This dissertation proposes analytic tools for dynamics and control problems in the perspective of large-scale relative motion without perturbations. Specifically, we develop an exact and efficient analytic solution of satellite relative motion using a direct geometrical approach in spherical coordinates. The resulting solution is then transformed into general parametric equations of cycloids and trochoids. With this transformation, the dissertation presents new findings for design rules and classifications of closed and periodic parametric relative orbits. A new observation from the findings states that the orbit shape resulting from the relative motion dynamics of circular orbit cases in polar views are exactly the same as the parametric curves of cycloids and trochoids. The dynamics problem of satellite relative motion is expanded to include the design of satellite constellations for multiple satellite systems. A Parametric Constellation (PC) is developed to create an identical constellation pattern, or repeating space track, of target satellites with respect to a base satellite. In this PC theory, the number of target satellites is distributed using a real number system for node spacing. While using a base satellite orbit as the rotating reference frame, the PC theory consists of satellite phasing rules and closed form formulae for designing repeating space tracks. The evaluation of the PC theory is illustrated through it’s comparison to the existing Flower Constellation theory in terms of node spacing distribution and constellation design process. For the control problems, the efficient analytic solution is applied to the reference trajectory of satellite relative tracking control systems for inter-satellite links. Two types of relative tracking control systems are developed and each is evaluated to determine which is more appropriate for practical applications of inter-satellite links. All of the proposed analytic solutions and tools in this dissertation will be useful for the mission analysis and design of relative motions involving a two or more satellite system. / Ph. D.

Formation flying of satellites describes a mission in which a set of satellites arrange their position with respect to one another. In this paper, satellite formation flying guidance and control algorithms are investigated in terms of required velocity increment Delta-v, and tracking error for a Chief/Deputy satellite system. Different control methods covering continuous and impulsive laws are implemented and tested for Low Earth Orbit (LEO). Sliding Mode, Feedback Linearization and Model Predictive Controllers are compared to an Impulsive Feedback Law which tracks the mean orbital element differences. Sliding Mode and Feedback Linearization controllers use the same dynamic model which includes Earth Oblateness perturbations. On the other hand, Model Predictive Control with Multi-Objective Cost Function is based on the Clohessy–Wiltshire equations, which do not account for any perturbation and do not cover the eccentricity of the orbit. The comparison was done for two different missions both including Earth Oblateness effects only. A relative orbit mission, which was based on the Prisma Satellite Mission and a rendezvous mission, was implemented. The reference trajectory for the controllers was generated with Yamanaka and Ankersen’s state transition matrix, while a separate method was used for the Impulsive Law. In both of the missions, it was observed that the implemented Impulsive Law outperformed in terms of Delta-v, 1.2 to 3.5 times smaller than the continuous control approaches, while the continuous controllers had a smaller tracking error, 2 to 8.3 times less, both in terms of root mean square error and maximum error in the steady state. Finally, this study shows that the tracking error and Delta-v has inversely proportional relationship. / Formationsflygning av satelliter innebär att en grupp satelliter flyger tillsammans och anpassar sina relativa lägen i förhållande till varandra. I detta examensarbete studerades regleralgoritmer för formationsflygande satelliter med fokus på bränsleförbrukning och positionsavvikelse genom ”Chief & Deputy”-metoden. Olika reglermetoder har studerats, t.ex. Sliding Mode- och Feedback Linearization-reglering för formationsflygningsfall i låg jordbana med J2-störning samt en Model Predictive-reglering för fall med relativ rörelse baserad på Clohessy-Wiltshire-ekvationerna. Vidare studerades en reglermetod baserad på impulsframdrivning. De fyra reglermetoderna implementerades på två olika rymduppdrag. Först ett uppdrag baserat på Prisma-satelliterna för två satelliter i relativ omloppsbana och sedan ett Rendezvous-uppdrag. Referensbanan för alla reglermetoder, utom för implusmetoden, har tagits fram med hjälp av Yamanakas och Ankersens tillståndsmatris. Resultaten visar att den implementerade impulsmetoden presterar bättre med avseende på bränsleförbrukning, medan de kontinuerliga reglermetoderna producerade mindre relativ positionsavvikelse, både med avseende på kvadratiskt medelvärde och maximalt värde.