Browsing by Author "Roberts, Jennifer A."

Now showing 1 - 3 of 3
  • Thumbnail Image
    ItemOpen Access
    Development of a relative motion model for satellite formation flying around L2
    (Cranfield University; School of Engineering, 2004-12-18T10:57:38Z) Roberts, Jennifer A.
    A technique for satellite formation flying modelling in LEO is applied at L2. Analytical solutions to the equations of motion of a hub satellite relative to L2 are used to define a halo reference orbit. An expression for the gravity gradient is obtained at the hub and the linearised equations of motion of the mirror satellites relative to the hub are derived. The relative motion model is implemented in Matlab/Simulink and evaluated for different initial conditions. The analytical solutions to the equations of relative motion are derived. These and other equations of motion are compared to the Satellite Tool Kit numerical orbit propagator.
  • Thumbnail Image
    ItemOpen Access
    The Development of high fidelity linearized J2 models for satellite formation flying control
    (2005-02-16T00:00:00Z) Roberts, Jennifer A.; Roberts, Peter C. E.
    The inclusion of the linearized J2 effect in the Hill equations of relative motion gives greater insight into satellite formation flying dynamics, and the opportunity to investigate alternative feedback control strategies for the station keeping task. The work of Schweighart and Sedwick is verified and extended as time varying and analytical models are developed to incorporate the J2 perturbation and its effects on the relative motion of two or more satellites in LEO. Analysis is performed in detail to determine the best modelling strategy for satellite formation keeping in the J2 perturbed environment. The analytical J2 model is found to capture relative motion the most accurately, but only given specific initial conditions. The time varying model captures leader-follower motion better than the Hill equation and analytical J2 models. LQR control laws are designed and performance evaluated for the basic Hill equations and the time varying and analytical J2 models using Matlab/Simulink and the Satellite Tool Kit.
  • Thumbnail Image
    ItemOpen Access
    Satellite formation flying for an interferometry mission
    (Cranfield University, 2005-10) Roberts, Jennifer A.; Hobbs, S. E.
    The autonomous formation flying of multiple spacecraft to replace a single large satellite will be an enabling technology for many future missions. In this research, the current status of formation flying missions and technologies is determined, and the Darwin nulling interferometry mission, which aims to detect and characterise extrasolar planets, is selected as the research focus. Darwin requires high precision formation flying of multiple telescopes near the Sun-Earth L2 point. A comprehensive account of current research in astrobiology is presented which provides the motivation for a Darwin-type mission. Astrobiology is integral to the definition of formation manoeuvres and target identification. The system design issues associated with developing a higher resolution, Planet Imager mission are also explored through a preliminary mission design. Relative dynamics models for satellite formation flying control in Low Earth Orbit (LEO) and L2 are developed and methods of incorporating the Earth oblateness perturbation (J2) into the equations of relative motion to improve model fidelity are investigated. The linearised J2 effect is included in the Hill equations in time averaged and time varying form. The models are verified against the Satellite Tool Kit (STK) numerical orbit propagator, and applied to optimal control system design and evaluation for formation keeping tasks. The ‘reference orbit’ modelling approach applied in LEO is applied to the development of a new formation flying model at L2. In this case, linearised equations of motion of the mirror satellites relative to the hub are derived and performance evaluated for different initial conditions. These and other higher order models are compared to STK. The linearised model is applied to controller design for station keeping and formation manoeuvring tasks suitable for a Darwin-type mission, and the role of the model in developing controllers for a load levelling guidance system is explored.