Graph-Based Multi-Objective Trajectory Optimization for Repeat Ground Track Orbital Transfer by Low-Thrust Propulsion

Abstract

Earth observation satellites can improve the flexibility of observation sites by having “maneuverability,” and low-thrust obtained by ion thruster will be a promising method for orbital change for micro-satellites. Designing low-thrust trajectories for these satellites is a multi-revolution and multi-objective (time/fuel-optimal) optimization problem, which usually requires high computational cost to solve numerically. This paper derives an analytical and approximate optimal orbit change strategy between two circular orbits with the same semi-major axis and different local time of ascending node, and proposes a graph-based method to optimize the multi-objective criteria. The optimal control problem results in a problem to search a switching point on the proposed graph, and mission designers can design an approximate switching point on this graph, by using two heuristic and reasonable assumptions that 1) the optimal thrust direction should be tangential to orbit and 2) the optimal thrust magnitude should be bang-bang control with an intermediate coast. Finally, numerical simulation with feedback control algorithm taking thrust margin demonstrates that the proposed method can be applicable in the presence of deterministic and stochastic fluctuation of aerodynamic disturbances.