Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.     

Necessary conditions for the optimality of singular arcs of spacecraft trajectories subject to multiple gravitational bodies

This document analyzes the optimality of intermediate thrust arcs (singular arcs) of spacecraft trajectories subject to multiple gravitational bodies. A series of necessary conditions for optimality are formally derived, including the generalized Legendre–Clebsch condition. As the order of singular optimality turns out to be two, an explicit formula for the singular optimal control is also presented. These analytical outcomes are validated by showing that they are identical to Lawden’s classical result if the equations of motion are reduced for a central gravity field. Practical utility is demonstrated by applying these analytical derivations to a candidate optimal trajectory near the Moon subject to solar and Earth perturbation. While the candidate optimal trajectory turns out to be bang-singular-bang, the intermediate thrust arc satisfies all the necessary conditions for optimality.