A two-stage differential corrector is applied to finding optimal low-thrust trajectories, both with two-body dynamics and with the circular restricted three body problem (CRTBP) dynamics. The first stage of the differential corrector ensures that dynamics are followed, and the second stage finds the least squares solution to minimize the sum of delta-v squared. Then, a homotopic approach is used with indirect multiple shooting to transition the delta-v squared solution to the minimum fuel mass solution, with constrained thrust. The approach is found to be robust to poor initial guesses, even converging when the initial guess consists of points pulled from a random distribution, with the constraint that the endpoints and time of flight must remain fixed. This robustness to initial guess is highly desirable especially for transfers in three-body dynamics, when it can be difficult to find a good initial guess.