Continuous-thrust collision avoidance manoeuvres optimization

In the last few decades, space debris have become one of the most important hazards for space activities; preventing their formation is the best mitigation option, and avoiding an impact can be of fundamental importance for a mission’s success. This study proposes four methods to design a continuous-thrust collision avoidance manoeuvre (CAM), which have been developed in the perspective of finding a fast and reliable approach, suitable for on-board implementation. The objective function to be minimized is the collision probability at the nominal time of closest approach. The first approach consists in the conversion from an analytical fuel-optimal impulsive manoeuvre to a finite-burn arc through an indirect optimal control model. In the second and third approach the collision probability is considered as a terminal constraint in a minimum-fuel or minimum-energy optimal control problem. These first three approaches require time consuming numerical iterations. The last method is based on the linearisation of the energy optimal problem resulting in a semi-analytical method. All these approaches are compared in terms of efficiency and robustness in a simulated scenario with Keplerian and circular orbits.