Nonlinear optimization of low-thrust trajectory for satellite formation: Legendre pseudospectral approach

In this paper, we propose a method to determine fuel-optimal trajectories for satellite formation maneuver subjected to collision avoidance using low-thrust continuous propulsion. Final bounded desired formation is obtained by including energy-matching condition and final geometry configuration constraints in the optimization formulation. The dynamics model used is a newly developed exact nonlinear relative dynamics considering eccentricity and earth oblateness. Resulting nonlinear optimal control problem is transcribed into nonlinear programming problem by a direct transcription method called Legendre pseudospectral method. The nonlinear programming problem is then solved using a sparse nonlinear optimization algorithm named SNOPT. Examples are presented across a range of applications. These examples demonstrate the applicability of Legendre pseudospectral method to optimal trajectory design for formation maneuver.