Robust Optimal Trajectory Planning for Robots by Stochastic Optimization

In the optimal control of industrial, field or service robots, the standard procedure is to determine first offline a reference trajectory and a feedforward control, based on some selected nominal values of the unknown stochastic model parameters, and to correct then the inevitable and increasing deviation of the state or performance of the robot from the prescribed state or performance of the system by online measurement and control actions. Due to the stochastic variations of the model parameters, increasing measurement and correction actions are needed during the process. By optimal stochastic trajectory planning (OSTP), based on stochastic optimization methods, the available a priori and sample information about the robot and its working environment is incorporated into the control process. Consequently, more robust reference trajectories and feedforward controls are obtained which cause much less online control actions. In order to maintain a high quality of the guiding functions, the reference trajectory and the feedforward control can be updated at some later time points such that additional information about the control process is available. After the presentation of the Adaptive Optimal Stochastic Trajectory Planning (AOSTP) procedure based on stochastic optimization methods, several numerical techniques for the computation of robust reference trajectories and feedforward controls under real-time conditions are presented. Additionally, numerical examples for a Manutec r3 industrial robot are discussed. The first one demonstrates real-time solutions of (OSTP) based on a sensitivity analysis of a before-hand calculated reference trajectory. The second shows the differences between reference trajectories based on deterministic methods and the stochastic methods introduced in this paper. Based on simulations of the robots behavior, the increased robustness of stochastic reference trajectories is demonstrated.     

Lefschetz pencil structures for 2-calibrated manifolds

We prove that for closed 2-calibrated manifolds there always exist Lefschetz pencil structures. This generalizes similar results for symplectic and contact manifolds. To cite this article: A. Ibort, D. Marti´nez Torres, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Photochemische Reaktionen. 78. Mitteilung. Anwendung der π → π*-induzierten Cyclisierung von α,β-ungesättigten γ-Dimethoxymethylketonen auf 19-Methoxy- bzw. 19-Dimethoxy-Steroid-enone und -dienone

Irradiation at 254 nm of 19-dimethoxyandrost-4-en-17 β-ol-3-one acetate ( 8 ) afforded the epimeric cyclization products 9 (yield 20%) and 10 (4%). Similar transformations were also achieved with the analogous dimethoxy-enone 24 (→ 25 , 65%), and-dienone 30 (→ 31 , 72%), and with the methoxy-enone 33 (→ 34 , 30%), and-dienone 35 (→ 36 , 17%).     

Synthesis and Structure of Functionalized Cyclododecadiynes and -dienes

The cyclododecadiynes 3b–d, 8b–d , and 10b–c with functionalities in two propargylic positions, as well as the monofunctionalized diyne 13b have been prepared from simple open-chain building blocks. In the DMPU ( = N,N'-dimethylpropyleneurea)-assisted ring-closing alkylation of 1,7-diynes, the twelve-membered ring compounds have been prepared in yields of 16–55%. The preparation of the diene-diyne 15 and the cyclododeca-5,11-diyne-1,4-dione 18 are described.     

Effects of the chain microstructure on the properties of polyketones terpolymers characterized by scanning force microscopy

A new approach is described to tailor properties of polyketones based on the controlled modification of the block structure by varying the polymerization process. Ethylene-propylene-CO (ECOPCO) terblock copolymers with similar composition but different chain microstructures have been synthesized using either preset polymerization (PSP) or pulsed-feed polymerization (PFP), respectively. Whereas by PSP an ABC-triblock structure is obtained, the PFP results in [AB]_n-multiblock structure. In this paper we investigate the influence of the chain microstructure on the mechanical behavior and the surface properties.SFM phase images display a phase-separated bulk morphology where triblock polymers due to the larger block lengths form coarser structures than the multiblock samples. If the ECO content is above 50%, partially crystalline lamellar structures can be found, which in case of the multiblock sample form a continuous network of lamellar-like ECO rich domains. All ECOPCO terpolymers reveal elastomeric behavior with an elastic recovery of at least 82% but tensile strength and elongation vary with the block length of the chain microstructures. Differences in elasticity are explained by the formation of different amounts of cross-links consisting of blocks of parallel-aligned ECO chain segments or crystalline lamellae. It can be shown that the surface morphology differs from bulk morphology, mainly by the point that no distinct phase separation appears but ECO rich domains can be detected. Surface tension measurements enable to correlate the surface energy with surface composition and surface morphology.     

A study of the plasma column with attention to the region near the wall

The ambipolar diffusion problem in a positive column is studied when charged particle inertia, heating and the mobility variation of positive ions in the radial electric field are taken into consideration. The atomic ion motion in their respective parent gases is approximated by the hard sphere model. The problem was also solved by approximate methods and compared with the precision numerical calculations. A simple formula for number density of charged particles at the boundary plasma-sheath was found.The authors would like to thank Professor .Veis for the support of this work. We are also grateful to Dr. I.Koinár and Dr. V.Jukl for their guidance in computer programming.     

Total synthesis of (-)-spirotryprostatin B: synthesis and related studies

The total synthesis of spirotryprostatin B, a cytostatic spiro[pyrrolidine-3,3'-oxindole] alkaloid, is described. The key step of the synthetic approach consists of the application of the MgI2-mediated ring-expansion reaction of a spiro[cyclopropane-1,3'-oxindole] with an aldimine, leading to rapid assembly of the spirotryprostatin core. The route documents the installation of the prenyl side chain by Julia-Kocieński olefination of a key aldehyde precursor, a transformation that ultimately allows for facile synthesis of analogues and facilitates structure-activity relationships studies.     

Orientation of the α- and γ-modification of elastic polypropylene at uniaxial stretching

New metallocene catalysts applied to propylene polymerization expand the range of properties of polypropylene (PP), resulting in semi-crystalline materials having crystallinities below 60% up to X-ray amorphous highly elastic ones. To date the origin of the unique elastic mechanical behavior of such low crystalline PP is not completely understood. Therefore, the microscopic orientation of those PPs due to uniaxial stretching was investigated using wide-(WAXS) and small-angle X-ray scattering (SAXS). The aim of this study was to correlate these orientations or changes in the developed fiber textures with the macroscopic stress-strain behavior. This includes efforts to come closer to the main question of the nature of the physical cross-links in these not chemical cross-linked homopolymers, which is the reason for the high elastic behavior. Therefore, high molecular weight metallocene PPs showing different crystallinities (0-36%) were stretched to several elongations and the structural changes during the deformation were recorded by X-ray scattering. Stress-strain measurements show the great potential of these PPs as a thermoplastic rubber material. For quantitative analysis and discussion of the polymer chain orientations, the orientation functions were calculated. Correlations between the orientation functions and the stress-strain curves allow an interpretation of the macroscopic behavior on a microscopic scale. A higher cross-linking density in elongated samples indicates that the network, which is responsible for the elasticity, mainly built up by strain-induced morphology changes and chain orientations.