Nonlinear Optimization of Low-Thrust Trajectory for Satellite Formation: Legendre Pseudospectral Approach

In this paper, we focus on the design of a fuel-optimal maneuver strategy to reconfigure satellite formation using a low-thrust propulsion system. We cast it as an optimization problem with a desired final satellite formation configuration subject to collision avoidance constraints on the paths of the chief and all deputy satellites. The satellite terminal orbit states corresponding to this desired formation configuration are ensured by imposing an energy-matching condition and final geometry configuration constraints in the problem formulation. In addition, we adopt our recently developed relative satellite kinematics model to accurately describe relative satellite orbit geometry in the presence of J(2) effects. The resulting nonlinear optimal control problem is converted into a nonlinear programming problem by the application of the Legendre pseudospectral method and is then solved by using a sparse nonlinear optimization software named TOMLAB/SNOPT. Simulation results demonstrate the efficiency of our proposed method in designing fuel-optimal maneuvers for a wide class of satellite formation problems.