Optimization of low-thrust interplanetary trajectories using collocation and nonlinear programming

The method of collocation with nonlinear programming is applied to the determination of minimum-time, low-thrust interplanetary transfer trajectories. Since the vehicle motor operates continuously, the minimum-time trajectories are also propellant minimizing. The numerical solution method requires that the transfer be divided into three phases: escape from the departure planet, heliocentric flight, and arrival at the destination planet. Two-body gravitational models are used in each phase and the transformation from planetocentric coordinates to heliocentric coordinates and vice-versa is incorporated as a set of nonlinear constraints on the problem variables. No a priori assumptions on the optimal control time history are required. An Earth-to-Mars transfer with a very low thrust acceleration of 0.0001 g is used as an example.