Assessment of State Vector Representations for Convex Low-Thrust Trajectory Optimization

The choice of the coordinate representation of the state vector has a considerable impact on the performance of numerical methods in astrodynamics. This is especially true for sequential convex programming techniques in the case of successive linearization of nonlinear dynamics. In this work, various coordinate representations are assessed for the low-thrust trajectory optimization problem. In particular, standard coordinate sets are considered (i.e., Cartesian, spherical, cylindrical, and modified equinoctial elements), and non-standard coordinates (two sets based on Kustaanheimo-Stiefel coordinates and modified orbital elements) are introduced that result in linear dynamics in the unperturbed case. In addition, two metrics tailored to convex optimization are proposed to assess the linearization accuracy of the dynamical system. Numerical simulations are performed to compare the indices, and also the performance of each state vector representation for orbital transfers to two asteroids.