ANALYTICAL ALGEBICAL VIBRANT ANALYSIS

CSE

An overview is presented on the current status of main mathematical computation methods for the multiloop corrections to single-scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present, massless single-scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero-scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods. Researchers often deal with the synthesis of the kinematic structure of a robotic manipulator to determine the optimal manipulator for a given task. This approach can lower the cost of the manipulator and allow it to achieve poses that might be unreachable by universal manipulators in an existing constrained environment. Numerical methods are broadly used to find the optimum design but they often require an estimated initial kinematic structure as input, especially if local-optimum-search algorithms are used. This paper presents four different algorithms for such an estimation using the standard Denavit-Hartenberg convention. Two of the algorithms are able to reach a given position and the other two can reach both position and orientation using Bezier splines approximation and vector algebra. The results are demonstrated with three chosen example poses and are evaluated by measuring manipulability and the total link length of the final kinematic structures.

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