A hybrid trajectory optimization technique for the mars sample return mission

A hybrid trajectory optimization technique is presented for the Mars Sample Return Mission. The mission considered in this paper originates from the orbit of Mars and ends in a high altitude Earth orbit. A thrust-coast-thrust sequence is utilized. The specific impulse is held constant during the thrust phases. A Calculus of Variations (COV) approach is used to determine the thrust direction in the heliocentric segment, which lasts till the spacecraft enters the sphere-of-influence of the Earth. The unknown parameters in this segment are the initial costates for each of the thrust phases, and the thrust switch times. The spacecraft is controlled in the geocentric phase using a feedback law that targets the desired energy and eccentricity. This control law is parameterized by a single gain. The two segments are combined together and all the free parameters are optimized to determine the entire trajectory. This hybrid approach reduces the sensitivity of the optimization problem without appreciably affecting the amount of fuel required and it also provides a means for checking the optimality of COV based solutions.