Five-Dimensional Warped Product Space-Time with Time-Dependent Warping and a Scalar Field in the Bulk

We consider gravity in a five-dimensional warped product space-time, with a time-dependent warp factor and a time-dependent extra dimension. The five-dimensional field equations are derived for a spatially flat FRW brane, and the energy conditions and the nature of bulk geometry are examined. It is found that the expansion of the four-dimensional universe depends on its location along the extra dimension and is different at different locations in the bulk space-time. At low energies, the trapping of fields within the brane implies a specific correlation between the warp factor and the extra-dimensional scale factor. Generally, the bulk is not conformally flat. At high energies, the bulk is assumed to be sourced by a scalar field with self-interaction. The analysis shows that the potential of the scalar field source of gravity at a given position along the fifth dimension is related to the Hubble parameter on the brane at that position in the bulk.     

A multi-item transportation problem with mode of transportation preference by MCDM method in interval type-2 fuzzy environment

Neural Computing and Applications - In this paper, we employ all the parameters as trapezoidal interval type-2 fuzzy numbers to cope with ambiguity and vagueness problem. There are two issues being...     

Attitude Controller for Steady Hover of a Rotary-Wing Flying Robot

This paper presents an attitude controller for steady hover of CMERI’s Rotary-Wing Flying Robot. The main objective is to control the dynamic behaviour of the robot, which is complex in shape and motion as nonlinear aerodynamic forces and gravity acts on the system. Due to limited accuracy of the dynamic model, the attitude dynamics is conditionally stable where a minimum amount of attitude feedback is required for system stability. To compensate for conditional stability with improved disturbance rejection, an attitude controller is developed adopting cascade control loop architecture. The INS system feedback is used for outer control loop while the gyro feedback is adopted for the inner control loop to attain a high bandwidth, ensuring attitude stability with accelerated response required for a steady hover. The defined controller has introduced corrective control to mitigate the disturbance as sensed by the gyros before they actually do affect the output as the cascade control loop is more responsive than simply the INS loop feedback. In the proposed approach, the robot is modelled using well known “NASA Minimum Complexity Math Model” where robot dynamics is decoupled into Single Input Single Output system. Kalman filter is used to estimate the attitude from the high frequency based gyros aided by INS system feedback data while a matched pole-zero method is used to perform discretization. The stability of the system is evaluated using closed loop identification. The provided solution is tested on Hirobo Scheadu50 model and the system performance is analyzed using the proposed controller.