Efficient Methods for Traversing a Homotopy of Optimal Low-Thrust Trajectories

The state, time, and thrust-based homotopy method for solving the general low-thrust two-body fixed-time rendezvous problem for minimum-thrust and minimum-fuel trajectories has previously been established. The method is robust for solving n-revolution trajectories without the need for an initial guess of the unknown costates of the target solution. However, the generalized method is computationally expensive, requiring the thrust magnitude of an n-revolution trajectory to be reduced to a minimum feasible thrust to add or remove revolutions to the trajectory before raising the thrust magnitude again. This study investigates two alternative paths of traversing the homotopy which follow curves of minimum-fuel trajectories, and six continuation step guess-generation methods for improved computational efficiency. The maximum step size of each guess-generation method for parameterized points on each path is computed, and a total number of continuation steps is estimated for each pairing.