Designing Continuously Constrained Spacecraft Relative Trajectories for Proximity Operations

Abstract : This paper presents a new method for designing an optimal plan of impulsive maneuvers for spacecraft proximity operations. The proposed method accounts for the presence of linear continuous constraints on the spacecraft relative trajectory. Impulsive control and continuous constraints are brought together through the parameterization of the spacecraft relative trajectory between two consecutive maneuvers. This parameterization is used in order to develop a finite convex description of all the admissible trajectories. It enables the transformation of the continuous constraints on the spacecraft relative trajectory into a finite number of polynomial nonnegativity constraints. The resulting optimal control problem can be solved using semidefinite programming.