ANALYTICAL GUIDANCE FOR SPACECRAFT RELATIVE MOTION UNDER CONSTANT THRUST USING RELATIVE ORBIT ELEMENTS

This paper introduces novel analytical guidance solutions for spacecraft relative motion considering continuous, on-off thrust, and using Relative Orbit Elements as a geometrical representation of the dynamics. The solutions provide the relative state vector at any given time, accommodating any thrust magnitude along the three directions of the relative frame, as well as generic activation times and durations. Relative Orbit Elements geometrically interpret key aspects of the relative motion, including for example, the relative ellipse size, and the evolution of its center in time. The new solutions provide the guidance designer with a direct visualization of the thrust effects on the relative motion geometry, offering new possibilities for analytical guidance in the presence of continuous thrust engines, such as low thrust engines on nano-spacecraft. The paper presents the analytical solutions, and tests their effectiveness using a sample guidance thrust profile based on input-shaping, previously developed by one of the authors using classical Cartesian coordinates. The use of Relative Orbit Elements shows substantial benefits and added simplicity with respect to Cartesian-based approaches.