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 tra jectories. Since the vehicle motor operates continuously, the minimum- time trajectories are also propellant minimizing. The numerical soluti on method requires that the transfer be divided into three phases: esc ape from the departure planet, heliocentric flight, and arrival at the destination planet. Two-body gravitational models are used in each ph ase and the transformation from planetocentric coordinates to heliocen tric coordinates and vice-versa is incorporated as a set of nonlinear constraints on the problem variables. No a priori assumptions on the o ptimal control time history are required. An Earth-to-Mars transfer wi th a very low thrust acceleration of 0.0001 g is used as an example.