Problem A of the 9th China trajectory optimization competition: Results found at Tsinghua University

Abstract

This paper presents the crucial method for obtaining results of Tsinghua University in the 9th China Trajectory Optimization Competition (CTOC-9). To monitor the usage of the important frequency resources of GEO satellites, CTOC-9 focuses on the orbit design and trajectory optimization of satellite cluster flight for geostationary orbit (GEO) satellite beams monitoring missions. The three cluster satellite orbits and complex constraints cause much difficulties in the design and optimization. The search for the globally optimal mission trajectory with multi-impulse orbit maneuver is performed in two steps. The first step involves a roughly global search in the search space that has been bounded based on the fuel constraints, the monitoring conditions and the formation flying model of three monitoring cluster satellites. To bound the global search space, several legs are patched together to represent the whole trajectory of monitoring mission, and the impulses occurring in the patch points are estimated by the Hohmann transfer. And the particle swarm optimization (PSO) algorithm is modified and then employed to the multi-leg optimization. The second step involves the local optimization of the multi-impulse patched-conic legs which stand out from the roughly global search. The main task of the local optimization is to solve a series of J2 perturbed Lambert problems by the homotopic approach. Based on the impulsive results, some specific subtasks are selected and re-optimized to reduce the number of subtasks. Of the many trajectories found, the optimal trajectory submitted for the competition is reported. A post-competition result is reported, which is with the primary objective of 19.61 days, prior to the winner of 20.43 days.