AUTOMATIC FAIRING OF TWO-PARAMETER RATIONAL B-SPLINE MOTION

This paper deals with the problem of automatic fairing of two-parameter B

Noise smoothing for VR equipment in quaternions

Smooth motion generation is an important issue in the computer animation and virtual reality (VR) area. In general, the motion of a rigid body consists of translation and orientation. The former is described by a space curve in 3-dimensional Euclidean space, while the latter is represented by a curve in the unit quaternion space. Although there are well-known techniques for smoothing the translation curve in the Euclidean space, few results have been reported for smoothing motion as a whole. This paper improves the previous study and provides a more robust algorithm, which seeks to minimize the weighted sum of the strain-energy and the sum of the squared errors.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45883/1/10756_2004_Article_206666.pd

Diskrete Spin-Geometrie für Flächen

This thesis proposes a discrete framework for spin geometry of surfaces. Specifically, we discretize the basic notions in spin geometry, such as the spin structure, spin connection and Dirac operator. In this framework, two types of Dirac operators are closely related as in smooth case. Moreover, they both induce the discrete conformal immersion with prescribed mean curvature half-density.In dieser Arbeit wird ein diskreter Zugang zur Spin-Geometrie vorgestellt. Insbesondere diskretisieren wir die grundlegende Begriffe, wie zum Beispiel die Spin-Struktur, den Spin-Zusammenhang und den Dirac Operator. In diesem Rahmen sind zwei Varianten für den Dirac Operator eng verwandt wie in der glatten Theorie. Darüber hinaus induzieren beide die diskret-konforme Immersion mit vorgeschriebener Halbdichte der mittleren Krümmung

Ballbot-Inspired orbital refueling depot and fluid-slosh effects on Spacecraft attitude dynamics

Orbital refueling has become a subject of increasing interest as longer, deep space missions and manned missions to the Moon and Mars are being contemplated once again. For fueling depots to become part of the infrastructure in space capable of enhancing deployment and service operations, there remains a slew of technical, operational, and engineering challenges which must be overcome. In this thesis, focus is placed mainly on the issue of fluid slosh and its effects on the spacecraft dynamics and the design of an attitude control system. In pursuit of overcoming the attitude tracking errors and instability from the fluid slosh, a novel satellite design is presented based on an omnidirectional ball-balanced robot (ball-bot) which aims at minimizing the control effort required to stabilize the satellite while also maximizing the amount of fuel it can carry. The satellite is comprised of two primary elements: a spherical tank, containing the fuel payload and a cuboid bus, containing the attitude control system (ACS) and other subsystems. The satellite bus is mobile and can displace itself over the surface of the sphere and has a sunshield which is deployed in orbit which shields the spherical tank from solar radiation. The cube is mobile and can displace itself on the surface of the sphere to point to the sun ensuring the protection of the fuel payload. A presentation of the state-of-the-art of orbital fuel depots is first presented, and subsequently, a contextualization of orbital dynamics, along with the mathematical modeling of the satellite, is carried out, complemented by a discussion about the limitations of the work and the assumptions of the model. A simulation of the satellite¿s dynamics with the fluid slosh is conducted using Simulink and the sun-tracking of the cuboid-bus with Mathematica. Finally, a set of conclusions are presented and recommendations for future research and improvements, based on the conclusions, are made.Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructur

Energy management of three-dimensional minimum-time intercept

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission

Fuzzy-Model-Based (FMB) Control of a Spacecraft with Fuel Sloshing Dynamics

During the upper-stage separation and orbit injection, orbital control, and attitude maneuver, propellant slosh in partially-filled fuel tanks can cause dynamical instability or pointing errors. The spacecraft dynamics combined with propellant sloshing results in a highly nonlinear and coupled dynamic system that requires a complicated control law. This problem has been a long-standing concern for space missions. The purpose of this research is two fold. The first part is to investigate and develop nonlinear Takagi-Sugeno (T-S) fuzzy model-based controllers for a spacecraft with fuel sloshing considering the input constraints on the actuators. It includes i) a fuzzy controller/observer with a minimum upper-bound control input based on the parallel-distributed compensation (PDC) technique, ii) a fuzzy controller/observer based on the linear quadratic regulator (LQR) that uses the premises of the T-S model, and iii) a robust-optimal fuzzy-model-based controller/observer. The designed controllers are globally asymptotically stable and have a satisfactory performance and robustness. The second part of the research is to develop a mathematical model of a spinning spacecraft with fuel sloshing during high-g maneuvers. The equations of motion of a spacecraft with partially-filled multiple-tanks are derived using the Kane’s method. To do this, two spherical pendulums as an equivalent mechanical model of the fuel sloshing are adopted. The effect of the slosh model parameters on the spacecraft nutation angle is studied. The developed model is validated via several numerical simulations