Kinematic sensitivity of robot manipulators

Kinematic sensitivity vectors and matrices for open-loop, n degrees-of-freedom manipulators are derived. First-order sensitivity vectors are defined as partial derivatives of the manipulator's position and orientation with respect to its geometrical parameters. The four-parameter kinematic model is considered, as well as the five-parameter model in case of nominally parallel joint axes. Sensitivity vectors are expressed in terms of coordinate axes of manipulator frames. Second-order sensitivity vectors, the partial derivatives of first-order sensitivity vectors, are also considered. It is shown that second-order sensitivity vectors can be expressed as vector products of the first-order sensitivity vectors

Elastic and Diffractive Scattering after AdS/CFT

At high energies, elastic hadronic cross sections are believed to be dominated by vacuum exchange. In leading order of the leading $1/N_c$ expansion this exchange process has been identified as the BFKL {\em Pomeron} or its strong AdS dual the closed string graviton \cite{Brower:2006ea}. However difference of particle anti-particle cross sections are given by a so-called {\em Odderon} carrying C = -1 quantum numbers identified in weak coupling with odd numbers of exchanged gluons. Here we show that the dual description associates this with the Neveu-Schwartz ($B_{\mu\nu}$) sector of closed string theory. We also discuss the extension of the strong coupling treatment to central diffractive Higgs production at LHC.Comment: 7 pages, 3 figures; presented at International Conference on Elastic and Diffractive Scattering, EDS'09, CERN, July 3, 200

Saturation and Confinement: Analyticity, Unitarity and AdS/CFT Correspondence

In $1/N_c$ expansion, analyticity and crossing lead to crossing even and odd ($C=\pm 1$) vacuum exchanges at high-energy, the {\em Pomeron} and the {\em Odderon}. We discuss how, using {\em String/Gauge duality}, these can be identified with a reggeized {\em Graviton} and the anti-symmetric {\em Kalb-Ramond fields} in $AdS$ background. With confinement, these Regge singularities interpolate with glueball states. We also discuss unitarization based on eikonal sum in $AdS$.Comment: more references added. presented at ISMD 2008, 15-20 Sept. 200