Integrated Routing and Trajectory Design for Satellite Servicing

The integrated spacecraft routing and trajectory optimization problem was investigated for satellite servicing missions involving partial en route propellant replenishment. Unlike terrestrial routing problems, spacecraft operate in a dynamic environment, requiring optimization of spacecraft routing over a network with nonlinear and time-dependent trajectory costs. Two different formulations are proposed to address this problem. The first formulation, referred to as the arc-based formulation, defines variables based on arcs and uses an iterative decoupling scheme that alternates between mixed-integer linear programming and sequential nonlinear trajectory optimization. The second formulation, referred to as the path-based formulation, defines variables based on paths/routes and leverages column generation and a labeling algorithm to accelerate the identification of promising routes. Through a geosynchronous satellite servicing case study and numerical experiments, the computational tradeoffs between these two formulations were quantified in terms of solution optimality, computation time, and robustness against nonconverging or trivial solutions.