A rapid power descent phase trajectory optimization method with minimum fuel consumption for Mars pinpoint landing

Aiming at the Mars Pinpoint landing problem, a rapid trajectory optimization method with minimum fuel consumption during power descent phase is presented. Firstly, a trajectory optimization model with minimum fuel for Mars power descent phase is established; Secondly, the relationship between thrust magnitude and direction and costate variables is analyzed based on the maximum principle, and a conclusion that the lander should work at max or min thrust magnitude and the thrust direction should be in the direction of the costate vectors corresponding to the velocity states is obtained, on the basis of the conclusion the state and costate differential equations are converted to corresponding piecewise functions with constant thrust. Then, the analytical formulas of the piecewise functions are derived when the terminal time is given. Further, the algorithm flow chart of trajectory optimization for Mars powed descent phase is given. And last, mathematical simulation is conducted to compare the method to convex optimization method and polynomial method. Results show that the proposed method avoids the flaws of polynomial method and has more computational efficiency than convex optimization method.