506-996.pd

A Criticality Analysis of the GBC-32 Dry Storage Cask with Hanbit Nuclear Power Plant Unit 3 Fuel Assemblies from the Viewpoint of Burnup Credit

AbstractNuclear criticality safety analyses (NCSAs) considering burnup credit were performed for the GBC-32 cask. The used nuclear fuel assemblies (UNFAs) discharged from Hanbit Nuclear Power Plant Unit 3 Cycle 6 were loaded into the cask. Their axial burnup distributions and average discharge burnups were evaluated using the DeCART and Multi-purpose Analyzer for Static and Transient Effects of Reactors (MASTER) codes, and NCSAs were performed using SCALE 6.1/STandardized Analysis of Reactivity for Burnup Credit using SCALE (STARBUCS) and Monte Carlo N-Particle transport code, version 6 (MCNP 6). The axial burnup distributions were determined for 20 UNFAs with various initial enrichments and burnups, which were applied to the criticality analysis for the cask system. The UNFAs for 20- and 30-year cooling times were assumed to be stored in the cask. The criticality analyses indicated that keff values for UNFAs with nonuniform axial burnup distributions were larger than those with a uniform distribution, that is, the end effects were positive but much smaller than those with the reference distribution. The axial burnup distributions for 20 UNFAs had shapes that were more symmetrical with a less steep gradient in the upper region than the reference ones of the United States Department of Energy. These differences in the axial burnup distributions resulted in a significant reduction in end effects compared with the reference

Hierarchical overlapping coordination under nonlinear constraints

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76760/1/AIAA-1998-4795-679.pd

Influence of bank geometry on the electrical characteristics of printed organic field-effect transistors

The electrical characteristics of organic field-effect transistors (OFETs) based on small-molecule organic semiconductors (OSCs) have been significantly improved by employing various fabrication techniques in solution processes to enhance the OSC crystallinity. However, complicated fabrication and inhomogeneity of OFETs remain as challenges before commercialization. In this work, we have efficiently controlled the size and orientation of 6,13-bis(triisopropylsilylethynyl)-pentacene (TIPS-pentacene) crystalline domains by tuning the Cytop bank dimension, in which OSC inks are printed, to improve the device performance. The optimized bank pattern forms uniform thin film morphology and well-aligned TIPS-pentacene crystalline domains along the charge transport direction, resulting in four-fold increase in field-effect mobility and one third reduction in relative standard deviation.11Ysciescopu

Groebner bases and multidimensional FIR multirate systems

The polyphase representation with respect to sampling lattices in multidimensional (M-D) multirate signal processing allows us to identify perfect reconstruction (PR) filter banks with unimodular Laurent polynomial matrices, and various problems in the design and analysis of invertible MD multirate systems can be algebraically formulated with the aid of this representation. While the resulting algebraic problems can be solved in one dimension (1-D) by the Euclidean Division Algorithm, we show that Gröbner bases offers an effective solution to them in the M-D case