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As a result of the increasing number of satellites in Earth orbit and the continuous rise of potential for bigger payloads, notably due to the accelerated growth of the private sector, there are many new application areas. An important step for effectively using a multitude of satellites in a large-scale project is the navigational autonomy, meaning that the calculation and optimization of the trajectory takes place on-board the spacecraft. There are already semi-autonomous micro-satellites in operation like the PROBA satellite (ESA) which can complete tasks like attitude control, target identification during fly-by as well as taking pictures. These kind of micro-satellites are specially designed and developed for autonomous service. If the autonomy of trajectory calculation could be realised onboard a spacecraft which where not explicitly designed for this mode of operation, tasks like onorbit- assembly (OOA) or on-orbit-servicing (OOS) could be solved flexibly and with high efficiency. The limiting factor is the low processing power of spaceborne microprocessors which require scalable algorithms to solve the calculations to a sufficient degree of accuracy. For this reason a new approach to describing position and attitude via Bézier curves is examined in this paper. The motivation comes from Bézier curves having a low computing time due to their mathematically simple structure, which is why they are being used in computeraided design (CAD) programs and in general computer graphics almost exclusively. Another important part of calculation are the boundary conditions which ensure the protection of the instruments, avoiding collisions as well as aligning tools and cameras at specific targets during fly-by. The objective is to keep the processing power of the optimization process under the given constraints as low as possible by using Bézier curves to describe the trajectory. Furthermore, an analysis of the model [...]