Multi-phase trajectory optimization of space-based kinetic impactors for asteroid defense with multi-constraint

This paper presents a multi-phase nonlinear trajectory optimization model for space-based launch kinetic impactors, focusing on near-Earth asteroid defense. The model serves the purpose of analyzing space-based launch windows and obtaining optimal trajectories for achieving maximum deflection effectiveness. It comprises three phases: Earth-centered escape phase, heliocentric continuous low-thrust phase, and Keplerian flight phase. In the first phase, the impactor is considered to instantaneously acquire a significant velocity increment from space-based platform because of the extremely short duration of the space-based launch compared with the overall mission. By introducing the true anomaly of the impactor on the designated orbit, the launch velocity increment and launch window are obtained. In the second phase, by optimizing the direction of the low-thrust and the semi-latus rectum of the Keplerian orbit, the optimal shutdown time and state are obtained. In the last phase, the bilateral Keplerian motion between the impactor and the asteroid is considered, incorporating the true anomaly of the predicted impact point and the number of orbital revolutions to establish stringent temporal and spatial beneficial impact constraints. Subsequently, the parameterizable Lambert interception problem with multiple constraints is optimized using the Radau pseudospectral method. Results show that the proposed model has excellent adaptability for different deflection scenarios. Compared with the traditional ground-based continuous low-thrust flight scheme, the proposed method offers a larger launch window that is insensitive to the launch timing and can achieve a greater deflection distance while requiring lower launch capabilities.