OPTIMIZATION OF LOW-THRUST GRAVITY-ASSIST TRAJECTORIES WITH A REDUCED PARAMETERIZATION OF THE THRUST VECTOR

摘要

A low-thrust trajectory can be modeled as a sequence of impulses (ΔV) connected by conic arcs. Each ΔV is described by at least three coordinates. We investigate new ways of parameterizing the ΔV coordinates when optimizing low-thrust gravity-assist trajectories. For the ΔV magnitude coordinate, we use a set of on/off times to control the thrusting and coasting period of the trajectory. For the ΔV angles, we use parametric functions of time (i.e. Chebyshev Series) to approximate the optimal thrust angles. With the appropriate choice of parameters, the number of optimization variables and constraints (and thus convergence speed) may be reduced significantly, with albeit a small sacrifice in accuracy. The new formulation is particularly useful in mission design trade studies where hundreds of trajectories may be optimized over a wide range of design parameters (e.g. launch window).