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Homotopy methods have been widely utilized to solve low-thrust orbitaltransfer problems, however, it is not guaranteed that the optimal solution canbe obtained by the existing homotopy methods. In this paper, a new homotopymethod is presented, by which the optimal solution can be found withprobability one. Generalized sufficient conditions, which are derived from theparametrized Sard's theorem, are first developed. A new type of probability-onehomotopy formulation, which is custom-designed for solving minimum-timelow-thrust trajectory optimization problems and satisfies all these sufficientconditions, is then constructed. By tracking the continuous zero curveinitiated by an initial problem with known solution, the optimal solution ofthe original problem is guaranteed to be solved with probability one. Numericaldemonstrations in a three-dimensional time-optimal low-thrust orbital transferproblem with 43 revolutions is presented to illustrate the applications of themethod.

A New Probability-one Homotopy Method for Solving Minimum-Time Low-Thrust Orbital Transfer Problems