Analytical Guidance for Circular Orbit Transfers with Staging of Space Propulsion Systems

Abstract

This paper considers the combination of an analytical reference trajectory with linear state feedback control to allow for autonomous guidance and control of a spacecraft for coplanar circle-to-circle transfers with a stage-based propulsion system. Staging of electric propulsion components, such as tanks and thrusters, could allow small spacecraft to achieve high-V capabilities with current propulsion technology. In order to utilize these propulsion systems, further developments in guidance and control of such spacecraft are required due to limitations in computational power and communications. Analytical approximations for low-thrust trajectories could allow for computationally simple guidance and control of autonomous spacecraft for circle-to-circle transfers around large central bodies. Many trajectories have been developed for conventional propulsion systems, based either on their shape or input thrust, and applied for preliminary mission design. A previously developed analytical trajectory is extended to account for the effects of staging propulsion system components. In order to stabilize the trajectory in the presence of disturbances, a linear state feedback control law is designed with linear quadratic regulator methods. Finally, a methodology for determining the correct phasing between the spacecraft and a target object is developed and is practical to implement on power-limited computers. The use of the analytical reference trajectory is simulated on an orbit transfer from low-Earth orbit to geostationary orbit.